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                "exact": "200539/20",
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                "exact": "-501/200000",
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              {
                "exact": "539/200000",
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                "exact": "291/100000",
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              "decimal": 1.25
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                "exact": "40125/4",
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                "exact": "1/320",
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                "exact": "377/100000",
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                "exact": "10042",
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                "exact": "40211/4",
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                "exact": "211/40000",
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                "exact": "100549/10",
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                "exact": "549/100000",
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                "exact": "201141/20",
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                "exact": "1141/200000",
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                "exact": "50296/5",
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                "exact": "1227/200000",
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                "exact": "1313/200000",
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                "exact": "100807/10",
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                "exact": "807/100000",
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            "q": 39,
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              "exact": "97/20",
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                "exact": "277/25000",
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            ]
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                "exact": "1151/100000",
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                "exact": "101237/10",
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                "exact": "10128",
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                "exact": "683/50000",
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                "exact": "39515/4",
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                "exact": "40555/4",
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                "exact": "-97/8000",
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              {
                "exact": "111/8000",
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          {
            "q": 66,
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            "cost": {
              "exact": "43/10",
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                "exact": "3291/200000",
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                "exact": "101667/10",
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                "exact": "1667/100000",
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            "q": 79,
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              "exact": "158000/199901",
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            },
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              "exact": "11/5",
              "decimal": 2.2
            },
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              "exact": "121/500",
              "decimal": 0.242
            },
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              "exact": "979/500",
              "decimal": 1.958
            },
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              {
                "exact": "49901/5",
                "decimal": 9980.2
              },
              {
                "exact": "50121/5",
                "decimal": 10024.2
              }
            ],
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              {
                "exact": "-99/50000",
                "decimal": -0.00198
              },
              {
                "exact": "121/50000",
                "decimal": 0.00242
              }
            ]
          },
          {
            "q": 12,
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              "exact": "0",
              "decimal": 0.0
            },
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            },
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              "exact": "8800",
              "decimal": 8800.0
            },
            "x": {
              "exact": "3/25",
              "decimal": 0.12
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
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              "exact": "3/25",
              "decimal": 0.12
            },
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              "exact": "12/5",
              "decimal": 2.4
            },
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              "exact": "12/5",
              "decimal": 2.4
            },
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              "exact": "12/5",
              "decimal": 2.4
            },
            "risk_penalty_dollars": {
              "exact": "36/125",
              "decimal": 0.288
            },
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              "exact": "264/125",
              "decimal": 2.112
            },
            "terminal_mid_wealth": [
              {
                "exact": "49892/5",
                "decimal": 9978.4
              },
              {
                "exact": "50132/5",
                "decimal": 10026.4
              }
            ],
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              {
                "exact": "-27/12500",
                "decimal": -0.00216
              },
              {
                "exact": "33/12500",
                "decimal": 0.00264
              }
            ]
          },
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              "decimal": 0.0
            },
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              "exact": "0",
              "decimal": 0.0
            },
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              "decimal": 0.0
            },
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              "exact": "8700",
              "decimal": 8700.0
            },
            "x": {
              "exact": "13/100",
              "decimal": 0.13
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
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              "exact": "13/100",
              "decimal": 0.13
            },
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              "exact": "13/5",
              "decimal": 2.6
            },
            "nominal_expected_net_pnl": {
              "exact": "13/5",
              "decimal": 2.6
            },
            "worst_expected_net_pnl": {
              "exact": "13/5",
              "decimal": 2.6
            },
            "risk_penalty_dollars": {
              "exact": "169/500",
              "decimal": 0.338
            },
            "objective_dollars": {
              "exact": "1131/500",
              "decimal": 2.262
            },
            "terminal_mid_wealth": [
              {
                "exact": "49883/5",
                "decimal": 9976.6
              },
              {
                "exact": "50143/5",
                "decimal": 10028.6
              }
            ],
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              {
                "exact": "-117/50000",
                "decimal": -0.00234
              },
              {
                "exact": "143/50000",
                "decimal": 0.00286
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            ]
          },
          {
            "q": 14,
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              "exact": "0",
              "decimal": 0.0
            },
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              "exact": "0",
              "decimal": 0.0
            },
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              "decimal": 0.0
            },
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              "exact": "8600",
              "decimal": 8600.0
            },
            "x": {
              "exact": "7/50",
              "decimal": 0.14
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
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              "exact": "7/50",
              "decimal": 0.14
            },
            "expected_gross_pnl": {
              "exact": "14/5",
              "decimal": 2.8
            },
            "nominal_expected_net_pnl": {
              "exact": "14/5",
              "decimal": 2.8
            },
            "worst_expected_net_pnl": {
              "exact": "14/5",
              "decimal": 2.8
            },
            "risk_penalty_dollars": {
              "exact": "49/125",
              "decimal": 0.392
            },
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              "exact": "301/125",
              "decimal": 2.408
            },
            "terminal_mid_wealth": [
              {
                "exact": "49874/5",
                "decimal": 9974.8
              },
              {
                "exact": "50154/5",
                "decimal": 10030.8
              }
            ],
            "returns_prewealth": [
              {
                "exact": "-63/25000",
                "decimal": -0.00252
              },
              {
                "exact": "77/25000",
                "decimal": 0.00308
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            ]
          },
          {
            "q": 15,
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              "exact": "0",
              "decimal": 0.0
            },
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              "exact": "0",
              "decimal": 0.0
            },
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              "decimal": 0.0
            },
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              "exact": "8500",
              "decimal": 8500.0
            },
            "x": {
              "exact": "3/20",
              "decimal": 0.15
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "3/20",
              "decimal": 0.15
            },
            "expected_gross_pnl": {
              "exact": "3",
              "decimal": 3.0
            },
            "nominal_expected_net_pnl": {
              "exact": "3",
              "decimal": 3.0
            },
            "worst_expected_net_pnl": {
              "exact": "3",
              "decimal": 3.0
            },
            "risk_penalty_dollars": {
              "exact": "9/20",
              "decimal": 0.45
            },
            "objective_dollars": {
              "exact": "51/20",
              "decimal": 2.55
            },
            "terminal_mid_wealth": [
              {
                "exact": "9973",
                "decimal": 9973.0
              },
              {
                "exact": "10033",
                "decimal": 10033.0
              }
            ],
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              {
                "exact": "-27/10000",
                "decimal": -0.0027
              },
              {
                "exact": "33/10000",
                "decimal": 0.0033
              }
            ]
          },
          {
            "q": 16,
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              "exact": "0",
              "decimal": 0.0
            },
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              "exact": "0",
              "decimal": 0.0
            },
            "cost": {
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              "decimal": 0.0
            },
            "cash": {
              "exact": "8400",
              "decimal": 8400.0
            },
            "x": {
              "exact": "4/25",
              "decimal": 0.16
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "4/25",
              "decimal": 0.16
            },
            "expected_gross_pnl": {
              "exact": "16/5",
              "decimal": 3.2
            },
            "nominal_expected_net_pnl": {
              "exact": "16/5",
              "decimal": 3.2
            },
            "worst_expected_net_pnl": {
              "exact": "16/5",
              "decimal": 3.2
            },
            "risk_penalty_dollars": {
              "exact": "64/125",
              "decimal": 0.512
            },
            "objective_dollars": {
              "exact": "336/125",
              "decimal": 2.688
            },
            "terminal_mid_wealth": [
              {
                "exact": "49856/5",
                "decimal": 9971.2
              },
              {
                "exact": "50176/5",
                "decimal": 10035.2
              }
            ],
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              {
                "exact": "-9/3125",
                "decimal": -0.00288
              },
              {
                "exact": "11/3125",
                "decimal": 0.00352
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            ]
          },
          {
            "q": 17,
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              "exact": "0",
              "decimal": 0.0
            },
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              "exact": "0",
              "decimal": 0.0
            },
            "cost": {
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              "decimal": 0.0
            },
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              "exact": "8300",
              "decimal": 8300.0
            },
            "x": {
              "exact": "17/100",
              "decimal": 0.17
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            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
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              "decimal": 0.17
            },
            "expected_gross_pnl": {
              "exact": "17/5",
              "decimal": 3.4
            },
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              "exact": "17/5",
              "decimal": 3.4
            },
            "worst_expected_net_pnl": {
              "exact": "17/5",
              "decimal": 3.4
            },
            "risk_penalty_dollars": {
              "exact": "289/500",
              "decimal": 0.578
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            "objective_dollars": {
              "exact": "1411/500",
              "decimal": 2.822
            },
            "terminal_mid_wealth": [
              {
                "exact": "49847/5",
                "decimal": 9969.4
              },
              {
                "exact": "50187/5",
                "decimal": 10037.4
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            ],
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              {
                "exact": "-153/50000",
                "decimal": -0.00306
              },
              {
                "exact": "187/50000",
                "decimal": 0.00374
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            ]
          },
          {
            "q": 18,
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              "exact": "0",
              "decimal": 0.0
            },
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              "exact": "0",
              "decimal": 0.0
            },
            "cost": {
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              "decimal": 0.0
            },
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              "exact": "8200",
              "decimal": 8200.0
            },
            "x": {
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              "decimal": 0.18
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            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "9/50",
              "decimal": 0.18
            },
            "expected_gross_pnl": {
              "exact": "18/5",
              "decimal": 3.6
            },
            "nominal_expected_net_pnl": {
              "exact": "18/5",
              "decimal": 3.6
            },
            "worst_expected_net_pnl": {
              "exact": "18/5",
              "decimal": 3.6
            },
            "risk_penalty_dollars": {
              "exact": "81/125",
              "decimal": 0.648
            },
            "objective_dollars": {
              "exact": "369/125",
              "decimal": 2.952
            },
            "terminal_mid_wealth": [
              {
                "exact": "49838/5",
                "decimal": 9967.6
              },
              {
                "exact": "50198/5",
                "decimal": 10039.6
              }
            ],
            "returns_prewealth": [
              {
                "exact": "-81/25000",
                "decimal": -0.00324
              },
              {
                "exact": "99/25000",
                "decimal": 0.00396
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            ]
          },
          {
            "q": 19,
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              "exact": "0",
              "decimal": 0.0
            },
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              "exact": "0",
              "decimal": 0.0
            },
            "cost": {
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              "decimal": 0.0
            },
            "cash": {
              "exact": "8100",
              "decimal": 8100.0
            },
            "x": {
              "exact": "19/100",
              "decimal": 0.19
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            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
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              "exact": "19/100",
              "decimal": 0.19
            },
            "expected_gross_pnl": {
              "exact": "19/5",
              "decimal": 3.8
            },
            "nominal_expected_net_pnl": {
              "exact": "19/5",
              "decimal": 3.8
            },
            "worst_expected_net_pnl": {
              "exact": "19/5",
              "decimal": 3.8
            },
            "risk_penalty_dollars": {
              "exact": "361/500",
              "decimal": 0.722
            },
            "objective_dollars": {
              "exact": "1539/500",
              "decimal": 3.078
            },
            "terminal_mid_wealth": [
              {
                "exact": "49829/5",
                "decimal": 9965.8
              },
              {
                "exact": "50209/5",
                "decimal": 10041.8
              }
            ],
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              {
                "exact": "-171/50000",
                "decimal": -0.00342
              },
              {
                "exact": "209/50000",
                "decimal": 0.00418
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            ]
          },
          {
            "q": 20,
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              "decimal": 0.0
            },
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              "exact": "0",
              "decimal": 0.0
            },
            "cost": {
              "exact": "0",
              "decimal": 0.0
            },
            "cash": {
              "exact": "8000",
              "decimal": 8000.0
            },
            "x": {
              "exact": "1/5",
              "decimal": 0.2
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "1/5",
              "decimal": 0.2
            },
            "expected_gross_pnl": {
              "exact": "4",
              "decimal": 4.0
            },
            "nominal_expected_net_pnl": {
              "exact": "4",
              "decimal": 4.0
            },
            "worst_expected_net_pnl": {
              "exact": "4",
              "decimal": 4.0
            },
            "risk_penalty_dollars": {
              "exact": "4/5",
              "decimal": 0.8
            },
            "objective_dollars": {
              "exact": "16/5",
              "decimal": 3.2
            },
            "terminal_mid_wealth": [
              {
                "exact": "9964",
                "decimal": 9964.0
              },
              {
                "exact": "10044",
                "decimal": 10044.0
              }
            ],
            "returns_prewealth": [
              {
                "exact": "-9/2500",
                "decimal": -0.0036
              },
              {
                "exact": "11/2500",
                "decimal": 0.0044
              }
            ]
          },
          {
            "q": 21,
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              "decimal": 0.0
            },
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              "exact": "0",
              "decimal": 0.0
            },
            "cost": {
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              "decimal": 0.0
            },
            "cash": {
              "exact": "7900",
              "decimal": 7900.0
            },
            "x": {
              "exact": "21/100",
              "decimal": 0.21
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "21/100",
              "decimal": 0.21
            },
            "expected_gross_pnl": {
              "exact": "21/5",
              "decimal": 4.2
            },
            "nominal_expected_net_pnl": {
              "exact": "21/5",
              "decimal": 4.2
            },
            "worst_expected_net_pnl": {
              "exact": "21/5",
              "decimal": 4.2
            },
            "risk_penalty_dollars": {
              "exact": "441/500",
              "decimal": 0.882
            },
            "objective_dollars": {
              "exact": "1659/500",
              "decimal": 3.318
            },
            "terminal_mid_wealth": [
              {
                "exact": "49811/5",
                "decimal": 9962.2
              },
              {
                "exact": "50231/5",
                "decimal": 10046.2
              }
            ],
            "returns_prewealth": [
              {
                "exact": "-189/50000",
                "decimal": -0.00378
              },
              {
                "exact": "231/50000",
                "decimal": 0.00462
              }
            ]
          },
          {
            "q": 22,
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              "exact": "0",
              "decimal": 0.0
            },
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              "exact": "0",
              "decimal": 0.0
            },
            "cost": {
              "exact": "0",
              "decimal": 0.0
            },
            "cash": {
              "exact": "7800",
              "decimal": 7800.0
            },
            "x": {
              "exact": "11/50",
              "decimal": 0.22
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "11/50",
              "decimal": 0.22
            },
            "expected_gross_pnl": {
              "exact": "22/5",
              "decimal": 4.4
            },
            "nominal_expected_net_pnl": {
              "exact": "22/5",
              "decimal": 4.4
            },
            "worst_expected_net_pnl": {
              "exact": "22/5",
              "decimal": 4.4
            },
            "risk_penalty_dollars": {
              "exact": "121/125",
              "decimal": 0.968
            },
            "objective_dollars": {
              "exact": "429/125",
              "decimal": 3.432
            },
            "terminal_mid_wealth": [
              {
                "exact": "49802/5",
                "decimal": 9960.4
              },
              {
                "exact": "50242/5",
                "decimal": 10048.4
              }
            ],
            "returns_prewealth": [
              {
                "exact": "-99/25000",
                "decimal": -0.00396
              },
              {
                "exact": "121/25000",
                "decimal": 0.00484
              }
            ]
          },
          {
            "q": 23,
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              "exact": "0",
              "decimal": 0.0
            },
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              "exact": "0",
              "decimal": 0.0
            },
            "cost": {
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              "decimal": 0.0
            },
            "cash": {
              "exact": "7700",
              "decimal": 7700.0
            },
            "x": {
              "exact": "23/100",
              "decimal": 0.23
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "23/100",
              "decimal": 0.23
            },
            "expected_gross_pnl": {
              "exact": "23/5",
              "decimal": 4.6
            },
            "nominal_expected_net_pnl": {
              "exact": "23/5",
              "decimal": 4.6
            },
            "worst_expected_net_pnl": {
              "exact": "23/5",
              "decimal": 4.6
            },
            "risk_penalty_dollars": {
              "exact": "529/500",
              "decimal": 1.058
            },
            "objective_dollars": {
              "exact": "1771/500",
              "decimal": 3.542
            },
            "terminal_mid_wealth": [
              {
                "exact": "49793/5",
                "decimal": 9958.6
              },
              {
                "exact": "50253/5",
                "decimal": 10050.6
              }
            ],
            "returns_prewealth": [
              {
                "exact": "-207/50000",
                "decimal": -0.00414
              },
              {
                "exact": "253/50000",
                "decimal": 0.00506
              }
            ]
          },
          {
            "q": 24,
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              "exact": "0",
              "decimal": 0.0
            },
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              "exact": "0",
              "decimal": 0.0
            },
            "cost": {
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            },
            "cash": {
              "exact": "7600",
              "decimal": 7600.0
            },
            "x": {
              "exact": "6/25",
              "decimal": 0.24
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "6/25",
              "decimal": 0.24
            },
            "expected_gross_pnl": {
              "exact": "24/5",
              "decimal": 4.8
            },
            "nominal_expected_net_pnl": {
              "exact": "24/5",
              "decimal": 4.8
            },
            "worst_expected_net_pnl": {
              "exact": "24/5",
              "decimal": 4.8
            },
            "risk_penalty_dollars": {
              "exact": "144/125",
              "decimal": 1.152
            },
            "objective_dollars": {
              "exact": "456/125",
              "decimal": 3.648
            },
            "terminal_mid_wealth": [
              {
                "exact": "49784/5",
                "decimal": 9956.8
              },
              {
                "exact": "50264/5",
                "decimal": 10052.8
              }
            ],
            "returns_prewealth": [
              {
                "exact": "-27/6250",
                "decimal": -0.00432
              },
              {
                "exact": "33/6250",
                "decimal": 0.00528
              }
            ]
          },
          {
            "q": 25,
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              "exact": "0",
              "decimal": 0.0
            },
            "commission": {
              "exact": "0",
              "decimal": 0.0
            },
            "cost": {
              "exact": "0",
              "decimal": 0.0
            },
            "cash": {
              "exact": "7500",
              "decimal": 7500.0
            },
            "x": {
              "exact": "1/4",
              "decimal": 0.25
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "1/4",
              "decimal": 0.25
            },
            "expected_gross_pnl": {
              "exact": "5",
              "decimal": 5.0
            },
            "nominal_expected_net_pnl": {
              "exact": "5",
              "decimal": 5.0
            },
            "worst_expected_net_pnl": {
              "exact": "5",
              "decimal": 5.0
            },
            "risk_penalty_dollars": {
              "exact": "5/4",
              "decimal": 1.25
            },
            "objective_dollars": {
              "exact": "15/4",
              "decimal": 3.75
            },
            "terminal_mid_wealth": [
              {
                "exact": "9955",
                "decimal": 9955.0
              },
              {
                "exact": "10055",
                "decimal": 10055.0
              }
            ],
            "returns_prewealth": [
              {
                "exact": "-9/2000",
                "decimal": -0.0045
              },
              {
                "exact": "11/2000",
                "decimal": 0.0055
              }
            ]
          },
          {
            "q": 26,
            "feasible": true,
            "spread": {
              "exact": "0",
              "decimal": 0.0
            },
            "commission": {
              "exact": "0",
              "decimal": 0.0
            },
            "cost": {
              "exact": "0",
              "decimal": 0.0
            },
            "cash": {
              "exact": "7400",
              "decimal": 7400.0
            },
            "x": {
              "exact": "13/50",
              "decimal": 0.26
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "13/50",
              "decimal": 0.26
            },
            "expected_gross_pnl": {
              "exact": "26/5",
              "decimal": 5.2
            },
            "nominal_expected_net_pnl": {
              "exact": "26/5",
              "decimal": 5.2
            },
            "worst_expected_net_pnl": {
              "exact": "26/5",
              "decimal": 5.2
            },
            "risk_penalty_dollars": {
              "exact": "169/125",
              "decimal": 1.352
            },
            "objective_dollars": {
              "exact": "481/125",
              "decimal": 3.848
            },
            "terminal_mid_wealth": [
              {
                "exact": "49766/5",
                "decimal": 9953.2
              },
              {
                "exact": "50286/5",
                "decimal": 10057.2
              }
            ],
            "returns_prewealth": [
              {
                "exact": "-117/25000",
                "decimal": -0.00468
              },
              {
                "exact": "143/25000",
                "decimal": 0.00572
              }
            ]
          },
          {
            "q": 27,
            "feasible": true,
            "spread": {
              "exact": "0",
              "decimal": 0.0
            },
            "commission": {
              "exact": "0",
              "decimal": 0.0
            },
            "cost": {
              "exact": "0",
              "decimal": 0.0
            },
            "cash": {
              "exact": "7300",
              "decimal": 7300.0
            },
            "x": {
              "exact": "27/100",
              "decimal": 0.27
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "27/100",
              "decimal": 0.27
            },
            "expected_gross_pnl": {
              "exact": "27/5",
              "decimal": 5.4
            },
            "nominal_expected_net_pnl": {
              "exact": "27/5",
              "decimal": 5.4
            },
            "worst_expected_net_pnl": {
              "exact": "27/5",
              "decimal": 5.4
            },
            "risk_penalty_dollars": {
              "exact": "729/500",
              "decimal": 1.458
            },
            "objective_dollars": {
              "exact": "1971/500",
              "decimal": 3.942
            },
            "terminal_mid_wealth": [
              {
                "exact": "49757/5",
                "decimal": 9951.4
              },
              {
                "exact": "50297/5",
                "decimal": 10059.4
              }
            ],
            "returns_prewealth": [
              {
                "exact": "-243/50000",
                "decimal": -0.00486
              },
              {
                "exact": "297/50000",
                "decimal": 0.00594
              }
            ]
          },
          {
            "q": 28,
            "feasible": true,
            "spread": {
              "exact": "0",
              "decimal": 0.0
            },
            "commission": {
              "exact": "0",
              "decimal": 0.0
            },
            "cost": {
              "exact": "0",
              "decimal": 0.0
            },
            "cash": {
              "exact": "7200",
              "decimal": 7200.0
            },
            "x": {
              "exact": "7/25",
              "decimal": 0.28
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "7/25",
              "decimal": 0.28
            },
            "expected_gross_pnl": {
              "exact": "28/5",
              "decimal": 5.6
            },
            "nominal_expected_net_pnl": {
              "exact": "28/5",
              "decimal": 5.6
            },
            "worst_expected_net_pnl": {
              "exact": "28/5",
              "decimal": 5.6
            },
            "risk_penalty_dollars": {
              "exact": "196/125",
              "decimal": 1.568
            },
            "objective_dollars": {
              "exact": "504/125",
              "decimal": 4.032
            },
            "terminal_mid_wealth": [
              {
                "exact": "49748/5",
                "decimal": 9949.6
              },
              {
                "exact": "50308/5",
                "decimal": 10061.6
              }
            ],
            "returns_prewealth": [
              {
                "exact": "-63/12500",
                "decimal": -0.00504
              },
              {
                "exact": "77/12500",
                "decimal": 0.00616
              }
            ]
          },
          {
            "q": 29,
            "feasible": true,
            "spread": {
              "exact": "0",
              "decimal": 0.0
            },
            "commission": {
              "exact": "0",
              "decimal": 0.0
            },
            "cost": {
              "exact": "0",
              "decimal": 0.0
            },
            "cash": {
              "exact": "7100",
              "decimal": 7100.0
            },
            "x": {
              "exact": "29/100",
              "decimal": 0.29
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "29/100",
              "decimal": 0.29
            },
            "expected_gross_pnl": {
              "exact": "29/5",
              "decimal": 5.8
            },
            "nominal_expected_net_pnl": {
              "exact": "29/5",
              "decimal": 5.8
            },
            "worst_expected_net_pnl": {
              "exact": "29/5",
              "decimal": 5.8
            },
            "risk_penalty_dollars": {
              "exact": "841/500",
              "decimal": 1.682
            },
            "objective_dollars": {
              "exact": "2059/500",
              "decimal": 4.118
            },
            "terminal_mid_wealth": [
              {
                "exact": "49739/5",
                "decimal": 9947.8
              },
              {
                "exact": "50319/5",
                "decimal": 10063.8
              }
            ],
            "returns_prewealth": [
              {
                "exact": "-261/50000",
                "decimal": -0.00522
              },
              {
                "exact": "319/50000",
                "decimal": 0.00638
              }
            ]
          },
          {
            "q": 30,
            "feasible": true,
            "spread": {
              "exact": "0",
              "decimal": 0.0
            },
            "commission": {
              "exact": "0",
              "decimal": 0.0
            },
            "cost": {
              "exact": "0",
              "decimal": 0.0
            },
            "cash": {
              "exact": "7000",
              "decimal": 7000.0
            },
            "x": {
              "exact": "3/10",
              "decimal": 0.3
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "3/10",
              "decimal": 0.3
            },
            "expected_gross_pnl": {
              "exact": "6",
              "decimal": 6.0
            },
            "nominal_expected_net_pnl": {
              "exact": "6",
              "decimal": 6.0
            },
            "worst_expected_net_pnl": {
              "exact": "6",
              "decimal": 6.0
            },
            "risk_penalty_dollars": {
              "exact": "9/5",
              "decimal": 1.8
            },
            "objective_dollars": {
              "exact": "21/5",
              "decimal": 4.2
            },
            "terminal_mid_wealth": [
              {
                "exact": "9946",
                "decimal": 9946.0
              },
              {
                "exact": "10066",
                "decimal": 10066.0
              }
            ],
            "returns_prewealth": [
              {
                "exact": "-27/5000",
                "decimal": -0.0054
              },
              {
                "exact": "33/5000",
                "decimal": 0.0066
              }
            ]
          },
          {
            "q": 31,
            "feasible": true,
            "spread": {
              "exact": "0",
              "decimal": 0.0
            },
            "commission": {
              "exact": "0",
              "decimal": 0.0
            },
            "cost": {
              "exact": "0",
              "decimal": 0.0
            },
            "cash": {
              "exact": "6900",
              "decimal": 6900.0
            },
            "x": {
              "exact": "31/100",
              "decimal": 0.31
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "31/100",
              "decimal": 0.31
            },
            "expected_gross_pnl": {
              "exact": "31/5",
              "decimal": 6.2
            },
            "nominal_expected_net_pnl": {
              "exact": "31/5",
              "decimal": 6.2
            },
            "worst_expected_net_pnl": {
              "exact": "31/5",
              "decimal": 6.2
            },
            "risk_penalty_dollars": {
              "exact": "961/500",
              "decimal": 1.922
            },
            "objective_dollars": {
              "exact": "2139/500",
              "decimal": 4.278
            },
            "terminal_mid_wealth": [
              {
                "exact": "49721/5",
                "decimal": 9944.2
              },
              {
                "exact": "50341/5",
                "decimal": 10068.2
              }
            ],
            "returns_prewealth": [
              {
                "exact": "-279/50000",
                "decimal": -0.00558
              },
              {
                "exact": "341/50000",
                "decimal": 0.00682
              }
            ]
          },
          {
            "q": 32,
            "feasible": true,
            "spread": {
              "exact": "0",
              "decimal": 0.0
            },
            "commission": {
              "exact": "0",
              "decimal": 0.0
            },
            "cost": {
              "exact": "0",
              "decimal": 0.0
            },
            "cash": {
              "exact": "6800",
              "decimal": 6800.0
            },
            "x": {
              "exact": "8/25",
              "decimal": 0.32
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "8/25",
              "decimal": 0.32
            },
            "expected_gross_pnl": {
              "exact": "32/5",
              "decimal": 6.4
            },
            "nominal_expected_net_pnl": {
              "exact": "32/5",
              "decimal": 6.4
            },
            "worst_expected_net_pnl": {
              "exact": "32/5",
              "decimal": 6.4
            },
            "risk_penalty_dollars": {
              "exact": "256/125",
              "decimal": 2.048
            },
            "objective_dollars": {
              "exact": "544/125",
              "decimal": 4.352
            },
            "terminal_mid_wealth": [
              {
                "exact": "49712/5",
                "decimal": 9942.4
              },
              {
                "exact": "50352/5",
                "decimal": 10070.4
              }
            ],
            "returns_prewealth": [
              {
                "exact": "-18/3125",
                "decimal": -0.00576
              },
              {
                "exact": "22/3125",
                "decimal": 0.00704
              }
            ]
          },
          {
            "q": 33,
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              "exact": "0",
              "decimal": 0.0
            },
            "commission": {
              "exact": "0",
              "decimal": 0.0
            },
            "cost": {
              "exact": "0",
              "decimal": 0.0
            },
            "cash": {
              "exact": "6700",
              "decimal": 6700.0
            },
            "x": {
              "exact": "33/100",
              "decimal": 0.33
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "33/100",
              "decimal": 0.33
            },
            "expected_gross_pnl": {
              "exact": "33/5",
              "decimal": 6.6
            },
            "nominal_expected_net_pnl": {
              "exact": "33/5",
              "decimal": 6.6
            },
            "worst_expected_net_pnl": {
              "exact": "33/5",
              "decimal": 6.6
            },
            "risk_penalty_dollars": {
              "exact": "1089/500",
              "decimal": 2.178
            },
            "objective_dollars": {
              "exact": "2211/500",
              "decimal": 4.422
            },
            "terminal_mid_wealth": [
              {
                "exact": "49703/5",
                "decimal": 9940.6
              },
              {
                "exact": "50363/5",
                "decimal": 10072.6
              }
            ],
            "returns_prewealth": [
              {
                "exact": "-297/50000",
                "decimal": -0.00594
              },
              {
                "exact": "363/50000",
                "decimal": 0.00726
              }
            ]
          },
          {
            "q": 34,
            "feasible": true,
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              "exact": "0",
              "decimal": 0.0
            },
            "commission": {
              "exact": "0",
              "decimal": 0.0
            },
            "cost": {
              "exact": "0",
              "decimal": 0.0
            },
            "cash": {
              "exact": "6600",
              "decimal": 6600.0
            },
            "x": {
              "exact": "17/50",
              "decimal": 0.34
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "17/50",
              "decimal": 0.34
            },
            "expected_gross_pnl": {
              "exact": "34/5",
              "decimal": 6.8
            },
            "nominal_expected_net_pnl": {
              "exact": "34/5",
              "decimal": 6.8
            },
            "worst_expected_net_pnl": {
              "exact": "34/5",
              "decimal": 6.8
            },
            "risk_penalty_dollars": {
              "exact": "289/125",
              "decimal": 2.312
            },
            "objective_dollars": {
              "exact": "561/125",
              "decimal": 4.488
            },
            "terminal_mid_wealth": [
              {
                "exact": "49694/5",
                "decimal": 9938.8
              },
              {
                "exact": "50374/5",
                "decimal": 10074.8
              }
            ],
            "returns_prewealth": [
              {
                "exact": "-153/25000",
                "decimal": -0.00612
              },
              {
                "exact": "187/25000",
                "decimal": 0.00748
              }
            ]
          },
          {
            "q": 35,
            "feasible": true,
            "spread": {
              "exact": "0",
              "decimal": 0.0
            },
            "commission": {
              "exact": "0",
              "decimal": 0.0
            },
            "cost": {
              "exact": "0",
              "decimal": 0.0
            },
            "cash": {
              "exact": "6500",
              "decimal": 6500.0
            },
            "x": {
              "exact": "7/20",
              "decimal": 0.35
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "7/20",
              "decimal": 0.35
            },
            "expected_gross_pnl": {
              "exact": "7",
              "decimal": 7.0
            },
            "nominal_expected_net_pnl": {
              "exact": "7",
              "decimal": 7.0
            },
            "worst_expected_net_pnl": {
              "exact": "7",
              "decimal": 7.0
            },
            "risk_penalty_dollars": {
              "exact": "49/20",
              "decimal": 2.45
            },
            "objective_dollars": {
              "exact": "91/20",
              "decimal": 4.55
            },
            "terminal_mid_wealth": [
              {
                "exact": "9937",
                "decimal": 9937.0
              },
              {
                "exact": "10077",
                "decimal": 10077.0
              }
            ],
            "returns_prewealth": [
              {
                "exact": "-63/10000",
                "decimal": -0.0063
              },
              {
                "exact": "77/10000",
                "decimal": 0.0077
              }
            ]
          },
          {
            "q": 36,
            "feasible": true,
            "spread": {
              "exact": "0",
              "decimal": 0.0
            },
            "commission": {
              "exact": "0",
              "decimal": 0.0
            },
            "cost": {
              "exact": "0",
              "decimal": 0.0
            },
            "cash": {
              "exact": "6400",
              "decimal": 6400.0
            },
            "x": {
              "exact": "9/25",
              "decimal": 0.36
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "9/25",
              "decimal": 0.36
            },
            "expected_gross_pnl": {
              "exact": "36/5",
              "decimal": 7.2
            },
            "nominal_expected_net_pnl": {
              "exact": "36/5",
              "decimal": 7.2
            },
            "worst_expected_net_pnl": {
              "exact": "36/5",
              "decimal": 7.2
            },
            "risk_penalty_dollars": {
              "exact": "324/125",
              "decimal": 2.592
            },
            "objective_dollars": {
              "exact": "576/125",
              "decimal": 4.608
            },
            "terminal_mid_wealth": [
              {
                "exact": "49676/5",
                "decimal": 9935.2
              },
              {
                "exact": "50396/5",
                "decimal": 10079.2
              }
            ],
            "returns_prewealth": [
              {
                "exact": "-81/12500",
                "decimal": -0.00648
              },
              {
                "exact": "99/12500",
                "decimal": 0.00792
              }
            ]
          },
          {
            "q": 37,
            "feasible": true,
            "spread": {
              "exact": "0",
              "decimal": 0.0
            },
            "commission": {
              "exact": "0",
              "decimal": 0.0
            },
            "cost": {
              "exact": "0",
              "decimal": 0.0
            },
            "cash": {
              "exact": "6300",
              "decimal": 6300.0
            },
            "x": {
              "exact": "37/100",
              "decimal": 0.37
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "37/100",
              "decimal": 0.37
            },
            "expected_gross_pnl": {
              "exact": "37/5",
              "decimal": 7.4
            },
            "nominal_expected_net_pnl": {
              "exact": "37/5",
              "decimal": 7.4
            },
            "worst_expected_net_pnl": {
              "exact": "37/5",
              "decimal": 7.4
            },
            "risk_penalty_dollars": {
              "exact": "1369/500",
              "decimal": 2.738
            },
            "objective_dollars": {
              "exact": "2331/500",
              "decimal": 4.662
            },
            "terminal_mid_wealth": [
              {
                "exact": "49667/5",
                "decimal": 9933.4
              },
              {
                "exact": "50407/5",
                "decimal": 10081.4
              }
            ],
            "returns_prewealth": [
              {
                "exact": "-333/50000",
                "decimal": -0.00666
              },
              {
                "exact": "407/50000",
                "decimal": 0.00814
              }
            ]
          },
          {
            "q": 38,
            "feasible": true,
            "spread": {
              "exact": "0",
              "decimal": 0.0
            },
            "commission": {
              "exact": "0",
              "decimal": 0.0
            },
            "cost": {
              "exact": "0",
              "decimal": 0.0
            },
            "cash": {
              "exact": "6200",
              "decimal": 6200.0
            },
            "x": {
              "exact": "19/50",
              "decimal": 0.38
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "19/50",
              "decimal": 0.38
            },
            "expected_gross_pnl": {
              "exact": "38/5",
              "decimal": 7.6
            },
            "nominal_expected_net_pnl": {
              "exact": "38/5",
              "decimal": 7.6
            },
            "worst_expected_net_pnl": {
              "exact": "38/5",
              "decimal": 7.6
            },
            "risk_penalty_dollars": {
              "exact": "361/125",
              "decimal": 2.888
            },
            "objective_dollars": {
              "exact": "589/125",
              "decimal": 4.712
            },
            "terminal_mid_wealth": [
              {
                "exact": "49658/5",
                "decimal": 9931.6
              },
              {
                "exact": "50418/5",
                "decimal": 10083.6
              }
            ],
            "returns_prewealth": [
              {
                "exact": "-171/25000",
                "decimal": -0.00684
              },
              {
                "exact": "209/25000",
                "decimal": 0.00836
              }
            ]
          },
          {
            "q": 39,
            "feasible": true,
            "spread": {
              "exact": "0",
              "decimal": 0.0
            },
            "commission": {
              "exact": "0",
              "decimal": 0.0
            },
            "cost": {
              "exact": "0",
              "decimal": 0.0
            },
            "cash": {
              "exact": "6100",
              "decimal": 6100.0
            },
            "x": {
              "exact": "39/100",
              "decimal": 0.39
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "39/100",
              "decimal": 0.39
            },
            "expected_gross_pnl": {
              "exact": "39/5",
              "decimal": 7.8
            },
            "nominal_expected_net_pnl": {
              "exact": "39/5",
              "decimal": 7.8
            },
            "worst_expected_net_pnl": {
              "exact": "39/5",
              "decimal": 7.8
            },
            "risk_penalty_dollars": {
              "exact": "1521/500",
              "decimal": 3.042
            },
            "objective_dollars": {
              "exact": "2379/500",
              "decimal": 4.758
            },
            "terminal_mid_wealth": [
              {
                "exact": "49649/5",
                "decimal": 9929.8
              },
              {
                "exact": "50429/5",
                "decimal": 10085.8
              }
            ],
            "returns_prewealth": [
              {
                "exact": "-351/50000",
                "decimal": -0.00702
              },
              {
                "exact": "429/50000",
                "decimal": 0.00858
              }
            ]
          },
          {
            "q": 40,
            "feasible": true,
            "spread": {
              "exact": "0",
              "decimal": 0.0
            },
            "commission": {
              "exact": "0",
              "decimal": 0.0
            },
            "cost": {
              "exact": "0",
              "decimal": 0.0
            },
            "cash": {
              "exact": "6000",
              "decimal": 6000.0
            },
            "x": {
              "exact": "2/5",
              "decimal": 0.4
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "2/5",
              "decimal": 0.4
            },
            "expected_gross_pnl": {
              "exact": "8",
              "decimal": 8.0
            },
            "nominal_expected_net_pnl": {
              "exact": "8",
              "decimal": 8.0
            },
            "worst_expected_net_pnl": {
              "exact": "8",
              "decimal": 8.0
            },
            "risk_penalty_dollars": {
              "exact": "16/5",
              "decimal": 3.2
            },
            "objective_dollars": {
              "exact": "24/5",
              "decimal": 4.8
            },
            "terminal_mid_wealth": [
              {
                "exact": "9928",
                "decimal": 9928.0
              },
              {
                "exact": "10088",
                "decimal": 10088.0
              }
            ],
            "returns_prewealth": [
              {
                "exact": "-9/1250",
                "decimal": -0.0072
              },
              {
                "exact": "11/1250",
                "decimal": 0.0088
              }
            ]
          },
          {
            "q": 41,
            "feasible": true,
            "spread": {
              "exact": "0",
              "decimal": 0.0
            },
            "commission": {
              "exact": "0",
              "decimal": 0.0
            },
            "cost": {
              "exact": "0",
              "decimal": 0.0
            },
            "cash": {
              "exact": "5900",
              "decimal": 5900.0
            },
            "x": {
              "exact": "41/100",
              "decimal": 0.41
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "41/100",
              "decimal": 0.41
            },
            "expected_gross_pnl": {
              "exact": "41/5",
              "decimal": 8.2
            },
            "nominal_expected_net_pnl": {
              "exact": "41/5",
              "decimal": 8.2
            },
            "worst_expected_net_pnl": {
              "exact": "41/5",
              "decimal": 8.2
            },
            "risk_penalty_dollars": {
              "exact": "1681/500",
              "decimal": 3.362
            },
            "objective_dollars": {
              "exact": "2419/500",
              "decimal": 4.838
            },
            "terminal_mid_wealth": [
              {
                "exact": "49631/5",
                "decimal": 9926.2
              },
              {
                "exact": "50451/5",
                "decimal": 10090.2
              }
            ],
            "returns_prewealth": [
              {
                "exact": "-369/50000",
                "decimal": -0.00738
              },
              {
                "exact": "451/50000",
                "decimal": 0.00902
              }
            ]
          },
          {
            "q": 42,
            "feasible": true,
            "spread": {
              "exact": "0",
              "decimal": 0.0
            },
            "commission": {
              "exact": "0",
              "decimal": 0.0
            },
            "cost": {
              "exact": "0",
              "decimal": 0.0
            },
            "cash": {
              "exact": "5800",
              "decimal": 5800.0
            },
            "x": {
              "exact": "21/50",
              "decimal": 0.42
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "21/50",
              "decimal": 0.42
            },
            "expected_gross_pnl": {
              "exact": "42/5",
              "decimal": 8.4
            },
            "nominal_expected_net_pnl": {
              "exact": "42/5",
              "decimal": 8.4
            },
            "worst_expected_net_pnl": {
              "exact": "42/5",
              "decimal": 8.4
            },
            "risk_penalty_dollars": {
              "exact": "441/125",
              "decimal": 3.528
            },
            "objective_dollars": {
              "exact": "609/125",
              "decimal": 4.872
            },
            "terminal_mid_wealth": [
              {
                "exact": "49622/5",
                "decimal": 9924.4
              },
              {
                "exact": "50462/5",
                "decimal": 10092.4
              }
            ],
            "returns_prewealth": [
              {
                "exact": "-189/25000",
                "decimal": -0.00756
              },
              {
                "exact": "231/25000",
                "decimal": 0.00924
              }
            ]
          },
          {
            "q": 43,
            "feasible": true,
            "spread": {
              "exact": "0",
              "decimal": 0.0
            },
            "commission": {
              "exact": "0",
              "decimal": 0.0
            },
            "cost": {
              "exact": "0",
              "decimal": 0.0
            },
            "cash": {
              "exact": "5700",
              "decimal": 5700.0
            },
            "x": {
              "exact": "43/100",
              "decimal": 0.43
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "43/100",
              "decimal": 0.43
            },
            "expected_gross_pnl": {
              "exact": "43/5",
              "decimal": 8.6
            },
            "nominal_expected_net_pnl": {
              "exact": "43/5",
              "decimal": 8.6
            },
            "worst_expected_net_pnl": {
              "exact": "43/5",
              "decimal": 8.6
            },
            "risk_penalty_dollars": {
              "exact": "1849/500",
              "decimal": 3.698
            },
            "objective_dollars": {
              "exact": "2451/500",
              "decimal": 4.902
            },
            "terminal_mid_wealth": [
              {
                "exact": "49613/5",
                "decimal": 9922.6
              },
              {
                "exact": "50473/5",
                "decimal": 10094.6
              }
            ],
            "returns_prewealth": [
              {
                "exact": "-387/50000",
                "decimal": -0.00774
              },
              {
                "exact": "473/50000",
                "decimal": 0.00946
              }
            ]
          },
          {
            "q": 44,
            "feasible": true,
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              "exact": "0",
              "decimal": 0.0
            },
            "commission": {
              "exact": "0",
              "decimal": 0.0
            },
            "cost": {
              "exact": "0",
              "decimal": 0.0
            },
            "cash": {
              "exact": "5600",
              "decimal": 5600.0
            },
            "x": {
              "exact": "11/25",
              "decimal": 0.44
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "11/25",
              "decimal": 0.44
            },
            "expected_gross_pnl": {
              "exact": "44/5",
              "decimal": 8.8
            },
            "nominal_expected_net_pnl": {
              "exact": "44/5",
              "decimal": 8.8
            },
            "worst_expected_net_pnl": {
              "exact": "44/5",
              "decimal": 8.8
            },
            "risk_penalty_dollars": {
              "exact": "484/125",
              "decimal": 3.872
            },
            "objective_dollars": {
              "exact": "616/125",
              "decimal": 4.928
            },
            "terminal_mid_wealth": [
              {
                "exact": "49604/5",
                "decimal": 9920.8
              },
              {
                "exact": "50484/5",
                "decimal": 10096.8
              }
            ],
            "returns_prewealth": [
              {
                "exact": "-99/12500",
                "decimal": -0.00792
              },
              {
                "exact": "121/12500",
                "decimal": 0.00968
              }
            ]
          },
          {
            "q": 45,
            "feasible": true,
            "spread": {
              "exact": "0",
              "decimal": 0.0
            },
            "commission": {
              "exact": "0",
              "decimal": 0.0
            },
            "cost": {
              "exact": "0",
              "decimal": 0.0
            },
            "cash": {
              "exact": "5500",
              "decimal": 5500.0
            },
            "x": {
              "exact": "9/20",
              "decimal": 0.45
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "9/20",
              "decimal": 0.45
            },
            "expected_gross_pnl": {
              "exact": "9",
              "decimal": 9.0
            },
            "nominal_expected_net_pnl": {
              "exact": "9",
              "decimal": 9.0
            },
            "worst_expected_net_pnl": {
              "exact": "9",
              "decimal": 9.0
            },
            "risk_penalty_dollars": {
              "exact": "81/20",
              "decimal": 4.05
            },
            "objective_dollars": {
              "exact": "99/20",
              "decimal": 4.95
            },
            "terminal_mid_wealth": [
              {
                "exact": "9919",
                "decimal": 9919.0
              },
              {
                "exact": "10099",
                "decimal": 10099.0
              }
            ],
            "returns_prewealth": [
              {
                "exact": "-81/10000",
                "decimal": -0.0081
              },
              {
                "exact": "99/10000",
                "decimal": 0.0099
              }
            ]
          },
          {
            "q": 46,
            "feasible": true,
            "spread": {
              "exact": "0",
              "decimal": 0.0
            },
            "commission": {
              "exact": "0",
              "decimal": 0.0
            },
            "cost": {
              "exact": "0",
              "decimal": 0.0
            },
            "cash": {
              "exact": "5400",
              "decimal": 5400.0
            },
            "x": {
              "exact": "23/50",
              "decimal": 0.46
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "23/50",
              "decimal": 0.46
            },
            "expected_gross_pnl": {
              "exact": "46/5",
              "decimal": 9.2
            },
            "nominal_expected_net_pnl": {
              "exact": "46/5",
              "decimal": 9.2
            },
            "worst_expected_net_pnl": {
              "exact": "46/5",
              "decimal": 9.2
            },
            "risk_penalty_dollars": {
              "exact": "529/125",
              "decimal": 4.232
            },
            "objective_dollars": {
              "exact": "621/125",
              "decimal": 4.968
            },
            "terminal_mid_wealth": [
              {
                "exact": "49586/5",
                "decimal": 9917.2
              },
              {
                "exact": "50506/5",
                "decimal": 10101.2
              }
            ],
            "returns_prewealth": [
              {
                "exact": "-207/25000",
                "decimal": -0.00828
              },
              {
                "exact": "253/25000",
                "decimal": 0.01012
              }
            ]
          },
          {
            "q": 47,
            "feasible": true,
            "spread": {
              "exact": "0",
              "decimal": 0.0
            },
            "commission": {
              "exact": "0",
              "decimal": 0.0
            },
            "cost": {
              "exact": "0",
              "decimal": 0.0
            },
            "cash": {
              "exact": "5300",
              "decimal": 5300.0
            },
            "x": {
              "exact": "47/100",
              "decimal": 0.47
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "47/100",
              "decimal": 0.47
            },
            "expected_gross_pnl": {
              "exact": "47/5",
              "decimal": 9.4
            },
            "nominal_expected_net_pnl": {
              "exact": "47/5",
              "decimal": 9.4
            },
            "worst_expected_net_pnl": {
              "exact": "47/5",
              "decimal": 9.4
            },
            "risk_penalty_dollars": {
              "exact": "2209/500",
              "decimal": 4.418
            },
            "objective_dollars": {
              "exact": "2491/500",
              "decimal": 4.982
            },
            "terminal_mid_wealth": [
              {
                "exact": "49577/5",
                "decimal": 9915.4
              },
              {
                "exact": "50517/5",
                "decimal": 10103.4
              }
            ],
            "returns_prewealth": [
              {
                "exact": "-423/50000",
                "decimal": -0.00846
              },
              {
                "exact": "517/50000",
                "decimal": 0.01034
              }
            ]
          },
          {
            "q": 48,
            "feasible": true,
            "spread": {
              "exact": "0",
              "decimal": 0.0
            },
            "commission": {
              "exact": "0",
              "decimal": 0.0
            },
            "cost": {
              "exact": "0",
              "decimal": 0.0
            },
            "cash": {
              "exact": "5200",
              "decimal": 5200.0
            },
            "x": {
              "exact": "12/25",
              "decimal": 0.48
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "12/25",
              "decimal": 0.48
            },
            "expected_gross_pnl": {
              "exact": "48/5",
              "decimal": 9.6
            },
            "nominal_expected_net_pnl": {
              "exact": "48/5",
              "decimal": 9.6
            },
            "worst_expected_net_pnl": {
              "exact": "48/5",
              "decimal": 9.6
            },
            "risk_penalty_dollars": {
              "exact": "576/125",
              "decimal": 4.608
            },
            "objective_dollars": {
              "exact": "624/125",
              "decimal": 4.992
            },
            "terminal_mid_wealth": [
              {
                "exact": "49568/5",
                "decimal": 9913.6
              },
              {
                "exact": "50528/5",
                "decimal": 10105.6
              }
            ],
            "returns_prewealth": [
              {
                "exact": "-27/3125",
                "decimal": -0.00864
              },
              {
                "exact": "33/3125",
                "decimal": 0.01056
              }
            ]
          },
          {
            "q": 49,
            "feasible": true,
            "spread": {
              "exact": "0",
              "decimal": 0.0
            },
            "commission": {
              "exact": "0",
              "decimal": 0.0
            },
            "cost": {
              "exact": "0",
              "decimal": 0.0
            },
            "cash": {
              "exact": "5100",
              "decimal": 5100.0
            },
            "x": {
              "exact": "49/100",
              "decimal": 0.49
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "49/100",
              "decimal": 0.49
            },
            "expected_gross_pnl": {
              "exact": "49/5",
              "decimal": 9.8
            },
            "nominal_expected_net_pnl": {
              "exact": "49/5",
              "decimal": 9.8
            },
            "worst_expected_net_pnl": {
              "exact": "49/5",
              "decimal": 9.8
            },
            "risk_penalty_dollars": {
              "exact": "2401/500",
              "decimal": 4.802
            },
            "objective_dollars": {
              "exact": "2499/500",
              "decimal": 4.998
            },
            "terminal_mid_wealth": [
              {
                "exact": "49559/5",
                "decimal": 9911.8
              },
              {
                "exact": "50539/5",
                "decimal": 10107.8
              }
            ],
            "returns_prewealth": [
              {
                "exact": "-441/50000",
                "decimal": -0.00882
              },
              {
                "exact": "539/50000",
                "decimal": 0.01078
              }
            ]
          },
          {
            "q": 50,
            "feasible": true,
            "spread": {
              "exact": "0",
              "decimal": 0.0
            },
            "commission": {
              "exact": "0",
              "decimal": 0.0
            },
            "cost": {
              "exact": "0",
              "decimal": 0.0
            },
            "cash": {
              "exact": "5000",
              "decimal": 5000.0
            },
            "x": {
              "exact": "1/2",
              "decimal": 0.5
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "1/2",
              "decimal": 0.5
            },
            "expected_gross_pnl": {
              "exact": "10",
              "decimal": 10.0
            },
            "nominal_expected_net_pnl": {
              "exact": "10",
              "decimal": 10.0
            },
            "worst_expected_net_pnl": {
              "exact": "10",
              "decimal": 10.0
            },
            "risk_penalty_dollars": {
              "exact": "5",
              "decimal": 5.0
            },
            "objective_dollars": {
              "exact": "5",
              "decimal": 5.0
            },
            "terminal_mid_wealth": [
              {
                "exact": "9910",
                "decimal": 9910.0
              },
              {
                "exact": "10110",
                "decimal": 10110.0
              }
            ],
            "returns_prewealth": [
              {
                "exact": "-9/1000",
                "decimal": -0.009
              },
              {
                "exact": "11/1000",
                "decimal": 0.011
              }
            ]
          },
          {
            "q": 51,
            "feasible": true,
            "spread": {
              "exact": "0",
              "decimal": 0.0
            },
            "commission": {
              "exact": "0",
              "decimal": 0.0
            },
            "cost": {
              "exact": "0",
              "decimal": 0.0
            },
            "cash": {
              "exact": "4900",
              "decimal": 4900.0
            },
            "x": {
              "exact": "51/100",
              "decimal": 0.51
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "51/100",
              "decimal": 0.51
            },
            "expected_gross_pnl": {
              "exact": "51/5",
              "decimal": 10.2
            },
            "nominal_expected_net_pnl": {
              "exact": "51/5",
              "decimal": 10.2
            },
            "worst_expected_net_pnl": {
              "exact": "51/5",
              "decimal": 10.2
            },
            "risk_penalty_dollars": {
              "exact": "2601/500",
              "decimal": 5.202
            },
            "objective_dollars": {
              "exact": "2499/500",
              "decimal": 4.998
            },
            "terminal_mid_wealth": [
              {
                "exact": "49541/5",
                "decimal": 9908.2
              },
              {
                "exact": "50561/5",
                "decimal": 10112.2
              }
            ],
            "returns_prewealth": [
              {
                "exact": "-459/50000",
                "decimal": -0.00918
              },
              {
                "exact": "561/50000",
                "decimal": 0.01122
              }
            ]
          },
          {
            "q": 52,
            "feasible": true,
            "spread": {
              "exact": "0",
              "decimal": 0.0
            },
            "commission": {
              "exact": "0",
              "decimal": 0.0
            },
            "cost": {
              "exact": "0",
              "decimal": 0.0
            },
            "cash": {
              "exact": "4800",
              "decimal": 4800.0
            },
            "x": {
              "exact": "13/25",
              "decimal": 0.52
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "13/25",
              "decimal": 0.52
            },
            "expected_gross_pnl": {
              "exact": "52/5",
              "decimal": 10.4
            },
            "nominal_expected_net_pnl": {
              "exact": "52/5",
              "decimal": 10.4
            },
            "worst_expected_net_pnl": {
              "exact": "52/5",
              "decimal": 10.4
            },
            "risk_penalty_dollars": {
              "exact": "676/125",
              "decimal": 5.408
            },
            "objective_dollars": {
              "exact": "624/125",
              "decimal": 4.992
            },
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              {
                "exact": "49532/5",
                "decimal": 9906.4
              },
              {
                "exact": "50572/5",
                "decimal": 10114.4
              }
            ],
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              {
                "exact": "-117/12500",
                "decimal": -0.00936
              },
              {
                "exact": "143/12500",
                "decimal": 0.01144
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            ]
          },
          {
            "q": 53,
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            },
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            },
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            },
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              "exact": "4700",
              "decimal": 4700.0
            },
            "x": {
              "exact": "53/100",
              "decimal": 0.53
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
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              "exact": "53/100",
              "decimal": 0.53
            },
            "expected_gross_pnl": {
              "exact": "53/5",
              "decimal": 10.6
            },
            "nominal_expected_net_pnl": {
              "exact": "53/5",
              "decimal": 10.6
            },
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              "exact": "53/5",
              "decimal": 10.6
            },
            "risk_penalty_dollars": {
              "exact": "2809/500",
              "decimal": 5.618
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              "exact": "2491/500",
              "decimal": 4.982
            },
            "terminal_mid_wealth": [
              {
                "exact": "49523/5",
                "decimal": 9904.6
              },
              {
                "exact": "50583/5",
                "decimal": 10116.6
              }
            ],
            "returns_prewealth": [
              {
                "exact": "-477/50000",
                "decimal": -0.00954
              },
              {
                "exact": "583/50000",
                "decimal": 0.01166
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            ]
          },
          {
            "q": 54,
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            },
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              "decimal": 0.0
            },
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            },
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              "exact": "4600",
              "decimal": 4600.0
            },
            "x": {
              "exact": "27/50",
              "decimal": 0.54
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
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              "exact": "27/50",
              "decimal": 0.54
            },
            "expected_gross_pnl": {
              "exact": "54/5",
              "decimal": 10.8
            },
            "nominal_expected_net_pnl": {
              "exact": "54/5",
              "decimal": 10.8
            },
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              "exact": "54/5",
              "decimal": 10.8
            },
            "risk_penalty_dollars": {
              "exact": "729/125",
              "decimal": 5.832
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              "exact": "621/125",
              "decimal": 4.968
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            "terminal_mid_wealth": [
              {
                "exact": "49514/5",
                "decimal": 9902.8
              },
              {
                "exact": "50594/5",
                "decimal": 10118.8
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            ],
            "returns_prewealth": [
              {
                "exact": "-243/25000",
                "decimal": -0.00972
              },
              {
                "exact": "297/25000",
                "decimal": 0.01188
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            ]
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          {
            "q": 55,
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            },
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            },
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              "decimal": 0.0
            },
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              "exact": "4500",
              "decimal": 4500.0
            },
            "x": {
              "exact": "11/20",
              "decimal": 0.55
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "11/20",
              "decimal": 0.55
            },
            "expected_gross_pnl": {
              "exact": "11",
              "decimal": 11.0
            },
            "nominal_expected_net_pnl": {
              "exact": "11",
              "decimal": 11.0
            },
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              "exact": "11",
              "decimal": 11.0
            },
            "risk_penalty_dollars": {
              "exact": "121/20",
              "decimal": 6.05
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              "exact": "99/20",
              "decimal": 4.95
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            "terminal_mid_wealth": [
              {
                "exact": "9901",
                "decimal": 9901.0
              },
              {
                "exact": "10121",
                "decimal": 10121.0
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            ],
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              {
                "exact": "-99/10000",
                "decimal": -0.0099
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              {
                "exact": "121/10000",
                "decimal": 0.0121
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            ]
          },
          {
            "q": 56,
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            },
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              "decimal": 0.0
            },
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            },
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              "exact": "4400",
              "decimal": 4400.0
            },
            "x": {
              "exact": "14/25",
              "decimal": 0.56
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
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              "exact": "14/25",
              "decimal": 0.56
            },
            "expected_gross_pnl": {
              "exact": "56/5",
              "decimal": 11.2
            },
            "nominal_expected_net_pnl": {
              "exact": "56/5",
              "decimal": 11.2
            },
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              "exact": "56/5",
              "decimal": 11.2
            },
            "risk_penalty_dollars": {
              "exact": "784/125",
              "decimal": 6.272
            },
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              "exact": "616/125",
              "decimal": 4.928
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            "terminal_mid_wealth": [
              {
                "exact": "49496/5",
                "decimal": 9899.2
              },
              {
                "exact": "50616/5",
                "decimal": 10123.2
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            ],
            "returns_prewealth": [
              {
                "exact": "-63/6250",
                "decimal": -0.01008
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              {
                "exact": "77/6250",
                "decimal": 0.01232
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            ]
          },
          {
            "q": 57,
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            },
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              "decimal": 0.0
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            },
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              "exact": "4300",
              "decimal": 4300.0
            },
            "x": {
              "exact": "57/100",
              "decimal": 0.57
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            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
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              "exact": "57/100",
              "decimal": 0.57
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            "expected_gross_pnl": {
              "exact": "57/5",
              "decimal": 11.4
            },
            "nominal_expected_net_pnl": {
              "exact": "57/5",
              "decimal": 11.4
            },
            "worst_expected_net_pnl": {
              "exact": "57/5",
              "decimal": 11.4
            },
            "risk_penalty_dollars": {
              "exact": "3249/500",
              "decimal": 6.498
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              "exact": "2451/500",
              "decimal": 4.902
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            "terminal_mid_wealth": [
              {
                "exact": "49487/5",
                "decimal": 9897.4
              },
              {
                "exact": "50627/5",
                "decimal": 10125.4
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            ],
            "returns_prewealth": [
              {
                "exact": "-513/50000",
                "decimal": -0.01026
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              {
                "exact": "627/50000",
                "decimal": 0.01254
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            ]
          },
          {
            "q": 58,
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            },
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              "exact": "0",
              "decimal": 0.0
            },
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              "decimal": 0.0
            },
            "cash": {
              "exact": "4200",
              "decimal": 4200.0
            },
            "x": {
              "exact": "29/50",
              "decimal": 0.58
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "29/50",
              "decimal": 0.58
            },
            "expected_gross_pnl": {
              "exact": "58/5",
              "decimal": 11.6
            },
            "nominal_expected_net_pnl": {
              "exact": "58/5",
              "decimal": 11.6
            },
            "worst_expected_net_pnl": {
              "exact": "58/5",
              "decimal": 11.6
            },
            "risk_penalty_dollars": {
              "exact": "841/125",
              "decimal": 6.728
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              "exact": "609/125",
              "decimal": 4.872
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            "terminal_mid_wealth": [
              {
                "exact": "49478/5",
                "decimal": 9895.6
              },
              {
                "exact": "50638/5",
                "decimal": 10127.6
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            ],
            "returns_prewealth": [
              {
                "exact": "-261/25000",
                "decimal": -0.01044
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              {
                "exact": "319/25000",
                "decimal": 0.01276
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            ]
          },
          {
            "q": 59,
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              "exact": "0",
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            },
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              "exact": "0",
              "decimal": 0.0
            },
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            },
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              "exact": "4100",
              "decimal": 4100.0
            },
            "x": {
              "exact": "59/100",
              "decimal": 0.59
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            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
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              "exact": "59/100",
              "decimal": 0.59
            },
            "expected_gross_pnl": {
              "exact": "59/5",
              "decimal": 11.8
            },
            "nominal_expected_net_pnl": {
              "exact": "59/5",
              "decimal": 11.8
            },
            "worst_expected_net_pnl": {
              "exact": "59/5",
              "decimal": 11.8
            },
            "risk_penalty_dollars": {
              "exact": "3481/500",
              "decimal": 6.962
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            "objective_dollars": {
              "exact": "2419/500",
              "decimal": 4.838
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            "terminal_mid_wealth": [
              {
                "exact": "49469/5",
                "decimal": 9893.8
              },
              {
                "exact": "50649/5",
                "decimal": 10129.8
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            ],
            "returns_prewealth": [
              {
                "exact": "-531/50000",
                "decimal": -0.01062
              },
              {
                "exact": "649/50000",
                "decimal": 0.01298
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            ]
          },
          {
            "q": 60,
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              "decimal": 0.0
            },
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              "exact": "0",
              "decimal": 0.0
            },
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              "decimal": 0.0
            },
            "cash": {
              "exact": "4000",
              "decimal": 4000.0
            },
            "x": {
              "exact": "3/5",
              "decimal": 0.6
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "3/5",
              "decimal": 0.6
            },
            "expected_gross_pnl": {
              "exact": "12",
              "decimal": 12.0
            },
            "nominal_expected_net_pnl": {
              "exact": "12",
              "decimal": 12.0
            },
            "worst_expected_net_pnl": {
              "exact": "12",
              "decimal": 12.0
            },
            "risk_penalty_dollars": {
              "exact": "36/5",
              "decimal": 7.2
            },
            "objective_dollars": {
              "exact": "24/5",
              "decimal": 4.8
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            "terminal_mid_wealth": [
              {
                "exact": "9892",
                "decimal": 9892.0
              },
              {
                "exact": "10132",
                "decimal": 10132.0
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            ],
            "returns_prewealth": [
              {
                "exact": "-27/2500",
                "decimal": -0.0108
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              {
                "exact": "33/2500",
                "decimal": 0.0132
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            ]
          },
          {
            "q": 61,
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              "decimal": 0.0
            },
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              "exact": "0",
              "decimal": 0.0
            },
            "cost": {
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              "decimal": 0.0
            },
            "cash": {
              "exact": "3900",
              "decimal": 3900.0
            },
            "x": {
              "exact": "61/100",
              "decimal": 0.61
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            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
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              "exact": "61/100",
              "decimal": 0.61
            },
            "expected_gross_pnl": {
              "exact": "61/5",
              "decimal": 12.2
            },
            "nominal_expected_net_pnl": {
              "exact": "61/5",
              "decimal": 12.2
            },
            "worst_expected_net_pnl": {
              "exact": "61/5",
              "decimal": 12.2
            },
            "risk_penalty_dollars": {
              "exact": "3721/500",
              "decimal": 7.442
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              "exact": "2379/500",
              "decimal": 4.758
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            "terminal_mid_wealth": [
              {
                "exact": "49451/5",
                "decimal": 9890.2
              },
              {
                "exact": "50671/5",
                "decimal": 10134.2
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            ],
            "returns_prewealth": [
              {
                "exact": "-549/50000",
                "decimal": -0.01098
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              {
                "exact": "671/50000",
                "decimal": 0.01342
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            ]
          },
          {
            "q": 62,
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            },
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              "exact": "0",
              "decimal": 0.0
            },
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              "decimal": 0.0
            },
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              "exact": "3800",
              "decimal": 3800.0
            },
            "x": {
              "exact": "31/50",
              "decimal": 0.62
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
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              "exact": "31/50",
              "decimal": 0.62
            },
            "expected_gross_pnl": {
              "exact": "62/5",
              "decimal": 12.4
            },
            "nominal_expected_net_pnl": {
              "exact": "62/5",
              "decimal": 12.4
            },
            "worst_expected_net_pnl": {
              "exact": "62/5",
              "decimal": 12.4
            },
            "risk_penalty_dollars": {
              "exact": "961/125",
              "decimal": 7.688
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            "objective_dollars": {
              "exact": "589/125",
              "decimal": 4.712
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            "terminal_mid_wealth": [
              {
                "exact": "49442/5",
                "decimal": 9888.4
              },
              {
                "exact": "50682/5",
                "decimal": 10136.4
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            ],
            "returns_prewealth": [
              {
                "exact": "-279/25000",
                "decimal": -0.01116
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              {
                "exact": "341/25000",
                "decimal": 0.01364
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            ]
          },
          {
            "q": 63,
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            },
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              "exact": "0",
              "decimal": 0.0
            },
            "cost": {
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            },
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              "exact": "3700",
              "decimal": 3700.0
            },
            "x": {
              "exact": "63/100",
              "decimal": 0.63
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
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              "exact": "63/100",
              "decimal": 0.63
            },
            "expected_gross_pnl": {
              "exact": "63/5",
              "decimal": 12.6
            },
            "nominal_expected_net_pnl": {
              "exact": "63/5",
              "decimal": 12.6
            },
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              "exact": "63/5",
              "decimal": 12.6
            },
            "risk_penalty_dollars": {
              "exact": "3969/500",
              "decimal": 7.938
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            "objective_dollars": {
              "exact": "2331/500",
              "decimal": 4.662
            },
            "terminal_mid_wealth": [
              {
                "exact": "49433/5",
                "decimal": 9886.6
              },
              {
                "exact": "50693/5",
                "decimal": 10138.6
              }
            ],
            "returns_prewealth": [
              {
                "exact": "-567/50000",
                "decimal": -0.01134
              },
              {
                "exact": "693/50000",
                "decimal": 0.01386
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            ]
          },
          {
            "q": 64,
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              "decimal": 0.0
            },
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              "exact": "0",
              "decimal": 0.0
            },
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            },
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              "exact": "3600",
              "decimal": 3600.0
            },
            "x": {
              "exact": "16/25",
              "decimal": 0.64
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "16/25",
              "decimal": 0.64
            },
            "expected_gross_pnl": {
              "exact": "64/5",
              "decimal": 12.8
            },
            "nominal_expected_net_pnl": {
              "exact": "64/5",
              "decimal": 12.8
            },
            "worst_expected_net_pnl": {
              "exact": "64/5",
              "decimal": 12.8
            },
            "risk_penalty_dollars": {
              "exact": "1024/125",
              "decimal": 8.192
            },
            "objective_dollars": {
              "exact": "576/125",
              "decimal": 4.608
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            "terminal_mid_wealth": [
              {
                "exact": "49424/5",
                "decimal": 9884.8
              },
              {
                "exact": "50704/5",
                "decimal": 10140.8
              }
            ],
            "returns_prewealth": [
              {
                "exact": "-36/3125",
                "decimal": -0.01152
              },
              {
                "exact": "44/3125",
                "decimal": 0.01408
              }
            ]
          },
          {
            "q": 65,
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              "decimal": 0.0
            },
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              "exact": "0",
              "decimal": 0.0
            },
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              "decimal": 0.0
            },
            "cash": {
              "exact": "3500",
              "decimal": 3500.0
            },
            "x": {
              "exact": "13/20",
              "decimal": 0.65
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "13/20",
              "decimal": 0.65
            },
            "expected_gross_pnl": {
              "exact": "13",
              "decimal": 13.0
            },
            "nominal_expected_net_pnl": {
              "exact": "13",
              "decimal": 13.0
            },
            "worst_expected_net_pnl": {
              "exact": "13",
              "decimal": 13.0
            },
            "risk_penalty_dollars": {
              "exact": "169/20",
              "decimal": 8.45
            },
            "objective_dollars": {
              "exact": "91/20",
              "decimal": 4.55
            },
            "terminal_mid_wealth": [
              {
                "exact": "9883",
                "decimal": 9883.0
              },
              {
                "exact": "10143",
                "decimal": 10143.0
              }
            ],
            "returns_prewealth": [
              {
                "exact": "-117/10000",
                "decimal": -0.0117
              },
              {
                "exact": "143/10000",
                "decimal": 0.0143
              }
            ]
          },
          {
            "q": 66,
            "feasible": true,
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              "exact": "0",
              "decimal": 0.0
            },
            "commission": {
              "exact": "0",
              "decimal": 0.0
            },
            "cost": {
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              "decimal": 0.0
            },
            "cash": {
              "exact": "3400",
              "decimal": 3400.0
            },
            "x": {
              "exact": "33/50",
              "decimal": 0.66
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "33/50",
              "decimal": 0.66
            },
            "expected_gross_pnl": {
              "exact": "66/5",
              "decimal": 13.2
            },
            "nominal_expected_net_pnl": {
              "exact": "66/5",
              "decimal": 13.2
            },
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              "exact": "66/5",
              "decimal": 13.2
            },
            "risk_penalty_dollars": {
              "exact": "1089/125",
              "decimal": 8.712
            },
            "objective_dollars": {
              "exact": "561/125",
              "decimal": 4.488
            },
            "terminal_mid_wealth": [
              {
                "exact": "49406/5",
                "decimal": 9881.2
              },
              {
                "exact": "50726/5",
                "decimal": 10145.2
              }
            ],
            "returns_prewealth": [
              {
                "exact": "-297/25000",
                "decimal": -0.01188
              },
              {
                "exact": "363/25000",
                "decimal": 0.01452
              }
            ]
          },
          {
            "q": 67,
            "feasible": true,
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              "exact": "0",
              "decimal": 0.0
            },
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              "exact": "0",
              "decimal": 0.0
            },
            "cost": {
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              "decimal": 0.0
            },
            "cash": {
              "exact": "3300",
              "decimal": 3300.0
            },
            "x": {
              "exact": "67/100",
              "decimal": 0.67
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "67/100",
              "decimal": 0.67
            },
            "expected_gross_pnl": {
              "exact": "67/5",
              "decimal": 13.4
            },
            "nominal_expected_net_pnl": {
              "exact": "67/5",
              "decimal": 13.4
            },
            "worst_expected_net_pnl": {
              "exact": "67/5",
              "decimal": 13.4
            },
            "risk_penalty_dollars": {
              "exact": "4489/500",
              "decimal": 8.978
            },
            "objective_dollars": {
              "exact": "2211/500",
              "decimal": 4.422
            },
            "terminal_mid_wealth": [
              {
                "exact": "49397/5",
                "decimal": 9879.4
              },
              {
                "exact": "50737/5",
                "decimal": 10147.4
              }
            ],
            "returns_prewealth": [
              {
                "exact": "-603/50000",
                "decimal": -0.01206
              },
              {
                "exact": "737/50000",
                "decimal": 0.01474
              }
            ]
          },
          {
            "q": 68,
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              "exact": "0",
              "decimal": 0.0
            },
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              "exact": "0",
              "decimal": 0.0
            },
            "cost": {
              "exact": "0",
              "decimal": 0.0
            },
            "cash": {
              "exact": "3200",
              "decimal": 3200.0
            },
            "x": {
              "exact": "17/25",
              "decimal": 0.68
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "17/25",
              "decimal": 0.68
            },
            "expected_gross_pnl": {
              "exact": "68/5",
              "decimal": 13.6
            },
            "nominal_expected_net_pnl": {
              "exact": "68/5",
              "decimal": 13.6
            },
            "worst_expected_net_pnl": {
              "exact": "68/5",
              "decimal": 13.6
            },
            "risk_penalty_dollars": {
              "exact": "1156/125",
              "decimal": 9.248
            },
            "objective_dollars": {
              "exact": "544/125",
              "decimal": 4.352
            },
            "terminal_mid_wealth": [
              {
                "exact": "49388/5",
                "decimal": 9877.6
              },
              {
                "exact": "50748/5",
                "decimal": 10149.6
              }
            ],
            "returns_prewealth": [
              {
                "exact": "-153/12500",
                "decimal": -0.01224
              },
              {
                "exact": "187/12500",
                "decimal": 0.01496
              }
            ]
          },
          {
            "q": 69,
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              "exact": "0",
              "decimal": 0.0
            },
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              "exact": "0",
              "decimal": 0.0
            },
            "cost": {
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              "decimal": 0.0
            },
            "cash": {
              "exact": "3100",
              "decimal": 3100.0
            },
            "x": {
              "exact": "69/100",
              "decimal": 0.69
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "69/100",
              "decimal": 0.69
            },
            "expected_gross_pnl": {
              "exact": "69/5",
              "decimal": 13.8
            },
            "nominal_expected_net_pnl": {
              "exact": "69/5",
              "decimal": 13.8
            },
            "worst_expected_net_pnl": {
              "exact": "69/5",
              "decimal": 13.8
            },
            "risk_penalty_dollars": {
              "exact": "4761/500",
              "decimal": 9.522
            },
            "objective_dollars": {
              "exact": "2139/500",
              "decimal": 4.278
            },
            "terminal_mid_wealth": [
              {
                "exact": "49379/5",
                "decimal": 9875.8
              },
              {
                "exact": "50759/5",
                "decimal": 10151.8
              }
            ],
            "returns_prewealth": [
              {
                "exact": "-621/50000",
                "decimal": -0.01242
              },
              {
                "exact": "759/50000",
                "decimal": 0.01518
              }
            ]
          },
          {
            "q": 70,
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              "exact": "0",
              "decimal": 0.0
            },
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              "exact": "0",
              "decimal": 0.0
            },
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              "exact": "0",
              "decimal": 0.0
            },
            "cash": {
              "exact": "3000",
              "decimal": 3000.0
            },
            "x": {
              "exact": "7/10",
              "decimal": 0.7
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "7/10",
              "decimal": 0.7
            },
            "expected_gross_pnl": {
              "exact": "14",
              "decimal": 14.0
            },
            "nominal_expected_net_pnl": {
              "exact": "14",
              "decimal": 14.0
            },
            "worst_expected_net_pnl": {
              "exact": "14",
              "decimal": 14.0
            },
            "risk_penalty_dollars": {
              "exact": "49/5",
              "decimal": 9.8
            },
            "objective_dollars": {
              "exact": "21/5",
              "decimal": 4.2
            },
            "terminal_mid_wealth": [
              {
                "exact": "9874",
                "decimal": 9874.0
              },
              {
                "exact": "10154",
                "decimal": 10154.0
              }
            ],
            "returns_prewealth": [
              {
                "exact": "-63/5000",
                "decimal": -0.0126
              },
              {
                "exact": "77/5000",
                "decimal": 0.0154
              }
            ]
          },
          {
            "q": 71,
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              "exact": "0",
              "decimal": 0.0
            },
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              "exact": "0",
              "decimal": 0.0
            },
            "cost": {
              "exact": "0",
              "decimal": 0.0
            },
            "cash": {
              "exact": "2900",
              "decimal": 2900.0
            },
            "x": {
              "exact": "71/100",
              "decimal": 0.71
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "71/100",
              "decimal": 0.71
            },
            "expected_gross_pnl": {
              "exact": "71/5",
              "decimal": 14.2
            },
            "nominal_expected_net_pnl": {
              "exact": "71/5",
              "decimal": 14.2
            },
            "worst_expected_net_pnl": {
              "exact": "71/5",
              "decimal": 14.2
            },
            "risk_penalty_dollars": {
              "exact": "5041/500",
              "decimal": 10.082
            },
            "objective_dollars": {
              "exact": "2059/500",
              "decimal": 4.118
            },
            "terminal_mid_wealth": [
              {
                "exact": "49361/5",
                "decimal": 9872.2
              },
              {
                "exact": "50781/5",
                "decimal": 10156.2
              }
            ],
            "returns_prewealth": [
              {
                "exact": "-639/50000",
                "decimal": -0.01278
              },
              {
                "exact": "781/50000",
                "decimal": 0.01562
              }
            ]
          },
          {
            "q": 72,
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              "exact": "0",
              "decimal": 0.0
            },
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              "exact": "0",
              "decimal": 0.0
            },
            "cost": {
              "exact": "0",
              "decimal": 0.0
            },
            "cash": {
              "exact": "2800",
              "decimal": 2800.0
            },
            "x": {
              "exact": "18/25",
              "decimal": 0.72
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "18/25",
              "decimal": 0.72
            },
            "expected_gross_pnl": {
              "exact": "72/5",
              "decimal": 14.4
            },
            "nominal_expected_net_pnl": {
              "exact": "72/5",
              "decimal": 14.4
            },
            "worst_expected_net_pnl": {
              "exact": "72/5",
              "decimal": 14.4
            },
            "risk_penalty_dollars": {
              "exact": "1296/125",
              "decimal": 10.368
            },
            "objective_dollars": {
              "exact": "504/125",
              "decimal": 4.032
            },
            "terminal_mid_wealth": [
              {
                "exact": "49352/5",
                "decimal": 9870.4
              },
              {
                "exact": "50792/5",
                "decimal": 10158.4
              }
            ],
            "returns_prewealth": [
              {
                "exact": "-81/6250",
                "decimal": -0.01296
              },
              {
                "exact": "99/6250",
                "decimal": 0.01584
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            ]
          },
          {
            "q": 73,
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              "exact": "0",
              "decimal": 0.0
            },
            "commission": {
              "exact": "0",
              "decimal": 0.0
            },
            "cost": {
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              "decimal": 0.0
            },
            "cash": {
              "exact": "2700",
              "decimal": 2700.0
            },
            "x": {
              "exact": "73/100",
              "decimal": 0.73
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "73/100",
              "decimal": 0.73
            },
            "expected_gross_pnl": {
              "exact": "73/5",
              "decimal": 14.6
            },
            "nominal_expected_net_pnl": {
              "exact": "73/5",
              "decimal": 14.6
            },
            "worst_expected_net_pnl": {
              "exact": "73/5",
              "decimal": 14.6
            },
            "risk_penalty_dollars": {
              "exact": "5329/500",
              "decimal": 10.658
            },
            "objective_dollars": {
              "exact": "1971/500",
              "decimal": 3.942
            },
            "terminal_mid_wealth": [
              {
                "exact": "49343/5",
                "decimal": 9868.6
              },
              {
                "exact": "50803/5",
                "decimal": 10160.6
              }
            ],
            "returns_prewealth": [
              {
                "exact": "-657/50000",
                "decimal": -0.01314
              },
              {
                "exact": "803/50000",
                "decimal": 0.01606
              }
            ]
          },
          {
            "q": 74,
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              "exact": "0",
              "decimal": 0.0
            },
            "commission": {
              "exact": "0",
              "decimal": 0.0
            },
            "cost": {
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              "decimal": 0.0
            },
            "cash": {
              "exact": "2600",
              "decimal": 2600.0
            },
            "x": {
              "exact": "37/50",
              "decimal": 0.74
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "37/50",
              "decimal": 0.74
            },
            "expected_gross_pnl": {
              "exact": "74/5",
              "decimal": 14.8
            },
            "nominal_expected_net_pnl": {
              "exact": "74/5",
              "decimal": 14.8
            },
            "worst_expected_net_pnl": {
              "exact": "74/5",
              "decimal": 14.8
            },
            "risk_penalty_dollars": {
              "exact": "1369/125",
              "decimal": 10.952
            },
            "objective_dollars": {
              "exact": "481/125",
              "decimal": 3.848
            },
            "terminal_mid_wealth": [
              {
                "exact": "49334/5",
                "decimal": 9866.8
              },
              {
                "exact": "50814/5",
                "decimal": 10162.8
              }
            ],
            "returns_prewealth": [
              {
                "exact": "-333/25000",
                "decimal": -0.01332
              },
              {
                "exact": "407/25000",
                "decimal": 0.01628
              }
            ]
          },
          {
            "q": 75,
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              "exact": "0",
              "decimal": 0.0
            },
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              "exact": "0",
              "decimal": 0.0
            },
            "cost": {
              "exact": "0",
              "decimal": 0.0
            },
            "cash": {
              "exact": "2500",
              "decimal": 2500.0
            },
            "x": {
              "exact": "3/4",
              "decimal": 0.75
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "3/4",
              "decimal": 0.75
            },
            "expected_gross_pnl": {
              "exact": "15",
              "decimal": 15.0
            },
            "nominal_expected_net_pnl": {
              "exact": "15",
              "decimal": 15.0
            },
            "worst_expected_net_pnl": {
              "exact": "15",
              "decimal": 15.0
            },
            "risk_penalty_dollars": {
              "exact": "45/4",
              "decimal": 11.25
            },
            "objective_dollars": {
              "exact": "15/4",
              "decimal": 3.75
            },
            "terminal_mid_wealth": [
              {
                "exact": "9865",
                "decimal": 9865.0
              },
              {
                "exact": "10165",
                "decimal": 10165.0
              }
            ],
            "returns_prewealth": [
              {
                "exact": "-27/2000",
                "decimal": -0.0135
              },
              {
                "exact": "33/2000",
                "decimal": 0.0165
              }
            ]
          },
          {
            "q": 76,
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              "exact": "0",
              "decimal": 0.0
            },
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              "exact": "0",
              "decimal": 0.0
            },
            "cost": {
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              "decimal": 0.0
            },
            "cash": {
              "exact": "2400",
              "decimal": 2400.0
            },
            "x": {
              "exact": "19/25",
              "decimal": 0.76
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "19/25",
              "decimal": 0.76
            },
            "expected_gross_pnl": {
              "exact": "76/5",
              "decimal": 15.2
            },
            "nominal_expected_net_pnl": {
              "exact": "76/5",
              "decimal": 15.2
            },
            "worst_expected_net_pnl": {
              "exact": "76/5",
              "decimal": 15.2
            },
            "risk_penalty_dollars": {
              "exact": "1444/125",
              "decimal": 11.552
            },
            "objective_dollars": {
              "exact": "456/125",
              "decimal": 3.648
            },
            "terminal_mid_wealth": [
              {
                "exact": "49316/5",
                "decimal": 9863.2
              },
              {
                "exact": "50836/5",
                "decimal": 10167.2
              }
            ],
            "returns_prewealth": [
              {
                "exact": "-171/12500",
                "decimal": -0.01368
              },
              {
                "exact": "209/12500",
                "decimal": 0.01672
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            ]
          },
          {
            "q": 77,
            "feasible": true,
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              "exact": "0",
              "decimal": 0.0
            },
            "commission": {
              "exact": "0",
              "decimal": 0.0
            },
            "cost": {
              "exact": "0",
              "decimal": 0.0
            },
            "cash": {
              "exact": "2300",
              "decimal": 2300.0
            },
            "x": {
              "exact": "77/100",
              "decimal": 0.77
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "77/100",
              "decimal": 0.77
            },
            "expected_gross_pnl": {
              "exact": "77/5",
              "decimal": 15.4
            },
            "nominal_expected_net_pnl": {
              "exact": "77/5",
              "decimal": 15.4
            },
            "worst_expected_net_pnl": {
              "exact": "77/5",
              "decimal": 15.4
            },
            "risk_penalty_dollars": {
              "exact": "5929/500",
              "decimal": 11.858
            },
            "objective_dollars": {
              "exact": "1771/500",
              "decimal": 3.542
            },
            "terminal_mid_wealth": [
              {
                "exact": "49307/5",
                "decimal": 9861.4
              },
              {
                "exact": "50847/5",
                "decimal": 10169.4
              }
            ],
            "returns_prewealth": [
              {
                "exact": "-693/50000",
                "decimal": -0.01386
              },
              {
                "exact": "847/50000",
                "decimal": 0.01694
              }
            ]
          },
          {
            "q": 78,
            "feasible": true,
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              "exact": "0",
              "decimal": 0.0
            },
            "commission": {
              "exact": "0",
              "decimal": 0.0
            },
            "cost": {
              "exact": "0",
              "decimal": 0.0
            },
            "cash": {
              "exact": "2200",
              "decimal": 2200.0
            },
            "x": {
              "exact": "39/50",
              "decimal": 0.78
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "39/50",
              "decimal": 0.78
            },
            "expected_gross_pnl": {
              "exact": "78/5",
              "decimal": 15.6
            },
            "nominal_expected_net_pnl": {
              "exact": "78/5",
              "decimal": 15.6
            },
            "worst_expected_net_pnl": {
              "exact": "78/5",
              "decimal": 15.6
            },
            "risk_penalty_dollars": {
              "exact": "1521/125",
              "decimal": 12.168
            },
            "objective_dollars": {
              "exact": "429/125",
              "decimal": 3.432
            },
            "terminal_mid_wealth": [
              {
                "exact": "49298/5",
                "decimal": 9859.6
              },
              {
                "exact": "50858/5",
                "decimal": 10171.6
              }
            ],
            "returns_prewealth": [
              {
                "exact": "-351/25000",
                "decimal": -0.01404
              },
              {
                "exact": "429/25000",
                "decimal": 0.01716
              }
            ]
          },
          {
            "q": 79,
            "feasible": true,
            "spread": {
              "exact": "0",
              "decimal": 0.0
            },
            "commission": {
              "exact": "0",
              "decimal": 0.0
            },
            "cost": {
              "exact": "0",
              "decimal": 0.0
            },
            "cash": {
              "exact": "2100",
              "decimal": 2100.0
            },
            "x": {
              "exact": "79/100",
              "decimal": 0.79
            },
            "post_cost_wealth": {
              "exact": "10000",
              "decimal": 10000.0
            },
            "post_weight_risky": {
              "exact": "79/100",
              "decimal": 0.79
            },
            "expected_gross_pnl": {
              "exact": "79/5",
              "decimal": 15.8
            },
            "nominal_expected_net_pnl": {
              "exact": "79/5",
              "decimal": 15.8
            },
            "worst_expected_net_pnl": {
              "exact": "79/5",
              "decimal": 15.8
            },
            "risk_penalty_dollars": {
              "exact": "6241/500",
              "decimal": 12.482
            },
            "objective_dollars": {
              "exact": "1659/500",
              "decimal": 3.318
            },
            "terminal_mid_wealth": [
              {
                "exact": "49289/5",
                "decimal": 9857.8
              },
              {
                "exact": "50869/5",
                "decimal": 10173.8
              }
            ],
            "returns_prewealth": [
              {
                "exact": "-711/50000",
                "decimal": -0.01422
              },
              {
                "exact": "869/50000",
                "decimal": 0.01738
              }
            ]
          },
          {
            "q": 80,
            "feasible": true,
            "spread": {
              "exact": "0",
              "decimal": 0.0
            },
            "commission": {
              "exact": "0",
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                "exact": "473/200000",
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              "exact": "0",
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              "exact": "9/5",
              "decimal": 1.8
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              "exact": "189/125",
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              {
                "exact": "50129/5",
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                "exact": "-111/50000",
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              {
                "exact": "129/50000",
                "decimal": 0.00258
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              "exact": "39/20",
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              "exact": "403/250",
              "decimal": 1.612
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                "exact": "199519/20",
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              {
                "exact": "200559/20",
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                "exact": "-481/200000",
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              {
                "exact": "559/200000",
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              "exact": "21/10",
              "decimal": 2.1
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              "exact": "21/10",
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              "exact": "427/250",
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                "exact": "100301/10",
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                "exact": "-259/100000",
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                "exact": "301/100000",
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                "exact": "129/40000",
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                "exact": "43/12500",
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              "exact": "51/20",
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                "exact": "731/200000",
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                "exact": "387/100000",
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                "exact": "817/200000",
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                "exact": "10043",
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                "exact": "989/200000",
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                "exact": "50258/5",
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                "exact": "129/25000",
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            "q": 25,
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                "exact": "40215/4",
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                "exact": "-37/8000",
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              {
                "exact": "43/8000",
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              "exact": "637/250",
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              {
                "exact": "100559/10",
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                "exact": "-481/100000",
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              {
                "exact": "559/100000",
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              "exact": "81/20",
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              "exact": "81/20",
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              "exact": "324/125",
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                "exact": "201161/20",
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                "exact": "1161/200000",
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              "exact": "329/125",
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                "exact": "50301/5",
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                "exact": "-259/50000",
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                "exact": "301/50000",
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            "q": 29,
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                "exact": "1247/200000",
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                "exact": "20129/2",
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                "exact": "129/20000",
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                "exact": "1333/200000",
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                "exact": "49704/5",
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                "exact": "50344/5",
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                "exact": "43/6250",
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                "exact": "201419/20",
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                "exact": "100731/10",
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                "exact": "-629/100000",
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                "exact": "731/100000",
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                "exact": "301/40000",
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            "q": 36,
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              "exact": "351/125",
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                "exact": "50387/5",
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                "exact": "-333/50000",
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                "exact": "387/50000",
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            "q": 37,
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              "exact": "111/20",
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              "exact": "703/250",
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                "exact": "201591/20",
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                "exact": "-1369/200000",
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                "exact": "1591/200000",
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          {
            "q": 38,
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              "exact": "61981/10",
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              "exact": "99981/10",
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              "exact": "38000/99981",
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              "exact": "38/5",
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            "nominal_expected_net_pnl": {
              "exact": "57/10",
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                "exact": "50559/5",
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                "exact": "559/50000",
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                "exact": "129/10000",
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                "exact": "1333/100000",
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              "exact": "176/125",
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                "exact": "50688/5",
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                "exact": "-37/3125",
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              {
                "exact": "43/3125",
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          },
          {
            "q": 65,
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                "exact": "40559/4",
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                "exact": "1419/100000",
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                "exact": "50731/5",
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                "exact": "731/50000",
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                "exact": "817/50000",
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            "q": 77,
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              "exact": "231/20",
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                "exact": "203311/20",
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              {
                "exact": "3311/200000",
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            "q": 78,
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              "exact": "99961/10",
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                "exact": "2227/500000",
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              "exact": "69/25",
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              "exact": "-56/125",
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                "exact": "1004661/100",
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                "exact": "4661/1000000",
                "decimal": 0.004661
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            "q": 24,
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              "exact": "17/25",
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              "exact": "-59/125",
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                "exact": "248817/25",
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              {
                "exact": "251217/25",
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                "exact": "-1183/250000",
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              {
                "exact": "1217/250000",
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              "exact": "9/4",
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              "exact": "29991/4",
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              "exact": "3/4",
              "decimal": 0.75
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              "exact": "3/4",
              "decimal": 0.75
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              "exact": "-1/2",
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                "exact": "40203/4",
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                "exact": "-197/40000",
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              {
                "exact": "203/40000",
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              "exact": "41/50",
              "decimal": 0.82
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              "exact": "-133/250",
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                "exact": "502641/50",
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                "exact": "2641/500000",
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                "exact": "1005489/100",
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                "exact": "5489/1000000",
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              "exact": "24/25",
              "decimal": 0.96
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              "exact": "-76/125",
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                "exact": "251424/25",
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                "exact": "-86/15625",
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                "exact": "89/15625",
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              "exact": "-163/250",
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                "exact": "1005903/100",
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              {
                "exact": "5903/1000000",
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              "exact": "11/10",
              "decimal": 1.1
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              "exact": "-7/10",
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              {
                "exact": "100611/10",
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                "exact": "-589/100000",
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              {
                "exact": "611/100000",
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                "exact": "6317/1000000",
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                "exact": "201429/20",
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                "exact": "-1371/200000",
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                "exact": "1429/200000",
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            "q": 36,
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              "exact": "31986/5",
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              "exact": "49986/5",
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              "exact": "1000/2777",
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              "exact": "108/25",
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                "exact": "617/40000",
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            "q": 76,
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              "exact": "-117/250",
              "decimal": -0.468
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                "exact": "199721/20",
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              {
                "exact": "200281/20",
                "decimal": 10014.05
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              {
                "exact": "-279/200000",
                "decimal": -0.001395
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              {
                "exact": "281/200000",
                "decimal": 0.001405
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            ]
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            "q": 8,
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              "exact": "1",
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              "exact": "45993/5",
              "decimal": 9198.6
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              "exact": "2/25",
              "decimal": 0.08
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              "exact": "49993/5",
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              "exact": "8/5",
              "decimal": 1.6
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              "exact": "1/5",
              "decimal": 0.2
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              "exact": "-7/25",
              "decimal": -0.28
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              "exact": "16/125",
              "decimal": 0.128
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              "exact": "-51/125",
              "decimal": -0.408
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              {
                "exact": "49921/5",
                "decimal": 9984.2
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              {
                "exact": "50081/5",
                "decimal": 10016.2
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              {
                "exact": "-79/50000",
                "decimal": -0.00158
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              {
                "exact": "81/50000",
                "decimal": 0.00162
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            ]
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          {
            "q": 9,
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              "exact": "1",
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            "cost": {
              "exact": "29/20",
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              "exact": "181971/20",
              "decimal": 9098.55
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              "exact": "9/100",
              "decimal": 0.09
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              "exact": "199971/20",
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              "exact": "2000/22219",
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              "exact": "9/5",
              "decimal": 1.8
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            "nominal_expected_net_pnl": {
              "exact": "7/20",
              "decimal": 0.35
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              "exact": "-19/100",
              "decimal": -0.19
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              "decimal": 0.162
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              "exact": "-44/125",
              "decimal": -0.352
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              {
                "exact": "199647/20",
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              {
                "exact": "200367/20",
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              {
                "exact": "-353/200000",
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              {
                "exact": "367/200000",
                "decimal": 0.001835
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              "exact": "17997/2",
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              "exact": "1/10",
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              "exact": "2",
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              "decimal": 0.5
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              "exact": "-3/10",
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                "exact": "19961/2",
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              {
                "exact": "20041/2",
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                "exact": "-39/20000",
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              {
                "exact": "41/20000",
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                "exact": "200453/20",
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                "exact": "-427/200000",
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              {
                "exact": "453/200000",
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              "decimal": 0.8
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                "exact": "49884/5",
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                "exact": "50124/5",
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                "exact": "31/12500",
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              "exact": "-21/125",
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                "exact": "200539/20",
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                "exact": "-501/200000",
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              {
                "exact": "539/200000",
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            "q": 14,
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                "exact": "99731/10",
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                "exact": "100291/10",
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                "exact": "-269/100000",
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              {
                "exact": "291/100000",
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              "exact": "-1/10",
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                "exact": "40125/4",
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                "exact": "-23/8000",
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              {
                "exact": "1/320",
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                "exact": "50167/5",
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                "exact": "-153/50000",
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              {
                "exact": "167/50000",
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              "exact": "-6/125",
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                "exact": "200711/20",
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                "exact": "-649/200000",
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              {
                "exact": "711/200000",
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                "exact": "99657/10",
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                "exact": "100377/10",
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                "exact": "-343/100000",
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              {
                "exact": "377/100000",
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              "exact": "199961/20",
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              "exact": "71/100",
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              "exact": "-3/250",
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                "exact": "200797/20",
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                "exact": "-723/200000",
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              {
                "exact": "797/200000",
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            "q": 20,
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              "exact": "9998",
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            "post_weight_risky": {
              "exact": "1000/4999",
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              "exact": "4",
              "decimal": 4.0
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              "exact": "2",
              "decimal": 2.0
            },
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              "exact": "4/5",
              "decimal": 0.8
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              "exact": "4/5",
              "decimal": 0.8
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              "exact": "0",
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            "terminal_mid_wealth": [
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                "exact": "9962",
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              {
                "exact": "10042",
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            "returns_prewealth": [
              {
                "exact": "-19/5000",
                "decimal": -0.0038
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              {
                "exact": "21/5000",
                "decimal": 0.0042
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            ]
          },
          {
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                "exact": "10128",
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                "exact": "203119/20",
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                "exact": "-2721/200000",
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              {
                "exact": "3119/200000",
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          {
            "q": 74,
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                "exact": "50081/5",
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                "exact": "367/200000",
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                "exact": "-2721/200000",
                "decimal": -0.013605
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              {
                "exact": "3119/200000",
                "decimal": 0.015595
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            "q": 74,
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              "exact": "37/10",
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              "exact": "1",
              "decimal": 1.0
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            "cost": {
              "exact": "47/10",
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              "exact": "25953/10",
              "decimal": 2595.3
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              "exact": "37/50",
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            "post_cost_wealth": {
              "exact": "99953/10",
              "decimal": 9995.3
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            "post_weight_risky": {
              "exact": "74000/99953",
              "decimal": 0.7403479635428651
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            "expected_gross_pnl": {
              "exact": "74/5",
              "decimal": 14.8
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            "nominal_expected_net_pnl": {
              "exact": "101/10",
              "decimal": 10.1
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              "exact": "101/10",
              "decimal": 10.1
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            "risk_penalty_dollars": {
              "exact": "1369/125",
              "decimal": 10.952
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            "objective_dollars": {
              "exact": "-213/250",
              "decimal": -0.852
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            "terminal_mid_wealth": [
              {
                "exact": "98621/10",
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              {
                "exact": "101581/10",
                "decimal": 10158.1
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              {
                "exact": "-1379/100000",
                "decimal": -0.01379
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              {
                "exact": "1581/100000",
                "decimal": 0.01581
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          {
            "q": 75,
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              "exact": "15/4",
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              "exact": "1",
              "decimal": 1.0
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            "cost": {
              "exact": "19/4",
              "decimal": 4.75
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              "exact": "9981/4",
              "decimal": 2495.25
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            "x": {
              "exact": "3/4",
              "decimal": 0.75
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            "post_cost_wealth": {
              "exact": "39981/4",
              "decimal": 9995.25
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            "post_weight_risky": {
              "exact": "10000/13327",
              "decimal": 0.7503564192991671
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            "expected_gross_pnl": {
              "exact": "15",
              "decimal": 15.0
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            "nominal_expected_net_pnl": {
              "exact": "41/4",
              "decimal": 10.25
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            "worst_expected_net_pnl": {
              "exact": "41/4",
              "decimal": 10.25
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            "risk_penalty_dollars": {
              "exact": "45/4",
              "decimal": 11.25
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            "objective_dollars": {
              "exact": "-1",
              "decimal": -1.0
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            "terminal_mid_wealth": [
              {
                "exact": "39441/4",
                "decimal": 9860.25
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              {
                "exact": "40641/4",
                "decimal": 10160.25
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            "returns_prewealth": [
              {
                "exact": "-559/40000",
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              {
                "exact": "641/40000",
                "decimal": 0.016025
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          {
            "q": 76,
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              "exact": "19/5",
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              "exact": "1",
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            "cost": {
              "exact": "24/5",
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            "cash": {
              "exact": "11976/5",
              "decimal": 2395.2
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              "exact": "19/25",
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            "post_cost_wealth": {
              "exact": "49976/5",
              "decimal": 9995.2
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            "post_weight_risky": {
              "exact": "4750/6247",
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            "expected_gross_pnl": {
              "exact": "76/5",
              "decimal": 15.2
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            "nominal_expected_net_pnl": {
              "exact": "52/5",
              "decimal": 10.4
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            "worst_expected_net_pnl": {
              "exact": "52/5",
              "decimal": 10.4
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            "risk_penalty_dollars": {
              "exact": "1444/125",
              "decimal": 11.552
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            "objective_dollars": {
              "exact": "-144/125",
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            "terminal_mid_wealth": [
              {
                "exact": "49292/5",
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              {
                "exact": "50812/5",
                "decimal": 10162.4
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            "returns_prewealth": [
              {
                "exact": "-177/12500",
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              {
                "exact": "203/12500",
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          {
            "q": 77,
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              "exact": "77/20",
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              "exact": "1",
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            "cost": {
              "exact": "97/20",
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            "cash": {
              "exact": "45903/20",
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            "x": {
              "exact": "77/100",
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            "post_cost_wealth": {
              "exact": "199903/20",
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            "post_weight_risky": {
              "exact": "14000/18173",
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            "expected_gross_pnl": {
              "exact": "77/5",
              "decimal": 15.4
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            "nominal_expected_net_pnl": {
              "exact": "211/20",
              "decimal": 10.55
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            "worst_expected_net_pnl": {
              "exact": "211/20",
              "decimal": 10.55
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            "risk_penalty_dollars": {
              "exact": "5929/500",
              "decimal": 11.858
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            "objective_dollars": {
              "exact": "-327/250",
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            "terminal_mid_wealth": [
              {
                "exact": "197131/20",
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              {
                "exact": "203291/20",
                "decimal": 10164.55
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            "returns_prewealth": [
              {
                "exact": "-2869/200000",
                "decimal": -0.014345
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              {
                "exact": "3291/200000",
                "decimal": 0.016455
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          {
            "q": 78,
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              "exact": "39/10",
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              "exact": "1",
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            "cost": {
              "exact": "49/10",
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            "cash": {
              "exact": "21951/10",
              "decimal": 2195.1
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            "x": {
              "exact": "39/50",
              "decimal": 0.78
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            "post_cost_wealth": {
              "exact": "99951/10",
              "decimal": 9995.1
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            "post_weight_risky": {
              "exact": "26000/33317",
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            "expected_gross_pnl": {
              "exact": "78/5",
              "decimal": 15.6
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            "nominal_expected_net_pnl": {
              "exact": "107/10",
              "decimal": 10.7
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            "worst_expected_net_pnl": {
              "exact": "107/10",
              "decimal": 10.7
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            "risk_penalty_dollars": {
              "exact": "1521/125",
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            "objective_dollars": {
              "exact": "-367/250",
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            "terminal_mid_wealth": [
              {
                "exact": "98547/10",
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              {
                "exact": "101667/10",
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            "returns_prewealth": [
              {
                "exact": "-1453/100000",
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              {
                "exact": "1667/100000",
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          {
            "q": 79,
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              "exact": "1",
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            "cost": {
              "exact": "99/20",
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            "cash": {
              "exact": "41901/20",
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              "exact": "79/100",
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            "post_cost_wealth": {
              "exact": "199901/20",
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            "post_weight_risky": {
              "exact": "158000/199901",
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            "expected_gross_pnl": {
              "exact": "79/5",
              "decimal": 15.8
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            "nominal_expected_net_pnl": {
              "exact": "217/20",
              "decimal": 10.85
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              "exact": "217/20",
              "decimal": 10.85
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            "risk_penalty_dollars": {
              "exact": "6241/500",
              "decimal": 12.482
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            "objective_dollars": {
              "exact": "-204/125",
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            "terminal_mid_wealth": [
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                "exact": "197057/20",
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              {
                "exact": "203377/20",
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              {
                "exact": "-2943/200000",
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              {
                "exact": "3377/200000",
                "decimal": 0.016885
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          {
            "q": 80,
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              "exact": "4",
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              "exact": "1",
              "decimal": 1.0
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            "cost": {
              "exact": "5",
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            "cash": {
              "exact": "1995",
              "decimal": 1995.0
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            "x": {
              "exact": "4/5",
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            "post_cost_wealth": {
              "exact": "9995",
              "decimal": 9995.0
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            "post_weight_risky": {
              "exact": "1600/1999",
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            "expected_gross_pnl": {
              "exact": "16",
              "decimal": 16.0
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            "nominal_expected_net_pnl": {
              "exact": "11",
              "decimal": 11.0
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              "exact": "11",
              "decimal": 11.0
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            "risk_penalty_dollars": {
              "exact": "64/5",
              "decimal": 12.8
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            "objective_dollars": {
              "exact": "-9/5",
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            "terminal_mid_wealth": [
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                "exact": "9851",
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                "exact": "10171",
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                "exact": "-149/10000",
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              {
                "exact": "171/10000",
                "decimal": 0.0171
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    "official_commission_examples": [
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        "price": {
          "exact": "25",
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          "exact": "1",
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        "q": 1000,
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          "exact": "25",
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          "exact": "5",
          "decimal": 5.0
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        "q": 1000,
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          "exact": "1/4",
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        "commission": {
          "exact": "5/2",
          "decimal": 2.5
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      {
        "q": 10,
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          "exact": "1/5",
          "decimal": 0.2
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        "commission": {
          "exact": "1/50",
          "decimal": 0.02
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    ]
  }
}