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0.2583333333333333, "call_chips": -47.25000000000003, "unchecked_action": "FOLD", "verified_low_action": "FOLD", "verified_high_action": "CALL", "unchecked_utility": 0, "verified_utility": 23.624999999999986, "gross": 23.624999999999986, "net": 11.024999999999986, "choice": "VERIFY" }, "utility": { "posterior_high": 0.25, "p_bluff": 0.2583333333333333, "call_chips": -47.25000000000003, "unchecked_action": "FOLD", "verified_low_action": "FOLD", "verified_high_action": "CALL", "unchecked_utility": 0, "verified_utility": 25.274999999999984, "gross": 25.274999999999984, "net": 12.674999999999985, "choice": "VERIFY" } }, { "family": "full-19", "draft": "low", "bonus_action": "FOLD", "bonus_chip_equivalent": 6.6, "fee": 12.6, "chip_gross": 23.624999999999986, "utility_gross": 21.974999999999987, "chip_net": 11.024999999999986, "utility_net": 9.374999999999988, "chip_choice": "VERIFY", "utility_choice": "VERIFY", "final_actions_unchanged": true, "chip": { "posterior_high": 0.25, "p_bluff": 0.2583333333333333, "call_chips": -47.25000000000003, "unchecked_action": "FOLD", "verified_low_action": "FOLD", "verified_high_action": "CALL", "unchecked_utility": 0.0, "verified_utility": 23.624999999999986, "gross": 23.624999999999986, "net": 11.024999999999986, "choice": "VERIFY" }, "utility": { "posterior_high": 0.25, "p_bluff": 0.2583333333333333, "call_chips": -47.25000000000003, "unchecked_action": "FOLD", "verified_low_action": "FOLD", "verified_high_action": "CALL", "unchecked_utility": 6.6, "verified_utility": 28.574999999999985, "gross": 21.974999999999987, "net": 9.374999999999988, "choice": "VERIFY" } }, { "family": "full-19", "draft": "high", "bonus_action": "CALL", "bonus_chip_equivalent": 6.6, "fee": 12.6, "chip_gross": 23.625000000000014, "utility_gross": 21.975000000000016, "chip_net": 11.025000000000015, "utility_net": 9.375000000000016, "chip_choice": "VERIFY", "utility_choice": "VERIFY", "final_actions_unchanged": true, "chip": { "posterior_high": 0.75, "p_bluff": 0.40833333333333327, "call_chips": 47.24999999999994, "unchecked_action": "CALL", "verified_low_action": "FOLD", "verified_high_action": "CALL", "unchecked_utility": 47.24999999999994, "verified_utility": 70.87499999999996, "gross": 23.625000000000014, "net": 11.025000000000015, "choice": "VERIFY" }, "utility": { "posterior_high": 0.75, "p_bluff": 0.40833333333333327, "call_chips": 47.24999999999994, "unchecked_action": "CALL", "verified_low_action": "FOLD", "verified_high_action": "CALL", "unchecked_utility": 53.849999999999945, "verified_utility": 75.82499999999996, "gross": 21.975000000000016, "net": 9.375000000000016, "choice": "VERIFY" } }, { "family": "full-19", "draft": "high", "bonus_action": "FOLD", "bonus_chip_equivalent": 6.6, "fee": 12.6, "chip_gross": 23.625000000000014, "utility_gross": 25.27500000000002, "chip_net": 11.025000000000015, "utility_net": 12.67500000000002, "chip_choice": "VERIFY", "utility_choice": "VERIFY", "final_actions_unchanged": true, "chip": { "posterior_high": 0.75, "p_bluff": 0.40833333333333327, "call_chips": 47.24999999999994, "unchecked_action": "CALL", "verified_low_action": "FOLD", "verified_high_action": "CALL", "unchecked_utility": 47.24999999999994, "verified_utility": 70.87499999999996, "gross": 23.625000000000014, "net": 11.025000000000015, "choice": "VERIFY" }, "utility": { "posterior_high": 0.75, "p_bluff": 0.40833333333333327, "call_chips": 47.24999999999994, "unchecked_action": "CALL", "verified_low_action": "FOLD", "verified_high_action": "CALL", "unchecked_utility": 47.24999999999994, "verified_utility": 72.52499999999996, "gross": 25.27500000000002, "net": 12.67500000000002, "choice": "VERIFY" } }, { "family": "full-20", "draft": "low", "bonus_action": "CALL", "bonus_chip_equivalent": 6.6, "fee": 8.4, "chip_gross": 15.75, "utility_gross": 17.4, "chip_net": 7.35, "utility_net": 8.999999999999998, "chip_choice": "VERIFY", "utility_choice": "VERIFY", "final_actions_unchanged": true, "chip": { "posterior_high": 0.25, "p_bluff": 0.21249999999999997, "call_chips": -31.50000000000003, "unchecked_action": "FOLD", "verified_low_action": "FOLD", "verified_high_action": "CALL", "unchecked_utility": 0, "verified_utility": 15.75, "gross": 15.75, "net": 7.35, "choice": "VERIFY" }, "utility": { "posterior_high": 0.25, "p_bluff": 0.21249999999999997, "call_chips": -31.50000000000003, "unchecked_action": "FOLD", "verified_low_action": "FOLD", "verified_high_action": "CALL", "unchecked_utility": 0, "verified_utility": 17.4, "gross": 17.4, "net": 8.999999999999998, "choice": "VERIFY" } }, { "family": "full-20", "draft": "low", "bonus_action": "FOLD", "bonus_chip_equivalent": 6.6, "fee": 8.4, "chip_gross": 15.75, "utility_gross": 14.1, "chip_net": 7.35, "utility_net": 5.699999999999999, "chip_choice": "VERIFY", "utility_choice": "VERIFY", "final_actions_unchanged": true, "chip": { "posterior_high": 0.25, "p_bluff": 0.21249999999999997, "call_chips": -31.50000000000003, "unchecked_action": "FOLD", "verified_low_action": "FOLD", "verified_high_action": "CALL", "unchecked_utility": 0.0, "verified_utility": 15.75, "gross": 15.75, "net": 7.35, "choice": "VERIFY" }, "utility": { "posterior_high": 0.25, "p_bluff": 0.21249999999999997, "call_chips": -31.50000000000003, "unchecked_action": "FOLD", "verified_low_action": "FOLD", "verified_high_action": "CALL", "unchecked_utility": 6.6, "verified_utility": 20.7, "gross": 14.1, "net": 5.699999999999999, "choice": "VERIFY" } }, { "family": "full-20", "draft": "high", "bonus_action": "CALL", "bonus_chip_equivalent": 6.6, "fee": 8.4, "chip_gross": 15.749999999999972, "utility_gross": 14.099999999999966, "chip_net": 7.349999999999971, "utility_net": 5.6999999999999655, "chip_choice": "VERIFY", "utility_choice": "VERIFY", "final_actions_unchanged": true, "chip": { "posterior_high": 0.75, "p_bluff": 0.28750000000000003, "call_chips": 31.50000000000003, "unchecked_action": "CALL", "verified_low_action": "FOLD", "verified_high_action": "CALL", "unchecked_utility": 31.50000000000003, "verified_utility": 47.25, "gross": 15.749999999999972, "net": 7.349999999999971, "choice": "VERIFY" }, "utility": { "posterior_high": 0.75, "p_bluff": 0.28750000000000003, "call_chips": 31.50000000000003, "unchecked_action": "CALL", "verified_low_action": "FOLD", "verified_high_action": "CALL", "unchecked_utility": 38.10000000000003, "verified_utility": 52.199999999999996, "gross": 14.099999999999966, "net": 5.6999999999999655, "choice": "VERIFY" } }, { "family": "full-20", "draft": "high", "bonus_action": "FOLD", "bonus_chip_equivalent": 6.6, "fee": 8.4, "chip_gross": 15.749999999999972, "utility_gross": 17.39999999999997, "chip_net": 7.349999999999971, "utility_net": 8.99999999999997, "chip_choice": "VERIFY", "utility_choice": "VERIFY", "final_actions_unchanged": true, "chip": { "posterior_high": 0.75, "p_bluff": 0.28750000000000003, "call_chips": 31.50000000000003, "unchecked_action": "CALL", "verified_low_action": "FOLD", "verified_high_action": "CALL", "unchecked_utility": 31.50000000000003, "verified_utility": 47.25, "gross": 15.749999999999972, "net": 7.349999999999971, "choice": "VERIFY" }, "utility": { "posterior_high": 0.75, "p_bluff": 0.28750000000000003, "call_chips": 31.50000000000003, "unchecked_action": "CALL", "verified_low_action": "FOLD", "verified_high_action": "CALL", "unchecked_utility": 31.50000000000003, "verified_utility": 48.9, "gross": 17.39999999999997, "net": 8.99999999999997, "choice": "VERIFY" } }, { "family": "full-21", "draft": "low", "bonus_action": "CALL", "bonus_chip_equivalent": 6.6, "fee": 16.8, "chip_gross": 31.5, "utility_gross": 33.15, "chip_net": 14.7, "utility_net": 16.349999999999998, "chip_choice": "VERIFY", "utility_choice": "VERIFY", "final_actions_unchanged": true, "chip": { "posterior_high": 0.25, "p_bluff": 0.17500000000000002, "call_chips": -63.0, "unchecked_action": "FOLD", "verified_low_action": "FOLD", "verified_high_action": "CALL", "unchecked_utility": 0, "verified_utility": 31.5, "gross": 31.5, "net": 14.7, "choice": "VERIFY" }, "utility": { "posterior_high": 0.25, "p_bluff": 0.17500000000000002, "call_chips": -63.0, "unchecked_action": "FOLD", "verified_low_action": "FOLD", "verified_high_action": "CALL", "unchecked_utility": 0, "verified_utility": 33.15, "gross": 33.15, "net": 16.349999999999998, "choice": "VERIFY" } }, { "family": "full-21", "draft": "low", "bonus_action": "FOLD", "bonus_chip_equivalent": 6.6, "fee": 16.8, "chip_gross": 31.5, "utility_gross": 29.85, "chip_net": 14.7, "utility_net": 13.05, "chip_choice": "VERIFY", "utility_choice": "VERIFY", "final_actions_unchanged": true, "chip": { "posterior_high": 0.25, "p_bluff": 0.17500000000000002, "call_chips": -63.0, "unchecked_action": "FOLD", "verified_low_action": "FOLD", "verified_high_action": "CALL", "unchecked_utility": 0.0, "verified_utility": 31.5, "gross": 31.5, "net": 14.7, "choice": "VERIFY" }, "utility": { "posterior_high": 0.25, "p_bluff": 0.17500000000000002, "call_chips": -63.0, "unchecked_action": "FOLD", "verified_low_action": "FOLD", "verified_high_action": "CALL", "unchecked_utility": 6.6, "verified_utility": 36.45, "gross": 29.85, "net": 13.05, "choice": "VERIFY" } }, { "family": "full-21", "draft": "high", "bonus_action": "CALL", "bonus_chip_equivalent": 6.6, "fee": 16.8, "chip_gross": 31.499999999999943, "utility_gross": 29.849999999999937, "chip_net": 14.699999999999942, "utility_net": 13.049999999999937, "chip_choice": "VERIFY", "utility_choice": "VERIFY", "final_actions_unchanged": true, "chip": { "posterior_high": 0.75, "p_bluff": 0.32500000000000007, "call_chips": 63.00000000000006, "unchecked_action": "CALL", "verified_low_action": "FOLD", "verified_high_action": "CALL", "unchecked_utility": 63.00000000000006, "verified_utility": 94.5, "gross": 31.499999999999943, "net": 14.699999999999942, "choice": "VERIFY" }, "utility": { "posterior_high": 0.75, "p_bluff": 0.32500000000000007, "call_chips": 63.00000000000006, "unchecked_action": "CALL", "verified_low_action": "FOLD", "verified_high_action": "CALL", "unchecked_utility": 69.60000000000005, "verified_utility": 99.44999999999999, "gross": 29.849999999999937, "net": 13.049999999999937, "choice": "VERIFY" } }, { "family": "full-21", "draft": "high", "bonus_action": "FOLD", "bonus_chip_equivalent": 6.6, "fee": 16.8, "chip_gross": 31.499999999999943, "utility_gross": 33.14999999999995, "chip_net": 14.699999999999942, "utility_net": 16.349999999999948, "chip_choice": "VERIFY", "utility_choice": "VERIFY", "final_actions_unchanged": true, "chip": { "posterior_high": 0.75, "p_bluff": 0.32500000000000007, "call_chips": 63.00000000000006, "unchecked_action": "CALL", "verified_low_action": "FOLD", "verified_high_action": "CALL", "unchecked_utility": 63.00000000000006, "verified_utility": 94.5, "gross": 31.499999999999943, "net": 14.699999999999942, "choice": "VERIFY" }, "utility": { "posterior_high": 0.75, "p_bluff": 0.32500000000000007, "call_chips": 63.00000000000006, "unchecked_action": "CALL", "verified_low_action": "FOLD", "verified_high_action": "CALL", "unchecked_utility": 63.00000000000006, "verified_utility": 96.15, "gross": 33.14999999999995, "net": 16.349999999999948, "choice": "VERIFY" } }, { "family": "full-22", "draft": "low", "bonus_action": "CALL", "bonus_chip_equivalent": 6.6, "fee": 10.5, "chip_gross": 19.6875, "utility_gross": 21.3375, "chip_net": 9.1875, "utility_net": 10.837499999999999, "chip_choice": "VERIFY", "utility_choice": "VERIFY", "final_actions_unchanged": true, "chip": { "posterior_high": 0.25, "p_bluff": 0.1625, "call_chips": -39.375, "unchecked_action": "FOLD", "verified_low_action": "FOLD", "verified_high_action": "CALL", "unchecked_utility": 0, "verified_utility": 19.6875, "gross": 19.6875, "net": 9.1875, "choice": "VERIFY" }, "utility": { "posterior_high": 0.25, "p_bluff": 0.1625, "call_chips": -39.375, "unchecked_action": "FOLD", "verified_low_action": "FOLD", "verified_high_action": "CALL", "unchecked_utility": 0, "verified_utility": 21.3375, "gross": 21.3375, "net": 10.837499999999999, "choice": "VERIFY" } }, { "family": "full-22", "draft": "low", "bonus_action": "FOLD", "bonus_chip_equivalent": 6.6, "fee": 10.5, "chip_gross": 19.6875, "utility_gross": 18.0375, "chip_net": 9.1875, "utility_net": 7.537500000000001, "chip_choice": "VERIFY", "utility_choice": "VERIFY", "final_actions_unchanged": true, "chip": { "posterior_high": 0.25, "p_bluff": 0.1625, "call_chips": -39.375, "unchecked_action": "FOLD", "verified_low_action": "FOLD", "verified_high_action": "CALL", "unchecked_utility": 0.0, "verified_utility": 19.6875, "gross": 19.6875, "net": 9.1875, "choice": "VERIFY" }, "utility": { "posterior_high": 0.25, "p_bluff": 0.1625, "call_chips": -39.375, "unchecked_action": "FOLD", "verified_low_action": "FOLD", "verified_high_action": "CALL", "unchecked_utility": 6.6, "verified_utility": 24.6375, "gross": 18.0375, "net": 7.537500000000001, "choice": "VERIFY" } }, { "family": "full-22", "draft": "high", "bonus_action": "CALL", "bonus_chip_equivalent": 6.6, "fee": 10.5, "chip_gross": 19.68749999999997, "utility_gross": 18.03749999999996, "chip_net": 9.187499999999972, "utility_net": 7.537499999999959, "chip_choice": "VERIFY", "utility_choice": "VERIFY", "final_actions_unchanged": true, "chip": { "posterior_high": 0.75, "p_bluff": 0.23750000000000002, "call_chips": 39.37500000000003, "unchecked_action": "CALL", "verified_low_action": "FOLD", "verified_high_action": "CALL", "unchecked_utility": 39.37500000000003, "verified_utility": 59.0625, "gross": 19.68749999999997, "net": 9.187499999999972, "choice": "VERIFY" }, "utility": { "posterior_high": 0.75, "p_bluff": 0.23750000000000002, "call_chips": 39.37500000000003, "unchecked_action": "CALL", "verified_low_action": "FOLD", "verified_high_action": "CALL", "unchecked_utility": 45.97500000000003, "verified_utility": 64.01249999999999, "gross": 18.03749999999996, "net": 7.537499999999959, "choice": "VERIFY" } }, { "family": "full-22", "draft": "high", "bonus_action": "FOLD", "bonus_chip_equivalent": 6.6, "fee": 10.5, "chip_gross": 19.68749999999997, "utility_gross": 21.33749999999997, "chip_net": 9.187499999999972, "utility_net": 10.83749999999997, "chip_choice": "VERIFY", "utility_choice": "VERIFY", "final_actions_unchanged": true, "chip": { "posterior_high": 0.75, "p_bluff": 0.23750000000000002, "call_chips": 39.37500000000003, "unchecked_action": "CALL", "verified_low_action": "FOLD", "verified_high_action": "CALL", "unchecked_utility": 39.37500000000003, "verified_utility": 59.0625, "gross": 19.68749999999997, "net": 9.187499999999972, "choice": "VERIFY" }, "utility": { "posterior_high": 0.75, "p_bluff": 0.23750000000000002, "call_chips": 39.37500000000003, "unchecked_action": "CALL", "verified_low_action": "FOLD", "verified_high_action": "CALL", "unchecked_utility": 39.37500000000003, "verified_utility": 60.7125, "gross": 21.33749999999997, "net": 10.83749999999997, "choice": "VERIFY" } }, { "family": "full-23", "draft": "low", "bonus_action": "CALL", "bonus_chip_equivalent": 6.6, "fee": 21.0, "chip_gross": 39.375, "utility_gross": 41.025, "chip_net": 18.375, "utility_net": 20.025, "chip_choice": "VERIFY", "utility_choice": "VERIFY", "final_actions_unchanged": true, "chip": { "posterior_high": 0.25, "p_bluff": 0.125, "call_chips": -78.75, "unchecked_action": "FOLD", "verified_low_action": "FOLD", "verified_high_action": "CALL", "unchecked_utility": 0, "verified_utility": 39.375, "gross": 39.375, "net": 18.375, "choice": "VERIFY" }, "utility": { "posterior_high": 0.25, "p_bluff": 0.125, "call_chips": -78.75, "unchecked_action": "FOLD", "verified_low_action": "FOLD", "verified_high_action": "CALL", "unchecked_utility": 0, "verified_utility": 41.025, "gross": 41.025, "net": 20.025, "choice": "VERIFY" } }, { "family": "full-23", "draft": "low", "bonus_action": "FOLD", "bonus_chip_equivalent": 6.6, "fee": 21.0, "chip_gross": 39.375, "utility_gross": 37.725, "chip_net": 18.375, "utility_net": 16.725, "chip_choice": "VERIFY", "utility_choice": "VERIFY", "final_actions_unchanged": true, "chip": { "posterior_high": 0.25, "p_bluff": 0.125, "call_chips": -78.75, "unchecked_action": "FOLD", "verified_low_action": "FOLD", "verified_high_action": "CALL", "unchecked_utility": 0.0, "verified_utility": 39.375, "gross": 39.375, "net": 18.375, "choice": "VERIFY" }, "utility": { "posterior_high": 0.25, "p_bluff": 0.125, "call_chips": -78.75, "unchecked_action": "FOLD", "verified_low_action": "FOLD", "verified_high_action": "CALL", "unchecked_utility": 6.6, "verified_utility": 44.325, "gross": 37.725, "net": 16.725, "choice": "VERIFY" } }, { "family": "full-23", "draft": "high", "bonus_action": "CALL", "bonus_chip_equivalent": 6.6, "fee": 21.0, "chip_gross": 39.37500000000006, "utility_gross": 37.72500000000005, "chip_net": 18.375000000000057, "utility_net": 16.72500000000005, "chip_choice": "VERIFY", "utility_choice": "VERIFY", "final_actions_unchanged": true, "chip": { "posterior_high": 0.75, "p_bluff": 0.27499999999999997, "call_chips": 78.74999999999994, "unchecked_action": "CALL", "verified_low_action": "FOLD", "verified_high_action": "CALL", "unchecked_utility": 78.74999999999994, "verified_utility": 118.125, "gross": 39.37500000000006, "net": 18.375000000000057, "choice": "VERIFY" }, "utility": { "posterior_high": 0.75, "p_bluff": 0.27499999999999997, "call_chips": 78.74999999999994, "unchecked_action": "CALL", "verified_low_action": "FOLD", "verified_high_action": "CALL", "unchecked_utility": 85.34999999999994, "verified_utility": 123.07499999999999, "gross": 37.72500000000005, "net": 16.72500000000005, "choice": "VERIFY" } }, { "family": "full-23", "draft": "high", "bonus_action": "FOLD", "bonus_chip_equivalent": 6.6, "fee": 21.0, "chip_gross": 39.37500000000006, "utility_gross": 41.02500000000006, "chip_net": 18.375000000000057, "utility_net": 20.025000000000063, "chip_choice": "VERIFY", "utility_choice": "VERIFY", "final_actions_unchanged": true, "chip": { "posterior_high": 0.75, "p_bluff": 0.27499999999999997, "call_chips": 78.74999999999994, "unchecked_action": "CALL", "verified_low_action": "FOLD", "verified_high_action": "CALL", "unchecked_utility": 78.74999999999994, "verified_utility": 118.125, "gross": 39.37500000000006, "net": 18.375000000000057, "choice": "VERIFY" }, "utility": { "posterior_high": 0.75, "p_bluff": 0.27499999999999997, "call_chips": 78.74999999999994, "unchecked_action": "CALL", "verified_low_action": "FOLD", "verified_high_action": "CALL", "unchecked_utility": 78.74999999999994, "verified_utility": 119.775, "gross": 41.02500000000006, "net": 20.025000000000063, "choice": "VERIFY" } } ], "all_checked_action_policies_unchanged": true, "caveat": "A checking difference can coexist with chip-optimal final actions. This construction alone neither identifies an actual bonus value nor establishes a model objective." }