{ "generated_unix_seconds": 1788565709, "engine": { "repository": "https://github.com/b-inary/postflop-solver", "commit": "9d1509fe5077d019825f833eed04b16d342dfda1", "crate_version": "0.1.0", "license": "AGPL-3.0-or-later", "cargo_features": "default-features = false (sequential; no bincode, rayon, zstd, or custom allocator)", "numeric_precision": "mostly f32 internally; f64 for selected summations, per upstream README", "algorithm": "Discounted CFR; gamma=3.0 and cumulative-strategy reset at powers of four, per upstream README/source", "rustc_version": "rustc 1.85.0 (4d91de4e4 2025-02-17)", "source_git_head_verified": "9d1509fe5077d019825f833eed04b16d342dfda1", "source_git_worktree_clean": true }, "config": { "question": "When must same-rank suit combinations map under a true hearts/spades relabel, and how can board/runout structure or exact-combination range weights break their within-spot equivalence?", "suit_permutation": "hearts <-> spades; clubs and diamonds fixed", "positions": [ "OOP", "IP" ], "game": "heads-up no-limit Texas Hold'em chip-EV postflop game", "street": "flop; every legal turn/river runout is evaluated exactly, with lossless isomorphic chance grouping where board and ranges permit", "starting_pot_chips": 100, "effective_stack_behind_chips": 100, "rake_rate": 0.0, "rake_cap_chips": 0.0, "flop_bet_sizes": [ "OOP: none (check only)", "IP: 75% pot" ], "flop_raise_sizes": [ "none", "none" ], "turn_bet_sizes": [ "none (check only)", "none (check only)" ], "river_bet_sizes": [ "none (check only)", "none (check only)" ], "add_allin_threshold": 0.0, "force_allin_threshold": 0.0, "merging_threshold": 0.0, "chance_model": "standard 52-card deck without replacement; all legal runouts evaluated exactly, with lossless range-aware isomorphic chance grouping", "ev_convention": "expected_values_detail/action EV and expected_values/mixed EV use the engine's node-relative chip-EV convention; fold is set to 0 where available; values are not equity, and cross-hand comparisons in this experiment are only made within the same node and scenario", "exploitability_definition": "global full-toy-game exploitability in chips, not a per-hand EV error bound", "exploitability_check_interval_iterations": 10, "range_interpretation": "each listed physical two-card combination has the stated independent initial weight; omitted combinations have weight zero", "compatible_reach_mass_definition": "the engine's current-node weighted legal-matchup mass for the focal hand: its own reach weight multiplied by the summed compatible opponent reach after card-collision removal; it is not a probability and can exceed 1", "scenarios": [ { "id": "symmetric", "purpose": "Board and both exact-combination ranges are invariant under hearts/spades exchange.", "oop_range": "AhJh:1,AsJs:1", "ip_range": "KhQh:1,KsQs:1,Ah5h:1,As5s:1", "flop": "Qc7h7s" }, { "id": "asymmetric", "purpose": "Only the IP bluff-candidate weights break hearts/spades exchangeability.", "oop_range": "AhJh:1,AsJs:1", "ip_range": "KhQh:1,KsQs:1,Ah5h:1,As5s:0.2", "flop": "Qc7h7s" }, { "id": "asymmetric_relabelled", "purpose": "Global hearts/spades relabel of the asymmetric scenario; the 1.0 and 0.2 weights move with their physical combinations.", "oop_range": "AsJs:1,AhJh:1", "ip_range": "KsQs:1,KhQh:1,As5s:1,Ah5h:0.2", "flop": "Qc7s7h" }, { "id": "board_asymmetric", "purpose": "Ranges are hearts/spades symmetric, but Qc7h2d breaks hearts/spades symmetry across future-card and blocker relationships; in particular Ah5h has a runner-runner heart-flush path while As5s cannot make a spade flush by the river.", "oop_range": "AhJh:1,AsJs:1", "ip_range": "KhQh:1,KsQs:1,Ah5h:1,As5s:1", "flop": "Qc7h2d" }, { "id": "board_asymmetric_relabelled", "purpose": "Global hearts/spades relabel of the board-asymmetric scenario.", "oop_range": "AsJs:1,AhJh:1", "ip_range": "KsQs:1,KhQh:1,As5s:1,Ah5h:1", "flop": "Qc7s2d" } ], "convergence_runs": [ { "id": "baseline", "target_exploitability_chips": 0.1, "max_iterations": 5000 }, { "id": "middle", "target_exploitability_chips": 0.01, "max_iterations": 10000 }, { "id": "tight", "target_exploitability_chips": 0.001, "max_iterations": 50000 } ] }, "results": [ { "scenario_id": "symmetric", "convergence_id": "baseline", "target_exploitability_chips": 0.1, "target_exploitability_pct_starting_pot": 0.1, "achieved_exploitability_chips": 0.07953644, "achieved_exploitability_pct_starting_pot": 0.07953644, "iterations": 50, "max_iterations": 5000, "runtime_ms": 30, "memory_uncompressed_bytes": 978928, "memory_compressed_bytes": 881724, "nodes": [ { "path": [], "acting_player": "OOP", "hands": [ { "hand": "AhJh", "compatible_reach_mass": 3.0, "mixed_ev_chips": 6.369133, "actions": [ { "action": "check", "strategy": 1.0, "action_ev_chips": 6.369133 } ] }, { "hand": "AsJs", "compatible_reach_mass": 3.0, "mixed_ev_chips": 6.369133, "actions": [ { "action": "check", "strategy": 1.0, "action_ev_chips": 6.369133 } ] } ] }, { "path": [ "check" ], "acting_player": "IP", "hands": [ { "hand": "Ah5h", "compatible_reach_mass": 1.0, "mixed_ev_chips": 33.066254, "actions": [ { "action": "check", "strategy": 0.26775664, "action_ev_chips": 32.979797 }, { "action": "bet_75", "strategy": 0.7322433, "action_ev_chips": 33.09787 } ] }, { "hand": "As5s", "compatible_reach_mass": 1.0, "mixed_ev_chips": 33.066254, "actions": [ { "action": "check", "strategy": 0.26775664, "action_ev_chips": 32.979797 }, { "action": "bet_75", "strategy": 0.7322433, "action_ev_chips": 33.09787 } ] }, { "hand": "KhQh", "compatible_reach_mass": 2.0, "mixed_ev_chips": 123.91319, "actions": [ { "action": "check", "strategy": 0.0, "action_ev_chips": 83.23232 }, { "action": "bet_75", "strategy": 1.0, "action_ev_chips": 123.91319 } ] }, { "hand": "KsQs", "compatible_reach_mass": 2.0, "mixed_ev_chips": 123.91319, "actions": [ { "action": "check", "strategy": 0.0, "action_ev_chips": 83.23232 }, { "action": "bet_75", "strategy": 1.0, "action_ev_chips": 123.91319 } ] } ] }, { "path": [ "check", "bet_75" ], "acting_player": "OOP", "hands": [ { "hand": "AhJh", "compatible_reach_mass": 2.7322433, "mixed_ev_chips": 0.42539406, "actions": [ { "action": "fold", "strategy": 0.27712846, "action_ev_chips": 0.0 }, { "action": "call", "strategy": 0.72287154, "action_ev_chips": 0.5884781 } ] }, { "hand": "AsJs", "compatible_reach_mass": 2.7322433, "mixed_ev_chips": 0.42539406, "actions": [ { "action": "fold", "strategy": 0.27712846, "action_ev_chips": 0.0 }, { "action": "call", "strategy": 0.72287154, "action_ev_chips": 0.5884781 } ] } ] } ] }, { "scenario_id": "symmetric", "convergence_id": "middle", "target_exploitability_chips": 0.01, "target_exploitability_pct_starting_pot": 0.01, "achieved_exploitability_chips": 0.009346008, "achieved_exploitability_pct_starting_pot": 0.009346008, "iterations": 510, "max_iterations": 10000, "runtime_ms": 257, "memory_uncompressed_bytes": 978928, "memory_compressed_bytes": 881724, "nodes": [ { "path": [], "acting_player": "OOP", "hands": [ { "hand": "AhJh", "compatible_reach_mass": 3.0, "mixed_ev_chips": 6.369808, "actions": [ { "action": "check", "strategy": 1.0, "action_ev_chips": 6.369808 } ] }, { "hand": "AsJs", "compatible_reach_mass": 3.0, "mixed_ev_chips": 6.369808, "actions": [ { "action": "check", "strategy": 1.0, "action_ev_chips": 6.369808 } ] } ] }, { "path": [ "check" ], "acting_player": "IP", "hands": [ { "hand": "Ah5h", "compatible_reach_mass": 1.0, "mixed_ev_chips": 32.985195, "actions": [ { "action": "check", "strategy": 0.2830175, "action_ev_chips": 32.979797 }, { "action": "bet_75", "strategy": 0.7169825, "action_ev_chips": 32.987328 } ] }, { "hand": "As5s", "compatible_reach_mass": 1.0, "mixed_ev_chips": 32.985195, "actions": [ { "action": "check", "strategy": 0.2830175, "action_ev_chips": 32.979797 }, { "action": "bet_75", "strategy": 0.7169825, "action_ev_chips": 32.987328 } ] }, { "hand": "KhQh", "compatible_reach_mass": 2.0, "mixed_ev_chips": 123.9527, "actions": [ { "action": "check", "strategy": 0.0, "action_ev_chips": 83.23232 }, { "action": "bet_75", "strategy": 1.0, "action_ev_chips": 123.9527 } ] }, { "hand": "KsQs", "compatible_reach_mass": 2.0, "mixed_ev_chips": 123.9527, "actions": [ { "action": "check", "strategy": 0.0, "action_ev_chips": 83.23232 }, { "action": "bet_75", "strategy": 1.0, "action_ev_chips": 123.9527 } ] } ] }, { "path": [ "check", "bet_75" ], "acting_player": "OOP", "hands": [ { "hand": "AhJh", "compatible_reach_mass": 2.7169824, "mixed_ev_chips": 0.052087538, "actions": [ { "action": "fold", "strategy": 0.27593404, "action_ev_chips": 0.0 }, { "action": "call", "strategy": 0.72406596, "action_ev_chips": 0.07193756 } ] }, { "hand": "AsJs", "compatible_reach_mass": 2.7169824, "mixed_ev_chips": 0.052087538, "actions": [ { "action": "fold", "strategy": 0.27593404, "action_ev_chips": 0.0 }, { "action": "call", "strategy": 0.72406596, "action_ev_chips": 0.07193756 } ] } ] } ] }, { "scenario_id": "symmetric", "convergence_id": "tight", "target_exploitability_chips": 0.001, "target_exploitability_pct_starting_pot": 0.001, "achieved_exploitability_chips": 0.0009918213, "achieved_exploitability_pct_starting_pot": 0.0009918213, "iterations": 3690, "max_iterations": 50000, "runtime_ms": 2135, "memory_uncompressed_bytes": 978928, "memory_compressed_bytes": 881724, "nodes": [ { "path": [], "acting_player": "OOP", "hands": [ { "hand": "AhJh", "compatible_reach_mass": 3.0, "mixed_ev_chips": 6.369816, "actions": [ { "action": "check", "strategy": 1.0, "action_ev_chips": 6.369816 } ] }, { "hand": "AsJs", "compatible_reach_mass": 3.0, "mixed_ev_chips": 6.369816, "actions": [ { "action": "check", "strategy": 1.0, "action_ev_chips": 6.369816 } ] } ] }, { "path": [ "check" ], "acting_player": "IP", "hands": [ { "hand": "Ah5h", "compatible_reach_mass": 1.0, "mixed_ev_chips": 32.979393, "actions": [ { "action": "check", "strategy": 0.28491208, "action_ev_chips": 32.979797 }, { "action": "bet_75", "strategy": 0.7150879, "action_ev_chips": 32.979233 } ] }, { "hand": "As5s", "compatible_reach_mass": 1.0, "mixed_ev_chips": 32.979393, "actions": [ { "action": "check", "strategy": 0.28491208, "action_ev_chips": 32.979797 }, { "action": "bet_75", "strategy": 0.7150879, "action_ev_chips": 32.979233 } ] }, { "hand": "KhQh", "compatible_reach_mass": 2.0, "mixed_ev_chips": 123.95558, "actions": [ { "action": "check", "strategy": 0.0, "action_ev_chips": 83.23232 }, { "action": "bet_75", "strategy": 1.0, "action_ev_chips": 123.95558 } ] }, { "hand": "KsQs", "compatible_reach_mass": 2.0, "mixed_ev_chips": 123.95558, "actions": [ { "action": "check", "strategy": 0.0, "action_ev_chips": 83.23232 }, { "action": "bet_75", "strategy": 1.0, "action_ev_chips": 123.95558 } ] } ] }, { "path": [ "check", "bet_75" ], "acting_player": "OOP", "hands": [ { "hand": "AhJh", "compatible_reach_mass": 2.715088, "mixed_ev_chips": 0.0053701564, "actions": [ { "action": "fold", "strategy": 0.27584654, "action_ev_chips": 0.0 }, { 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6.369129, "actions": [ { "action": "check", "strategy": 1.0, "action_ev_chips": 6.369129 } ] } ] }, { "path": [ "check" ], "acting_player": "IP", "hands": [ { "hand": "Ah5h", "compatible_reach_mass": 1.0, "mixed_ev_chips": 33.066246, "actions": [ { "action": "check", "strategy": 0.26775667, "action_ev_chips": 32.979797 }, { "action": "bet_75", "strategy": 0.7322433, "action_ev_chips": 33.097862 } ] }, { "hand": "As5s", "compatible_reach_mass": 0.2, "mixed_ev_chips": 100.0, "actions": [ { "action": "check", "strategy": 0.0, "action_ev_chips": 32.979797 }, { "action": "bet_75", "strategy": 1.0, "action_ev_chips": 100.0 } ] }, { "hand": "KhQh", "compatible_reach_mass": 2.0, "mixed_ev_chips": 112.04787, "actions": [ { "action": "check", "strategy": 0.0, "action_ev_chips": 83.23232 }, { "action": "bet_75", "strategy": 1.0, "action_ev_chips": 112.04787 } ] }, { "hand": "KsQs", "compatible_reach_mass": 2.0, "mixed_ev_chips": 111.86532, "actions": [ { "action": "check", "strategy": 0.0, "action_ev_chips": 83.23232 }, { "action": "bet_75", "strategy": 1.0, "action_ev_chips": 111.86532 } ] } ] }, { "path": [ "check", "bet_75" ], "acting_player": "OOP", "hands": [ { "hand": "AhJh", "compatible_reach_mass": 2.2, "mixed_ev_chips": 0.0, "actions": [ { "action": "fold", "strategy": 1.0, "action_ev_chips": 0.0 }, { "action": "call", "strategy": 0.0, "action_ev_chips": -21.659782 } ] }, { "hand": "AsJs", "compatible_reach_mass": 2.7322433, "mixed_ev_chips": 0.42539692, "actions": [ { "action": "fold", "strategy": 0.27712834, "action_ev_chips": 0.0 }, { "action": "call", "strategy": 0.7228717, "action_ev_chips": 0.5884819 } ] } ] } ] }, { "scenario_id": "asymmetric", "convergence_id": "middle", "target_exploitability_chips": 0.01, "target_exploitability_pct_starting_pot": 0.01, "achieved_exploitability_chips": 0.009199142, "achieved_exploitability_pct_starting_pot": 0.009199142, "iterations": 220, "max_iterations": 10000, "runtime_ms": 161, "memory_uncompressed_bytes": 1433216, "memory_compressed_bytes": 1279084, "nodes": [ { "path": [], "acting_player": "OOP", "hands": [ { "hand": "AhJh", "compatible_reach_mass": 2.2, "mixed_ev_chips": 0.0, "actions": [ { "action": "check", "strategy": 1.0, "action_ev_chips": 0.0 } ] }, { "hand": "AsJs", "compatible_reach_mass": 3.0, "mixed_ev_chips": 6.3698235, "actions": [ { "action": "check", "strategy": 1.0, "action_ev_chips": 6.3698235 } ] } ] }, { "path": [ "check" ], "acting_player": "IP", "hands": [ { "hand": "Ah5h", "compatible_reach_mass": 1.0, "mixed_ev_chips": 32.97174, "actions": [ { "action": "check", "strategy": 0.28169608, "action_ev_chips": 32.979797 }, { "action": "bet_75", "strategy": 0.718304, "action_ev_chips": 32.96858 } ] }, { "hand": "As5s", "compatible_reach_mass": 0.2, "mixed_ev_chips": 100.0, "actions": [ { "action": "check", "strategy": 0.0, "action_ev_chips": 32.979797 }, { "action": "bet_75", "strategy": 1.0, "action_ev_chips": 100.0 } ] }, { "hand": "KhQh", "compatible_reach_mass": 2.0, "mixed_ev_chips": 112.07114, "actions": [ { "action": "check", "strategy": 0.0, "action_ev_chips": 83.23232 }, { "action": "bet_75", "strategy": 1.0, "action_ev_chips": 112.07114 } ] }, { "hand": "KsQs", "compatible_reach_mass": 2.0, "mixed_ev_chips": 111.888245, "actions": [ { "action": "check", "strategy": 0.0, "action_ev_chips": 83.23232 }, { "action": "bet_75", "strategy": 1.0, "action_ev_chips": 111.888245 } ] } ] }, { "path": [ "check", "bet_75" ], "acting_player": "OOP", "hands": [ { "hand": "AhJh", "compatible_reach_mass": 2.2, "mixed_ev_chips": 0.0, "actions": [ { "action": "fold", "strategy": 1.0, "action_ev_chips": 0.0 }, { "action": "call", "strategy": 0.0, "action_ev_chips": -21.659782 } ] }, { "hand": "AsJs", "compatible_reach_mass": 2.718304, "mixed_ev_chips": 0.08467077, "actions": [ { "action": "fold", "strategy": 0.27573144, "action_ev_chips": 0.0 }, { "action": "call", "strategy": 0.72426856, "action_ev_chips": 0.11690521 } ] } ] } ] }, { "scenario_id": "asymmetric", "convergence_id": "tight", "target_exploitability_chips": 0.001, "target_exploitability_pct_starting_pot": 0.001, "achieved_exploitability_chips": 0.0009822845, "achieved_exploitability_pct_starting_pot": 0.0009822845, "iterations": 2590, "max_iterations": 50000, "runtime_ms": 2152, "memory_uncompressed_bytes": 1433216, "memory_compressed_bytes": 1279084, "nodes": [ { "path": [], "acting_player": "OOP", "hands": [ { "hand": "AhJh", "compatible_reach_mass": 2.2, "mixed_ev_chips": 0.0, "actions": [ { "action": "check", "strategy": 1.0, "action_ev_chips": 0.0 } ] }, { "hand": "AsJs", "compatible_reach_mass": 3.0, "mixed_ev_chips": 6.369816, "actions": [ { "action": "check", "strategy": 1.0, "action_ev_chips": 6.369816 } ] } ] }, { "path": [ "check" ], "acting_player": "IP", "hands": [ { "hand": "Ah5h", "compatible_reach_mass": 1.0, "mixed_ev_chips": 33.002586, "actions": [ { "action": "check", "strategy": 0.2851462, "action_ev_chips": 32.979797 }, { "action": "bet_75", "strategy": 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