{
  "engine_version": "0.16.0",
  "rules": "stud-high-uniform-showdown-v1",
  "study": "Remembering folded hearts",
  "total_sampled_showdowns": 1100000,
  "total_exact_completions": 2964,
  "main_results": [
    {
      "label": "Five active; 0 folded hearts",
      "active_players": 5,
      "known_folded_hearts": 0,
      "samples": 200000,
      "seeds": [
        "2026100511",
        "2026100512"
      ],
      "unseen_identities": 42,
      "unseen_hearts": 10,
      "flush_completion_exact": 0.2355936746180649,
      "flush_completion_sampled": 0.23488,
      "equity": 0.3700675,
      "equity_ci_low": 0.36795157373743714,
      "equity_ci_high": 0.37218342626256284,
      "outright_win": 0.370005,
      "tied_win": 0.000125,
      "per_seed_equity": [
        0.36988,
        0.370255
      ]
    },
    {
      "label": "Five active; 1 folded hearts",
      "active_players": 5,
      "known_folded_hearts": 1,
      "samples": 200000,
      "seeds": [
        "2026100521",
        "2026100522"
      ],
      "unseen_identities": 42,
      "unseen_hearts": 9,
      "flush_completion_exact": 0.19571160546770305,
      "flush_completion_sampled": 0.19609,
      "equity": 0.3385525,
      "equity_ci_low": 0.33647868442423795,
      "equity_ci_high": 0.340626315575762,
      "outright_win": 0.338485,
      "tied_win": 0.000135,
      "per_seed_equity": [
        0.33862,
        0.338485
      ]
    },
    {
      "label": "Five active; 2 folded hearts",
      "active_players": 5,
      "known_folded_hearts": 2,
      "samples": 200000,
      "seeds": [
        "2026100531",
        "2026100532"
      ],
      "unseen_identities": 42,
      "unseen_hearts": 8,
      "flush_completion_exact": 0.15797373358348965,
      "flush_completion_sampled": 0.158345,
      "equity": 0.308925,
      "equity_ci_low": 0.30690014871290044,
      "equity_ci_high": 0.31094985128709957,
      "outright_win": 0.30885,
      "tied_win": 0.00015,
      "per_seed_equity": [
        0.309305,
        0.308545
      ]
    },
    {
      "label": "Five active; 3 folded hearts",
      "active_players": 5,
      "known_folded_hearts": 3,
      "samples": 200000,
      "seeds": [
        "2026100541",
        "2026100542"
      ],
      "unseen_identities": 42,
      "unseen_hearts": 7,
      "flush_completion_exact": 0.12288930581613511,
      "flush_completion_sampled": 0.123235,
      "equity": 0.2814825,
      "equity_ci_low": 0.2795116892344995,
      "equity_ci_high": 0.28345331076550057,
      "outright_win": 0.281405,
      "tied_win": 0.000155,
      "per_seed_equity": [
        0.279635,
        0.28333
      ]
    }
  ],
  "controls": [
    {
      "label": "Five active; non-heart diamond control",
      "active_players": 5,
      "known_folded_hearts": 0,
      "samples": 100000,
      "seeds": [
        "2026100551"
      ],
      "unseen_identities": 42,
      "unseen_hearts": 10,
      "flush_completion_exact": 0.2355936746180649,
      "flush_completion_sampled": 0.23643,
      "equity": 0.37165,
      "equity_ci_low": 0.3686550224349177,
      "equity_ci_high": 0.37464497756508225,
      "outright_win": 0.37158,
      "tied_win": 0.00014,
      "per_seed_equity": [
        0.37165
      ]
    },
    {
      "label": "Two active; 0 folded hearts",
      "active_players": 2,
      "known_folded_hearts": 0,
      "samples": 100000,
      "seeds": [
        "2026100561"
      ],
      "unseen_identities": 42,
      "unseen_hearts": 10,
      "flush_completion_exact": 0.2355936746180649,
      "flush_completion_sampled": 0.23516,
      "equity": 0.636635,
      "equity_ci_low": 0.6336542808100967,
      "equity_ci_high": 0.6396157191899032,
      "outright_win": 0.63652,
      "tied_win": 0.00023,
      "per_seed_equity": [
        0.636635
      ]
    },
    {
      "label": "Two active; 3 folded hearts",
      "active_players": 2,
      "known_folded_hearts": 3,
      "samples": 100000,
      "seeds": [
        "2026100571"
      ],
      "unseen_identities": 42,
      "unseen_hearts": 7,
      "flush_completion_exact": 0.12288930581613511,
      "flush_completion_sampled": 0.12376,
      "equity": 0.576115,
      "equity_ci_low": 0.5730524321170808,
      "equity_ci_high": 0.5791775678829193,
      "outright_win": 0.576,
      "tied_win": 0.00023,
      "per_seed_equity": [
        0.576115
      ]
    }
  ],
  "known_matchup_checks": {
    "sixth_live_exact": {
      "equity": 0.2496626180836707,
      "exact_equity": {
        "numerator": "185",
        "denominator": "741"
      },
      "completions": 1482
    },
    "sixth_dead_exact": {
      "equity": 0.22941970310391363,
      "exact_equity": {
        "numerator": "170",
        "denominator": "741"
      },
      "completions": 1482
    }
  },
  "interpretation": "Uniform forced-showdown equity; all current active players continue. Current third-street exposed information only. No range inference, betting, future folds or rake. Changes in discarded suits affect both hero and opponents; deals across variants are not paired. Exact flush probabilities integrate unknown folded/burn identities.",
  "validation": "Every report and retained trace audited for distinct legal cards, retained known cards, excluded folded cards, visibility and conservation; every third-street flush frequency agrees with independent hypergeometric calculation within six standard errors."
}