{
  "schemaVersion": 1,
  "studyVersion": "1.0.0",
  "published": "2026-09-04",
  "generatedBy": "public/data/short-deck-equity/short-deck-equity-generator.mjs",
  "evidenceStatus": "Exact exhaustive enumeration of fixed, collision-free heads-up all-in matchups; not solver output, opening ranges, action advice, or population data.",
  "rules": {
    "standardHoldem": "52 cards (2 through ace); A-2-3-4-5 is the lowest straight; standard category order with full house above flush and straight above trips.",
    "shortDeckOfficial": "36 cards (6 through ace); A-6-7-8-9 is the lowest straight; flush above full house; straight above trips.",
    "shortDeckDeckOnlyCounterfactual": "The 36-card deck with only ordinary consecutive straights (10-J-Q-K-A through 6-7-8-9-10) and standard category order. Comparing this with standard Hold’em isolates removal of ranks 2 through 5 for the fixed cards.",
    "shortDeckLowStraightCounterfactual": "The same 36-card deck plus A-6-7-8-9 as the low straight, but standard category order with full house above flush. Comparing this with the deck-only counterfactual isolates the low-straight convention; comparing it with the official profile isolates the flush/full-house order swap."
  },
  "sampleSpaces": {
    "standardBoardsPerMatchup": 1712304,
    "shortDeckBoardsPerMatchup": 201376,
    "formula": "C(48,5) standard boards and C(32,5) short-deck boards after four fixed hole cards."
  },
  "matchupCount": 12,
  "matchups": [
    {
      "id": "aa-vs-kk",
      "hero": [
        "As",
        "Ah"
      ],
      "villain": [
        "Kc",
        "Kd"
      ],
      "label": "A♠ A♥ vs K♣ K♦",
      "question": "How much does the classic overpair edge compress?",
      "fixedSuitDisclosure": "One collision-free suit realization; this is not a suit-averaged hand-class result.",
      "standardHoldem": {
        "boards": 1712304,
        "wins": 1388072,
        "ties": 6538,
        "losses": 317694,
        "equityPct": 81.25549
      },
      "shortDeckConventionalStraightStandardCategoryOrder": {
        "boards": 201376,
        "wins": 148200,
        "ties": 2192,
        "losses": 50984,
        "equityPct": 74.137931
      },
      "shortDeckLowStraightStandardCategoryOrder": {
        "boards": 201376,
        "wins": 148200,
        "ties": 2674,
        "losses": 50502,
        "equityPct": 74.257608
      },
      "shortDeckOfficial": {
        "boards": 201376,
        "wins": 148200,
        "ties": 2674,
        "losses": 50502,
        "equityPct": 74.257608
      },
      "decomposition": {
        "deckRemovalEffectPp": -7.117559,
        "lowStraightEffectPp": 0.119677,
        "rankingSwapEffectPp": 0,
        "totalEffectPp": -6.997882,
        "roundingResidualPp": 0,
        "lowStraightBoardOutcomes": {
          "heroImproved": 482,
          "heroWorsened": 480,
          "unchanged": 200414
        },
        "rankingSwapBoardOutcomes": {
          "heroImproved": 612,
          "heroWorsened": 612,
          "unchanged": 200152
        }
      }
    },
    {
      "id": "aa-vs-jts",
      "hero": [
        "As",
        "Ah"
      ],
      "villain": [
        "Jc",
        "Tc"
      ],
      "label": "A♠ A♥ vs J♣ T♣",
      "question": "How much ground does a connected suited hand gain on aces?",
      "fixedSuitDisclosure": "One collision-free suit realization; this is not a suit-averaged hand-class result.",
      "standardHoldem": {
        "boards": 1712304,
        "wins": 1337569,
        "ties": 5757,
        "losses": 368978,
        "equityPct": 78.283266
      },
      "shortDeckConventionalStraightStandardCategoryOrder": {
        "boards": 201376,
        "wins": 127500,
        "ties": 1494,
        "losses": 72382,
        "equityPct": 63.685345
      },
      "shortDeckLowStraightStandardCategoryOrder": {
        "boards": 201376,
        "wins": 127500,
        "ties": 1494,
        "losses": 72382,
        "equityPct": 63.685345
      },
      "shortDeckOfficial": {
        "boards": 201376,
        "wins": 125206,
        "ties": 1494,
        "losses": 74676,
        "equityPct": 62.546182
      },
      "decomposition": {
        "deckRemovalEffectPp": -14.597921,
        "lowStraightEffectPp": 0,
        "rankingSwapEffectPp": -1.139163,
        "totalEffectPp": -15.737084,
        "roundingResidualPp": 0,
        "lowStraightBoardOutcomes": {
          "heroImproved": 0,
          "heroWorsened": 0,
          "unchanged": 201376
        },
        "rankingSwapBoardOutcomes": {
          "heroImproved": 112,
          "heroWorsened": 2406,
          "unchanged": 198858
        }
      }
    },
    {
      "id": "qq-vs-aks",
      "hero": [
        "Qs",
        "Qh"
      ],
      "villain": [
        "Ac",
        "Kc"
      ],
      "label": "Q♠ Q♥ vs A♣ K♣",
      "question": "Does the familiar pair-versus-two-overs race stay familiar?",
      "fixedSuitDisclosure": "One collision-free suit realization; this is not a suit-averaged hand-class result.",
      "standardHoldem": {
        "boards": 1712304,
        "wins": 917606,
        "ties": 6732,
        "losses": 787966,
        "equityPct": 53.785543
      },
      "shortDeckConventionalStraightStandardCategoryOrder": {
        "boards": 201376,
        "wins": 96131,
        "ties": 1307,
        "losses": 103938,
        "equityPct": 48.061586
      },
      "shortDeckLowStraightStandardCategoryOrder": {
        "boards": 201376,
        "wins": 93437,
        "ties": 2007,
        "losses": 105932,
        "equityPct": 46.897595
      },
      "shortDeckOfficial": {
        "boards": 201376,
        "wins": 91071,
        "ties": 2007,
        "losses": 108298,
        "equityPct": 45.722678
      },
      "decomposition": {
        "deckRemovalEffectPp": -5.723957,
        "lowStraightEffectPp": -1.163991,
        "rankingSwapEffectPp": -1.174917,
        "totalEffectPp": -8.062865,
        "roundingResidualPp": 0,
        "lowStraightBoardOutcomes": {
          "heroImproved": 698,
          "heroWorsened": 2694,
          "unchanged": 197984
        },
        "rankingSwapBoardOutcomes": {
          "heroImproved": 112,
          "heroWorsened": 2478,
          "unchanged": 198786
        }
      }
    },
    {
      "id": "qq-vs-ako",
      "hero": [
        "Qs",
        "Qh"
      ],
      "villain": [
        "Ac",
        "Kd"
      ],
      "label": "Q♠ Q♥ vs A♣ K♦",
      "question": "How much of the pair race belongs to suitedness?",
      "fixedSuitDisclosure": "One collision-free suit realization; this is not a suit-averaged hand-class result.",
      "standardHoldem": {
        "boards": 1712304,
        "wins": 975909,
        "ties": 5854,
        "losses": 730541,
        "equityPct": 57.164849
      },
      "shortDeckConventionalStraightStandardCategoryOrder": {
        "boards": 201376,
        "wins": 100075,
        "ties": 1263,
        "losses": 100038,
        "equityPct": 50.009187
      },
      "shortDeckLowStraightStandardCategoryOrder": {
        "boards": 201376,
        "wins": 97145,
        "ties": 1986,
        "losses": 102245,
        "equityPct": 48.733712
      },
      "shortDeckOfficial": {
        "boards": 201376,
        "wins": 96682,
        "ties": 1986,
        "losses": 102708,
        "equityPct": 48.503794
      },
      "decomposition": {
        "deckRemovalEffectPp": -7.155662,
        "lowStraightEffectPp": -1.275475,
        "rankingSwapEffectPp": -0.229918,
        "totalEffectPp": -8.661055,
        "roundingResidualPp": 0,
        "lowStraightBoardOutcomes": {
          "heroImproved": 721,
          "heroWorsened": 2930,
          "unchanged": 197725
        },
        "rankingSwapBoardOutcomes": {
          "heroImproved": 112,
          "heroWorsened": 575,
          "unchanged": 200689
        }
      }
    },
    {
      "id": "ako-vs-jts",
      "hero": [
        "As",
        "Kd"
      ],
      "villain": [
        "Jh",
        "Th"
      ],
      "label": "A♠ K♦ vs J♥ T♥",
      "question": "Can suited connectivity overtake offsuit high cards?",
      "fixedSuitDisclosure": "One collision-free suit realization; this is not a suit-averaged hand-class result.",
      "standardHoldem": {
        "boards": 1712304,
        "wins": 1003559,
        "ties": 7241,
        "losses": 701504,
        "equityPct": 58.820134
      },
      "shortDeckConventionalStraightStandardCategoryOrder": {
        "boards": 201376,
        "wins": 99350,
        "ties": 1496,
        "losses": 100530,
        "equityPct": 49.707016
      },
      "shortDeckLowStraightStandardCategoryOrder": {
        "boards": 201376,
        "wins": 99349,
        "ties": 1497,
        "losses": 100530,
        "equityPct": 49.706767
      },
      "shortDeckOfficial": {
        "boards": 201376,
        "wins": 98632,
        "ties": 1497,
        "losses": 101247,
        "equityPct": 49.350717
      },
      "decomposition": {
        "deckRemovalEffectPp": -9.113118,
        "lowStraightEffectPp": -0.000249,
        "rankingSwapEffectPp": -0.35605,
        "totalEffectPp": -9.469417,
        "roundingResidualPp": 0,
        "lowStraightBoardOutcomes": {
          "heroImproved": 0,
          "heroWorsened": 1,
          "unchanged": 201375
        },
        "rankingSwapBoardOutcomes": {
          "heroImproved": 108,
          "heroWorsened": 825,
          "unchanged": 200443
        }
      }
    },
    {
      "id": "aqo-vs-qjs",
      "hero": [
        "As",
        "Qd"
      ],
      "villain": [
        "Qh",
        "Jh"
      ],
      "label": "A♠ Q♦ vs Q♥ J♥",
      "question": "How much does domination protect an offsuit ace?",
      "fixedSuitDisclosure": "One collision-free suit realization; this is not a suit-averaged hand-class result.",
      "standardHoldem": {
        "boards": 1712304,
        "wins": 1157784,
        "ties": 24372,
        "losses": 530148,
        "equityPct": 68.327236
      },
      "shortDeckConventionalStraightStandardCategoryOrder": {
        "boards": 201376,
        "wins": 114418,
        "ties": 9149,
        "losses": 77809,
        "equityPct": 59.089713
      },
      "shortDeckLowStraightStandardCategoryOrder": {
        "boards": 201376,
        "wins": 114459,
        "ties": 9807,
        "losses": 77110,
        "equityPct": 59.273449
      },
      "shortDeckOfficial": {
        "boards": 201376,
        "wins": 114179,
        "ties": 9807,
        "losses": 77390,
        "equityPct": 59.134405
      },
      "decomposition": {
        "deckRemovalEffectPp": -9.237523,
        "lowStraightEffectPp": 0.183736,
        "rankingSwapEffectPp": -0.139044,
        "totalEffectPp": -9.192831,
        "roundingResidualPp": 0,
        "lowStraightBoardOutcomes": {
          "heroImproved": 699,
          "heroWorsened": 657,
          "unchanged": 200020
        },
        "rankingSwapBoardOutcomes": {
          "heroImproved": 42,
          "heroWorsened": 322,
          "unchanged": 201012
        }
      }
    },
    {
      "id": "aks-vs-qjs",
      "hero": [
        "Ac",
        "Kc"
      ],
      "villain": [
        "Qh",
        "Jh"
      ],
      "label": "A♣ K♣ vs Q♥ J♥",
      "question": "How are two suited broadway hands reordered?",
      "fixedSuitDisclosure": "One collision-free suit realization; this is not a suit-averaged hand-class result.",
      "standardHoldem": {
        "boards": 1712304,
        "wins": 1069685,
        "ties": 8518,
        "losses": 634101,
        "equityPct": 62.719237
      },
      "shortDeckConventionalStraightStandardCategoryOrder": {
        "boards": 201376,
        "wins": 111251,
        "ties": 1053,
        "losses": 89072,
        "equityPct": 55.506863
      },
      "shortDeckLowStraightStandardCategoryOrder": {
        "boards": 201376,
        "wins": 111885,
        "ties": 1688,
        "losses": 87803,
        "equityPct": 55.979362
      },
      "shortDeckOfficial": {
        "boards": 201376,
        "wins": 111908,
        "ties": 1688,
        "losses": 87780,
        "equityPct": 55.990783
      },
      "decomposition": {
        "deckRemovalEffectPp": -7.212374,
        "lowStraightEffectPp": 0.472499,
        "rankingSwapEffectPp": 0.011421,
        "totalEffectPp": -6.728454,
        "roundingResidualPp": 0,
        "lowStraightBoardOutcomes": {
          "heroImproved": 1269,
          "heroWorsened": 634,
          "unchanged": 199473
        },
        "rankingSwapBoardOutcomes": {
          "heroImproved": 848,
          "heroWorsened": 825,
          "unchanged": 199703
        }
      }
    },
    {
      "id": "aks-vs-same-suit-qj",
      "hero": [
        "Ac",
        "Kc"
      ],
      "villain": [
        "Qc",
        "Jc"
      ],
      "label": "A♣ K♣ vs Q♣ J♣",
      "question": "How much does shared-suit topology move the same ranks?",
      "fixedSuitDisclosure": "One collision-free suit realization; this is not a suit-averaged hand-class result.",
      "standardHoldem": {
        "boards": 1712304,
        "wins": 1124180,
        "ties": 10327,
        "losses": 577797,
        "equityPct": 65.954614
      },
      "shortDeckConventionalStraightStandardCategoryOrder": {
        "boards": 201376,
        "wins": 113347,
        "ties": 1194,
        "losses": 86835,
        "equityPct": 56.582711
      },
      "shortDeckLowStraightStandardCategoryOrder": {
        "boards": 201376,
        "wins": 114073,
        "ties": 1920,
        "losses": 85383,
        "equityPct": 57.12349
      },
      "shortDeckOfficial": {
        "boards": 201376,
        "wins": 114073,
        "ties": 1920,
        "losses": 85383,
        "equityPct": 57.12349
      },
      "decomposition": {
        "deckRemovalEffectPp": -9.371903,
        "lowStraightEffectPp": 0.540779,
        "rankingSwapEffectPp": 0,
        "totalEffectPp": -8.831124,
        "roundingResidualPp": 0,
        "lowStraightBoardOutcomes": {
          "heroImproved": 1452,
          "heroWorsened": 726,
          "unchanged": 199198
        },
        "rankingSwapBoardOutcomes": {
          "heroImproved": 0,
          "heroWorsened": 0,
          "unchanged": 201376
        }
      }
    },
    {
      "id": "98s-vs-ako",
      "hero": [
        "9c",
        "8c"
      ],
      "villain": [
        "Ah",
        "Kd"
      ],
      "label": "9♣ 8♣ vs A♥ K♦",
      "question": "What does deck compression do to a mid-low suited connector?",
      "fixedSuitDisclosure": "One collision-free suit realization; this is not a suit-averaged hand-class result.",
      "standardHoldem": {
        "boards": 1712304,
        "wins": 688098,
        "ties": 6774,
        "losses": 1017432,
        "equityPct": 40.383308
      },
      "shortDeckConventionalStraightStandardCategoryOrder": {
        "boards": 201376,
        "wins": 85222,
        "ties": 2263,
        "losses": 113891,
        "equityPct": 42.881724
      },
      "shortDeckLowStraightStandardCategoryOrder": {
        "boards": 201376,
        "wins": 90875,
        "ties": 2670,
        "losses": 107831,
        "equityPct": 45.789965
      },
      "shortDeckOfficial": {
        "boards": 201376,
        "wins": 91687,
        "ties": 2670,
        "losses": 107019,
        "equityPct": 46.193191
      },
      "decomposition": {
        "deckRemovalEffectPp": 2.498416,
        "lowStraightEffectPp": 2.908241,
        "rankingSwapEffectPp": 0.403226,
        "totalEffectPp": 5.809883,
        "roundingResidualPp": 0,
        "lowStraightBoardOutcomes": {
          "heroImproved": 7966,
          "heroWorsened": 2312,
          "unchanged": 191098
        },
        "rankingSwapBoardOutcomes": {
          "heroImproved": 928,
          "heroWorsened": 116,
          "unchanged": 200332
        }
      }
    },
    {
      "id": "76s-vs-ako",
      "hero": [
        "7c",
        "6c"
      ],
      "villain": [
        "Ah",
        "Kd"
      ],
      "label": "7♣ 6♣ vs A♥ K♦",
      "question": "Does the bottom suited connector retain its usual live-card profile?",
      "fixedSuitDisclosure": "One collision-free suit realization; this is not a suit-averaged hand-class result.",
      "standardHoldem": {
        "boards": 1712304,
        "wins": 720259,
        "ties": 6530,
        "losses": 985515,
        "equityPct": 42.254413
      },
      "shortDeckConventionalStraightStandardCategoryOrder": {
        "boards": 201376,
        "wins": 78455,
        "ties": 2486,
        "losses": 120435,
        "equityPct": 39.576712
      },
      "shortDeckLowStraightStandardCategoryOrder": {
        "boards": 201376,
        "wins": 84111,
        "ties": 2890,
        "losses": 114375,
        "equityPct": 42.485698
      },
      "shortDeckOfficial": {
        "boards": 201376,
        "wins": 84923,
        "ties": 2890,
        "losses": 113563,
        "equityPct": 42.888924
      },
      "decomposition": {
        "deckRemovalEffectPp": -2.677701,
        "lowStraightEffectPp": 2.908986,
        "rankingSwapEffectPp": 0.403226,
        "totalEffectPp": 0.634511,
        "roundingResidualPp": 0,
        "lowStraightBoardOutcomes": {
          "heroImproved": 7969,
          "heroWorsened": 2312,
          "unchanged": 191095
        },
        "rankingSwapBoardOutcomes": {
          "heroImproved": 928,
          "heroWorsened": 116,
          "unchanged": 200332
        }
      }
    },
    {
      "id": "a9s-vs-kk",
      "hero": [
        "As",
        "9s"
      ],
      "villain": [
        "Kh",
        "Kd"
      ],
      "label": "A♠ 9♠ vs K♥ K♦",
      "question": "How much does a holding at both ends of A-6-7-8-9 gain?",
      "fixedSuitDisclosure": "One collision-free suit realization; this is not a suit-averaged hand-class result.",
      "standardHoldem": {
        "boards": 1712304,
        "wins": 549116,
        "ties": 6241,
        "losses": 1156947,
        "equityPct": 32.251078
      },
      "shortDeckConventionalStraightStandardCategoryOrder": {
        "boards": 201376,
        "wins": 80536,
        "ties": 1890,
        "losses": 118950,
        "equityPct": 40.462121
      },
      "shortDeckLowStraightStandardCategoryOrder": {
        "boards": 201376,
        "wins": 87837,
        "ties": 2430,
        "losses": 111109,
        "equityPct": 44.221754
      },
      "shortDeckOfficial": {
        "boards": 201376,
        "wins": 90336,
        "ties": 2430,
        "losses": 108610,
        "equityPct": 45.462717
      },
      "decomposition": {
        "deckRemovalEffectPp": 8.211043,
        "lowStraightEffectPp": 3.759633,
        "rankingSwapEffectPp": 1.240963,
        "totalEffectPp": 13.211639,
        "roundingResidualPp": 0,
        "lowStraightBoardOutcomes": {
          "heroImproved": 7841,
          "heroWorsened": 538,
          "unchanged": 192997
        },
        "rankingSwapBoardOutcomes": {
          "heroImproved": 2619,
          "heroWorsened": 120,
          "unchanged": 198637
        }
      }
    },
    {
      "id": "a6s-vs-qq",
      "hero": [
        "Ac",
        "6c"
      ],
      "villain": [
        "Qh",
        "Qd"
      ],
      "label": "A♣ 6♣ vs Q♥ Q♦",
      "question": "How much does the other A-6-7-8-9 endpoint gain?",
      "fixedSuitDisclosure": "One collision-free suit realization; this is not a suit-averaged hand-class result.",
      "standardHoldem": {
        "boards": 1712304,
        "wins": 548133,
        "ties": 5810,
        "losses": 1158361,
        "equityPct": 32.181085
      },
      "shortDeckConventionalStraightStandardCategoryOrder": {
        "boards": 201376,
        "wins": 74167,
        "ties": 1739,
        "losses": 125470,
        "equityPct": 37.261888
      },
      "shortDeckLowStraightStandardCategoryOrder": {
        "boards": 201376,
        "wins": 81468,
        "ties": 2279,
        "losses": 117629,
        "equityPct": 41.021522
      },
      "shortDeckOfficial": {
        "boards": 201376,
        "wins": 83967,
        "ties": 2279,
        "losses": 115130,
        "equityPct": 42.262484
      },
      "decomposition": {
        "deckRemovalEffectPp": 5.080803,
        "lowStraightEffectPp": 3.759634,
        "rankingSwapEffectPp": 1.240962,
        "totalEffectPp": 10.081399,
        "roundingResidualPp": 0,
        "lowStraightBoardOutcomes": {
          "heroImproved": 7841,
          "heroWorsened": 538,
          "unchanged": 192997
        },
        "rankingSwapBoardOutcomes": {
          "heroImproved": 2619,
          "heroWorsened": 120,
          "unchanged": 198637
        }
      }
    }
  ]
}