{
  "schemaVersion": 1,
  "generatedAt": "2026-09-04",
  "question": "A true final-board freeroll starts from a tied current nut straight, has at least one legal completion that Hero wins, and has no legal completion that Hero loses.",
  "method": "Exhaustive enumeration of every legal final-board completion; exactly two hole cards and exactly three board cards form each five-card Omaha hand.",
  "assumptions": {
    "game": "heads-up four-card Pot-Limit Omaha high",
    "defaultStartingStreet": "turn",
    "deck": "standard 52-card deck",
    "players": 2,
    "futureBetting": "excluded",
    "completionDistribution": "each unordered final-board completion from the unseen physical cards is equally likely; order is irrelevant because future betting is excluded",
    "splitRule": "an equal best-five score gives each player half the pot"
  },
  "cases": [
    {
      "id": "locked-chop",
      "label": "Same straight, no live redraw",
      "question": "Does sharing the current straight create any way to scoop?",
      "board": [
        "9s",
        "8s",
        "7d",
        "2c"
      ],
      "hero": [
        "Jh",
        "Th",
        "Ac",
        "Kd"
      ],
      "villain": [
        "Jd",
        "Td",
        "3c",
        "4c"
      ],
      "currentCategory": "straight",
      "currentScore": [
        4,
        11
      ],
      "nutStraightHigh": 11,
      "startingStreet": "turn",
      "cardsToCome": 1,
      "legalCompletions": 40,
      "wins": 0,
      "ties": 40,
      "losses": 0,
      "equityPct": 50,
      "trueFreeroll": false
    },
    {
      "id": "nut-flush-freeroll",
      "label": "Nut-flush redraw",
      "question": "How much does an uncontested nut-flush redraw add on the river?",
      "board": [
        "9s",
        "8s",
        "7d",
        "2c"
      ],
      "hero": [
        "Jh",
        "Th",
        "As",
        "Ks"
      ],
      "villain": [
        "Jd",
        "Td",
        "3c",
        "4c"
      ],
      "currentCategory": "straight",
      "currentScore": [
        4,
        11
      ],
      "nutStraightHigh": 11,
      "startingStreet": "turn",
      "cardsToCome": 1,
      "legalCompletions": 40,
      "wins": 9,
      "ties": 31,
      "losses": 0,
      "equityPct": 61.25,
      "trueFreeroll": true
    },
    {
      "id": "higher-straight-freeroll",
      "label": "Higher-straight redraw",
      "question": "Can side-card connectivity freeroll the same made straight without a flush draw?",
      "board": [
        "Ts",
        "8s",
        "7d",
        "2c"
      ],
      "hero": [
        "Qh",
        "9h",
        "Jc",
        "3d"
      ],
      "villain": [
        "Jd",
        "9d",
        "4c",
        "5c"
      ],
      "currentCategory": "straight",
      "currentScore": [
        4,
        11
      ],
      "nutStraightHigh": 11,
      "startingStreet": "turn",
      "cardsToCome": 1,
      "legalCompletions": 40,
      "wins": 4,
      "ties": 36,
      "losses": 0,
      "equityPct": 55,
      "trueFreeroll": true
    },
    {
      "id": "dominated-flush-redraw",
      "label": "Dominated flush redraw",
      "question": "Is a lower flush redraw a freeroll when the opponent holds the nut redraw?",
      "board": [
        "9s",
        "8s",
        "7d",
        "2c"
      ],
      "hero": [
        "Jh",
        "Th",
        "5s",
        "3s"
      ],
      "villain": [
        "Jd",
        "Td",
        "As",
        "Ks"
      ],
      "currentCategory": "straight",
      "currentScore": [
        4,
        11
      ],
      "nutStraightHigh": 11,
      "startingStreet": "turn",
      "cardsToCome": 1,
      "legalCompletions": 40,
      "wins": 0,
      "ties": 33,
      "losses": 7,
      "equityPct": 41.25,
      "trueFreeroll": false
    },
    {
      "id": "pair-counter-redraw",
      "label": "Nut-flush redraw versus a set",
      "question": "Does a nut-flush redraw remain a freeroll against a set's full-house counter-redraw?",
      "board": [
        "9s",
        "8s",
        "7d",
        "2c"
      ],
      "hero": [
        "Jh",
        "Th",
        "As",
        "Ks"
      ],
      "villain": [
        "Jd",
        "Td",
        "2d",
        "2h"
      ],
      "currentCategory": "straight",
      "currentScore": [
        4,
        11
      ],
      "nutStraightHigh": 11,
      "startingStreet": "turn",
      "cardsToCome": 1,
      "legalCompletions": 40,
      "wins": 7,
      "ties": 23,
      "losses": 10,
      "equityPct": 46.25,
      "trueFreeroll": false
    },
    {
      "id": "pokerstars-flop-example",
      "label": "Published deep-stack flop example",
      "question": "What are the exact finite counts behind the current PokerStars per-1,000 illustration?",
      "board": [
        "9h",
        "8d",
        "7d"
      ],
      "hero": [
        "Ac",
        "As",
        "Jd",
        "Tc"
      ],
      "villain": [
        "Kd",
        "Qd",
        "Jh",
        "Th"
      ],
      "currentCategory": "straight",
      "currentScore": [
        4,
        11
      ],
      "nutStraightHigh": 11,
      "startingStreet": "flop",
      "cardsToCome": 2,
      "legalCompletions": 820,
      "wins": 28,
      "ties": 377,
      "losses": 415,
      "equityPct": 26.402439024390244,
      "trueFreeroll": false
    }
  ]
}