{
  "id": "omaha-odds",
  "version": "d132c675a387",
  "status": "published",
  "name": "Omaha Odds Calculator",
  "question": "How good are my four hole cards?",
  "summary": "Computes the exact equity of two Omaha hands against each other from the flop on: each hand’s chance to win or tie by the river, using exactly two hole cards and three board cards; five-card Omaha too.",
  "category": "game",
  "subcategory": "betting",
  "url": "https://www.acalculator.org/game/omaha-odds-calculator",
  "markdown": "https://www.acalculator.org/game/omaha-odds-calculator.md",
  "kind": "function",
  "method": "Equity = P(win) + P(tie) ÷ 2 over every board that can still come, each hand using exactly 2 hole cards and 3 board cards.",
  "assumptions": [
    "Heads-up: two known hands. Each plays its best 5-card hand of exactly 2 hole cards and exactly 3 board cards, under standard high-hand rankings (no hi-lo split). Suits never break a tie.",
    "All unseen cards are equally likely; the result is exact from the flop on. Before the flop there is no answer.",
    "Equity is the share of the pot won on average if both hands go to showdown; it ignores betting."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "hand1": {
        "title": "Your hand",
        "description": "Your hand: 4 cards (5 for five-card Omaha), rank then suit, such as Ah Ad Ks Qs (T or 10 for ten; c, d, h, s for the suits).",
        "type": "string",
        "maxLength": 30
      },
      "hand2": {
        "title": "Opponent’s hand",
        "description": "Opponent’s hand: 4 cards (5 for five-card Omaha), rank then suit, such as Ah Ad Ks Qs (T or 10 for ten; c, d, h, s for the suits).",
        "type": "string",
        "maxLength": 30
      },
      "board": {
        "title": "Board",
        "description": "The community cards dealt so far: the 3-card flop, 4 with the turn, or all 5.",
        "type": "string",
        "maxLength": 30
      }
    }
  },
  "outputs": {
    "equity1": {
      "label": "Your equity",
      "description": "Your share of the pot on average: your chance to win plus half the chance of a tie.",
      "format": "percent"
    },
    "equity2": {
      "label": "Opponent’s equity",
      "description": "The opponent’s chance to win plus half the chance of a tie.",
      "format": "percent"
    },
    "win1": {
      "label": "You win",
      "description": "The share of boards on which your best hand is better.",
      "format": "percent"
    },
    "win2": {
      "label": "Opponent wins",
      "description": "The share of boards on which the opponent’s best hand is better.",
      "format": "percent"
    },
    "tie": {
      "label": "Tie",
      "description": "The share of boards on which both best hands are equal and the pot is split.",
      "format": "percent"
    },
    "cards1": {
      "label": "Your cards",
      "description": "Your cards in standard form, such as Ah Ad Ks Qs.",
      "format": "text"
    },
    "cards2": {
      "label": "Opponent’s cards",
      "description": "The opponent’s cards in standard form.",
      "format": "text"
    },
    "method": {
      "label": "How it was counted",
      "description": "How many boards were counted.",
      "format": "text"
    },
    "hand1Now": {
      "label": "Your hand now",
      "description": "Your best hand on the board so far.",
      "format": "text"
    },
    "hand2Now": {
      "label": "Opponent’s hand now",
      "description": "The opponent’s best hand on the board so far.",
      "format": "text"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "hand1": "Ah Ad Ks Qs",
      "hand2": "Jh Th 9c 8c",
      "board": "Kh 7h 2c"
    },
    "outputs": {
      "equity1": 50.36585365853659,
      "equity2": 49.63414634146341,
      "win1": 50.36585365853659,
      "win2": 49.63414634146341,
      "tie": 0,
      "cards1": "Ah Ad Ks Qs",
      "cards2": "Jh Th 9c 8c",
      "method": "Exact: every one of 820 possible boards",
      "hand1Now": "One pair",
      "hand2Now": "High card"
    },
    "text": "Ah Ad Ks Qs against Jh Th 9c 8c has 50.37% equity."
  },
  "examples": [
    {
      "given": {
        "hand1": "Ah Ad Ks Qs",
        "hand2": "Jh Th 9c 8c",
        "board": "Kh 7h 2c"
      },
      "expect": {
        "equity1": 50.36585365853659,
        "win1": 50.36585365853659,
        "win2": 49.63414634146341,
        "tie": 0,
        "method": "Exact: every one of 820 possible boards",
        "hand1Now": "One pair",
        "hand2Now": "High card"
      },
      "source": "exact count of the 820 turn and river pairs (413 wins, 407 losses), independent Python 3 brute force in the progress log; Wikipedia, Omaha hold ’em (each player uses exactly two of four hole cards and exactly three board cards): https://en.wikipedia.org/wiki/Omaha_hold_%27em; Wikipedia, List of poker hands: https://en.wikipedia.org/wiki/List_of_poker_hands"
    },
    {
      "given": {
        "hand1": "Ah Ad Ks Qs",
        "hand2": "Jh Th 9c 8c",
        "board": "Kh 7h 2c 3d"
      },
      "expect": {
        "win1": 80,
        "win2": 20,
        "method": "Exact: every one of 40 possible boards"
      },
      "source": "exact count of the 40 rivers (32 wins, 8 losses), Python 3 brute force in the progress log; Wikipedia, Omaha hold ’em (each player uses exactly two of four hole cards and exactly three board cards): https://en.wikipedia.org/wiki/Omaha_hold_%27em; Wikipedia, List of poker hands: https://en.wikipedia.org/wiki/List_of_poker_hands"
    },
    {
      "given": {
        "hand1": "Jh Th 4c 5c",
        "hand2": "Js Ts 6d 7d",
        "board": "Ah Kd Qc 2s 3h"
      },
      "expect": {
        "tie": 100,
        "equity1": 50,
        "equity2": 50,
        "hand1Now": "Straight",
        "hand2Now": "Straight"
      },
      "source": "hand calculation in content.mdx: each hand’s best is A K Q J T; Python 3 brute force in the progress log; Wikipedia, Omaha hold ’em (each player uses exactly two of four hole cards and exactly three board cards): https://en.wikipedia.org/wiki/Omaha_hold_%27em; Wikipedia, List of poker hands: https://en.wikipedia.org/wiki/List_of_poker_hands"
    },
    {
      "given": {
        "hand1": "As Ks Qs Js",
        "hand2": "Ah Kh 2c 2d",
        "board": "Ts 9s 3h 4h 5d"
      },
      "expect": {
        "win2": 100,
        "equity1": 0,
        "method": "Exact: every one of 1 possible board",
        "hand1Now": "High card",
        "hand2Now": "Straight"
      },
      "source": "hand calculation in content.mdx: A♥ 2 from the hand with 3 4 5 from the board make a straight; the spade hand has only 2 board spades; Wikipedia, Omaha hold ’em (each player uses exactly two of four hole cards and exactly three board cards): https://en.wikipedia.org/wiki/Omaha_hold_%27em; Wikipedia, List of poker hands: https://en.wikipedia.org/wiki/List_of_poker_hands"
    },
    {
      "given": {
        "hand1": "Ah Ad 2c 3c 4d",
        "hand2": "Kh Kd Qs Js Tc",
        "board": "Ac 9h 9d"
      },
      "expect": {
        "win1": 99.86504723346829,
        "method": "Exact: every one of 741 possible boards",
        "hand1Now": "Full house",
        "hand2Now": "Two pair"
      },
      "source": "exact count of the 741 boards (740 wins, 1 loss: the K K turn and river), Python 3 brute force in the progress log; Wikipedia, Omaha hold ’em (each player uses exactly two of four hole cards and exactly three board cards): https://en.wikipedia.org/wiki/Omaha_hold_%27em; Wikipedia, List of poker hands: https://en.wikipedia.org/wiki/List_of_poker_hands"
    }
  ],
  "sources": [
    "Wikipedia, Omaha hold ’em (four hole cards; a hand uses exactly two hole cards and exactly three community cards). https://en.wikipedia.org/wiki/Omaha_hold_%27em (retrieved 2026-10-19)",
    "Wikipedia, List of poker hands (hand rankings). https://en.wikipedia.org/wiki/List_of_poker_hands (retrieved 2026-10-19)",
    "National Council on Problem Gambling, help and treatment (1-800-MY-RESET). https://www.ncpgambling.org/help-treatment/ (retrieved 2026-10-19)"
  ],
  "related": [
    "poker-equity",
    "poker-odds"
  ],
  "changelog": []
}