{
  "id": "poker-equity",
  "version": "d08ea6426339",
  "status": "published",
  "name": "Poker Equity Calculator",
  "question": "What is my hand’s poker equity?",
  "summary": "Computes the equity of two Texas hold’em hands against each other: the chance each wins or ties by the river, exact once the flop is out and estimated before it (exact on boards without a flush, sampled where a flush is possible).",
  "category": "game",
  "subcategory": "betting",
  "url": "https://www.acalculator.org/game/poker-equity-calculator",
  "markdown": "https://www.acalculator.org/game/poker-equity-calculator.md",
  "kind": "function",
  "method": "Equity = P(win) + P(tie) ÷ 2 over the boards that can still come: every board exactly from the flop on; before it, every board without a possible flush exactly (grouped by board ranks) plus 1,000 seeded samples of the boards where a flush is possible.",
  "assumptions": [
    "Heads-up: two known hands, each playing its best 5 of 7 cards under standard poker hand rankings. Suits never break a tie.",
    "All unseen cards are equally likely; no other player’s folded cards are known.",
    "Before the flop the equity is exact on every board where no flush is possible and estimated from 1,000 seeded samples of the boards where one is (standard error at most 0.46 percentage points); from the flop on it is exact.",
    "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: two cards, rank then suit, such as Ah Kh (T or 10 for ten; c, d, h, s for the suits).",
        "type": "string",
        "maxLength": 20
      },
      "hand2": {
        "title": "Opponent’s hand",
        "description": "Opponent’s hand: two cards, rank then suit, such as Ah Kh (T or 10 for ten; c, d, h, s for the suits).",
        "type": "string",
        "maxLength": 20
      },
      "board": {
        "title": "Board",
        "description": "The community cards dealt so far: none, 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 5-card hand is better.",
      "format": "percent"
    },
    "win2": {
      "label": "Opponent wins",
      "description": "The share of boards on which the opponent’s best 5-card 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 two cards in standard form: rank (T for ten) then lower-case suit, such as Th Td.",
      "format": "text"
    },
    "cards2": {
      "label": "Opponent’s cards",
      "description": "The opponent’s two cards in standard form, such as As Kc.",
      "format": "text"
    },
    "method": {
      "label": "How it was counted",
      "description": "Exact (every remaining board), or before the flop estimated (exact without flushes, flush boards sampled).",
      "format": "text"
    },
    "hand1Now": {
      "label": "Your hand now",
      "description": "Your best 5-card hand on the board so far (shown from the flop on).",
      "format": "text"
    },
    "hand2Now": {
      "label": "Opponent’s hand now",
      "description": "The opponent’s best 5-card hand on the board so far (shown from the flop on).",
      "format": "text"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "hand1": "Ah Kh",
      "hand2": "Qs Qd",
      "board": ""
    },
    "outputs": {
      "equity1": 46.02669228127716,
      "equity2": 53.97330771872284,
      "win1": 45.83606766088265,
      "win2": 53.782683098328334,
      "tie": 0.3812492407890188,
      "cards1": "Ah Kh",
      "cards2": "Qs Qd",
      "method": "Estimated: exact without flushes, 1,000 flush boards sampled"
    },
    "text": "Ah Kh against Qs Qd has 46.03% equity."
  },
  "examples": [
    {
      "given": {
        "hand1": "Ah Kh",
        "hand2": "Qs Qd",
        "board": "Qh 7h 2c"
      },
      "expect": {
        "equity1": 25.555555555555557,
        "win1": 25.555555555555557,
        "tie": 0,
        "method": "Exact: every one of 990 possible boards",
        "hand1Now": "High card",
        "hand2Now": "Three of a kind"
      },
      "source": "exact count of the 990 turn and river pairs (253 wins), Python 3 cross-check in the progress log"
    },
    {
      "given": {
        "hand1": "Ah Kh",
        "hand2": "Qs Qd",
        "board": "Qh 7h 2c 3d"
      },
      "expect": {
        "win1": 15.909090909090908,
        "win2": 84.0909090909091,
        "method": "Exact: every one of 44 possible boards"
      },
      "source": "hand calculation in content.mdx: 7 of the 44 rivers (the hearts that do not pair the board) win"
    },
    {
      "given": {
        "hand1": "As Ks",
        "hand2": "2c 2d",
        "board": "Ah 2h 7c Kd 9s"
      },
      "expect": {
        "win1": 0,
        "win2": 100,
        "equity1": 0,
        "hand1Now": "Two pair",
        "hand2Now": "Three of a kind"
      },
      "source": "hand calculation in content.mdx: three 2s beat aces and kings"
    },
    {
      "given": {
        "hand1": "Ah Ad",
        "hand2": "Kc Ks"
      },
      "expect": {
        "equity1": 81.25548967940273
      },
      "source": "exact enumeration of all 1,712,304 boards, Python 3 (progress log): 1,388,072 wins and 6,538 ties = 81.2555%; the page estimates the flush part from 1,000 boards, so 1% relative tolerance (under 2 standard errors at the 0.46-point bound)",
      "tolerance": 0.01
    }
  ],
  "sources": [
    "Wikipedia, List of poker hands (hand rankings): https://en.wikipedia.org/wiki/List_of_poker_hands",
    "Wikipedia, Poker probability (Texas hold ’em): https://en.wikipedia.org/wiki/Poker_probability",
    "Grinstead and Snell, Introduction to Probability, 2nd ed., American Mathematical Society, section 3.2, combinations: https://math.dartmouth.edu/~prob/prob/prob.pdf",
    "National Council on Problem Gambling, help and treatment (1-800-MY-RESET): https://www.ncpgambling.org/help-treatment/"
  ],
  "related": [
    "poker-odds",
    "blackjack",
    "implied-probability"
  ],
  "changelog": [
    {
      "date": "2026-09-28",
      "note": "Your cards and opponent’s cards outputs in standard form, used in the sentence (WP-70 QA)."
    },
    {
      "date": "2026-09-28",
      "note": "Preflop: exact on boards without a possible flush plus 1,000 sampled flush boards (standard error at most 0.46 points, was 0.5), in about 2 ms instead of 10,000 random boards."
    }
  ]
}