{
  "id": "poker-odds",
  "version": "9424c08ac63c",
  "status": "published",
  "name": "Poker Odds Calculator",
  "question": "What are my poker odds of hitting?",
  "summary": "Computes the exact chance of hitting one of your outs in Texas hold’em by the river or on the next card, compares it with the rule of 4 and 2, and gives the break-even chance from the pot odds.",
  "category": "game",
  "subcategory": "betting",
  "url": "https://www.acalculator.org/game/poker-odds-calculator",
  "markdown": "https://www.acalculator.org/game/poker-odds-calculator.md",
  "kind": "function",
  "method": "Flop: P(hit by river) = 1 − C(47 − outs, 2) ÷ C(47, 2) = 1 − (47 − outs)(46 − outs) ÷ 2162; turn: outs ÷ 46. Break-even chance = call ÷ (pot + call).",
  "assumptions": [
    "Only your two cards and the board are known: every unseen card is equally likely to come, including cards other players hold or folded.",
    "Every out gives you the hand you want and no out also helps an opponent more.",
    "The flop chance counts both the turn and the river, as when all the money goes in on the flop.",
    "Results are mathematics, not advice."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "outs": {
        "title": "Outs",
        "description": "The number of unseen cards that would give you the hand you want (9 for a flush draw).",
        "type": "integer",
        "minimum": 1,
        "maximum": 20
      },
      "street": {
        "title": "Cards to come",
        "description": "On the flop, two cards are still to come (turn and river); on the turn, one card (the river).",
        "type": "string",
        "enum": [
          "flop",
          "turn"
        ]
      },
      "pot": {
        "title": "Pot before the call",
        "description": "The money in the pot, including the bet you face, before you call.",
        "type": "number",
        "x-unit": "USD",
        "exclusiveMinimum": 0,
        "maximum": 1000000000
      },
      "call": {
        "title": "Amount to call",
        "description": "The amount you must put in to call.",
        "type": "number",
        "x-unit": "USD",
        "exclusiveMinimum": 0,
        "maximum": 1000000000
      }
    }
  },
  "outputs": {
    "chance": {
      "label": "Chance to hit by the river",
      "description": "The exact chance that at least one of the cards to come is one of your outs.",
      "format": "percent"
    },
    "next": {
      "label": "Chance to hit on the next card",
      "description": "Outs ÷ unseen cards: 47 on the flop, 46 on the turn.",
      "format": "percent"
    },
    "oddsAgainst": {
      "label": "Odds of hitting by the river",
      "description": "Misses to hits as “x to 1 against” when a miss is at least as likely, else hits to misses as “x to 1 in favour”; 2 decimals.",
      "format": "text"
    },
    "rule": {
      "label": "Rule of 4 and 2",
      "description": "The quick estimate: outs × 4 on the flop, outs × 2 on the turn, in percent.",
      "format": "percent"
    },
    "breakEven": {
      "label": "Break-even chance for the call",
      "description": "The chance a call needs to break even on this bet alone: call ÷ (pot + call).",
      "format": "percent"
    },
    "potOdds": {
      "label": "Pot odds",
      "description": "The pot to the call, as “x to 1”, rounded to 2 decimals.",
      "format": "text"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "outs": 9,
      "street": "flop",
      "pot": 100,
      "call": 20
    },
    "outputs": {
      "chance": 34.96762257169288,
      "next": 19.148936170212767,
      "oddsAgainst": "1.86 to 1 against",
      "rule": 36,
      "breakEven": 16.666666666666668,
      "potOdds": "5 to 1"
    },
    "text": "Outs: 9. The chance to hit by the river is 34.97% (1.86 to 1 against)."
  },
  "examples": [
    {
      "given": {
        "outs": 9,
        "street": "flop",
        "pot": 100,
        "call": 20
      },
      "expect": {
        "chance": 34.96762257169287,
        "next": 19.148936170212767,
        "oddsAgainst": "1.86 to 1 against",
        "rule": 36,
        "breakEven": 16.666666666666668,
        "potOdds": "5 to 1"
      },
      "source": "hand calculation in content.mdx: 1 − (38 × 37) ÷ (47 × 46) = 756/2162 = 34.97% (flush draw)"
    },
    {
      "given": {
        "outs": 8,
        "street": "turn"
      },
      "expect": {
        "chance": 17.391304347826086,
        "next": 17.391304347826086,
        "rule": 16,
        "oddsAgainst": "4.75 to 1 against"
      },
      "source": "hand calculation in content.mdx: 8 ÷ 46 = 17.39% (open-ended straight draw on the turn)"
    },
    {
      "given": {
        "outs": 15,
        "street": "flop",
        "pot": 50,
        "call": 50
      },
      "expect": {
        "chance": 54.11655874190565,
        "rule": 60,
        "breakEven": 50,
        "potOdds": "1 to 1",
        "oddsAgainst": "1.18 to 1 in favour"
      },
      "source": "hand calculation in content.mdx: 1 − (32 × 31) ÷ 2162 = 1170/2162 = 54.12%"
    }
  ],
  "sources": [
    "Grinstead and Snell, Introduction to Probability, 2nd ed., American Mathematical Society, section 3.2, combinations: https://math.dartmouth.edu/~prob/prob/prob.pdf",
    "Wikipedia, Poker probability (Texas hold ’em, outs): https://en.wikipedia.org/wiki/Poker_probability",
    "Wikipedia, Pot odds: https://en.wikipedia.org/wiki/Pot_odds",
    "National Council on Problem Gambling, help and treatment (1-800-MY-RESET): https://www.ncpgambling.org/help-treatment/"
  ],
  "related": [
    "poker-equity",
    "implied-probability",
    "blackjack"
  ],
  "changelog": [
    {
      "date": "2026-09-28",
      "note": "Odds of hitting read \"in favour\" above 50%; the pot must be above 0; sentence wording (WP-70 QA)."
    }
  ]
}