{
  "id": "implied-probability",
  "version": "7bc5a713aae3",
  "status": "published",
  "name": "Implied Probability Calculator",
  "question": "What is the implied probability?",
  "summary": "Computes the implied probability of American, decimal or fractional betting odds, the chance of losing, and the odds for and against as whole-number ratios.",
  "category": "game",
  "subcategory": "betting",
  "url": "https://www.acalculator.org/game/implied-probability-calculator",
  "markdown": "https://www.acalculator.org/game/implied-probability-calculator.md",
  "kind": "function",
  "method": "Implied probability = 100 ÷ d percent, where d is the decimal odds (American +A: 1 + A ÷ 100; −A: 1 + 100 ÷ A; fractional a/b: 1 + a ÷ b).",
  "assumptions": [
    "The implied probability includes the bookmaker’s margin, so it is usually higher than the true chance.",
    "The odds for and against are exact: 1 to (d − 1), written in lowest whole numbers.",
    "Results are mathematics, not betting advice."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "format": {
        "title": "Odds format",
        "description": "The format of the odds you type: American, decimal, or fractional.",
        "type": "string",
        "enum": [
          "american",
          "decimal",
          "fractional"
        ]
      },
      "odds": {
        "title": "Odds",
        "description": "The odds in the chosen format, for example −110, 1.91, or 10/11.",
        "type": "string",
        "maxLength": 30
      }
    }
  },
  "outputs": {
    "probability": {
      "label": "Implied probability",
      "description": "The win chance the odds imply: 1 ÷ decimal odds, in percent.",
      "format": "percent"
    },
    "against": {
      "label": "Chance of losing",
      "description": "The chance the odds imply that the bet loses: 100% − implied probability.",
      "format": "percent"
    },
    "oddsFor": {
      "label": "Odds in favour",
      "description": "The implied chances of winning to losing as a ratio of whole numbers in lowest terms.",
      "format": "text"
    },
    "oddsAgainst": {
      "label": "Odds against",
      "description": "The implied chances of losing to winning as a ratio of whole numbers in lowest terms.",
      "format": "text"
    },
    "oneIn": {
      "label": "One win in",
      "description": "The decimal odds: the number of tries per win that the odds imply on average.",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "format": "american",
      "odds": "-110"
    },
    "outputs": {
      "probability": 52.38095238095238,
      "against": 47.61904761904762,
      "oddsFor": "11 to 10",
      "oddsAgainst": "10 to 11",
      "oneIn": 1.9090909090909092
    },
    "text": "Odds of -110 imply a win chance of 52.38% (11 to 10 in favour)."
  },
  "examples": [
    {
      "given": {
        "format": "american",
        "odds": "-110"
      },
      "expect": {
        "probability": 52.38095238095238,
        "against": 47.61904761904762,
        "oddsFor": "11 to 10",
        "oddsAgainst": "10 to 11",
        "oneIn": 1.9090909090909092
      },
      "source": "hand calculation in content.mdx: d = 21/11; 11/21 = 52.380952…%"
    },
    {
      "given": {
        "format": "american",
        "odds": "+300"
      },
      "expect": {
        "probability": 25,
        "against": 75,
        "oddsFor": "1 to 3",
        "oddsAgainst": "3 to 1",
        "oneIn": 4
      },
      "source": "hand calculation in content.mdx: d = 4; 1 ÷ 4 = 25%"
    },
    {
      "given": {
        "format": "fractional",
        "odds": "6/4"
      },
      "expect": {
        "probability": 40,
        "oddsFor": "2 to 3",
        "oddsAgainst": "3 to 2"
      },
      "source": "hand calculation in content.mdx: 6/4 = 3/2, d = 5/2; 2/5 = 40%"
    },
    {
      "given": {
        "format": "decimal",
        "odds": "1.25"
      },
      "expect": {
        "probability": 80,
        "against": 20,
        "oddsFor": "4 to 1"
      },
      "source": "hand calculation in content.mdx: 1 ÷ 1.25 = 80%; d − 1 = 1/4"
    }
  ],
  "sources": [
    "Grinstead and Snell, Introduction to Probability, 2nd ed., American Mathematical Society, section 1.2, odds and probabilities (page 28): https://math.dartmouth.edu/~prob/prob/prob.pdf",
    "Wikipedia, Fixed-odds betting (fractional, decimal and moneyline odds, overround): https://en.wikipedia.org/wiki/Fixed-odds_betting",
    "National Council on Problem Gambling, help and treatment (1-800-MY-RESET): https://www.ncpgambling.org/help-treatment/"
  ],
  "related": [
    "odds",
    "no-vig",
    "betting-odds",
    "betting"
  ],
  "changelog": [
    {
      "date": "2026-09-28",
      "note": "Odds parser as on the odds calculator (shapes, decimal comma, same-price message); probability shown to 4 significant figures; sentence wording (WP-70 QA)."
    }
  ]
}