{
  "id": "odds",
  "version": "29b4333b0b2a",
  "status": "published",
  "name": "Odds Calculator",
  "question": "How do I convert betting odds?",
  "summary": "Converts betting odds between American, decimal and fractional formats and the implied probability, with exact fractions.",
  "category": "game",
  "subcategory": "betting",
  "url": "https://www.acalculator.org/game/odds-calculator",
  "markdown": "https://www.acalculator.org/game/odds-calculator.md",
  "kind": "function",
  "method": "Decimal odds d: American +A gives d = 1 + A ÷ 100, −A gives d = 1 + 100 ÷ A; fractional a/b gives d = 1 + a ÷ b; probability p% gives d = 100 ÷ p. Implied probability = 100 ÷ d percent.",
  "assumptions": [
    "Implied probability is 1 ÷ decimal odds. It includes the bookmaker’s margin, so the implied probabilities of all outcomes of one event add up to more than 100%.",
    "Conversions are exact fractions. Only American odds and the displayed decimals are rounded.",
    "Decimal odds must be above 1 and at most 1,000,001 (American +100,000,000).",
    "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, fractional, or an implied probability.",
        "type": "string",
        "enum": [
          "american",
          "decimal",
          "fractional",
          "probability"
        ]
      },
      "odds": {
        "title": "Odds",
        "description": "The odds in the chosen format, for example +150, 2.5, 3/2, or 40%.",
        "type": "string",
        "maxLength": 30
      }
    }
  },
  "outputs": {
    "probability": {
      "label": "Implied probability",
      "description": "The win chance the odds imply: 1 ÷ decimal odds, in percent.",
      "format": "percent"
    },
    "american": {
      "label": "American odds",
      "description": "Profit on a 100 stake (+) or the stake needed to win 100 (−), rounded to 2 decimals, halves away from 0.",
      "format": "text"
    },
    "decimal": {
      "label": "Decimal odds",
      "description": "The total return per 1 staked, stake included.",
      "format": "number"
    },
    "fractional": {
      "label": "Fractional odds",
      "description": "The exact profit per 1 staked (decimal odds − 1), as a fraction in lowest terms.",
      "format": "text"
    },
    "against": {
      "label": "Chance of losing",
      "description": "The chance the odds imply that the bet loses: 100% − implied probability.",
      "format": "percent"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "format": "american",
      "odds": "+150"
    },
    "outputs": {
      "probability": 40,
      "american": "+150",
      "decimal": 2.5,
      "fractional": "3/2",
      "against": 60
    },
    "text": "These odds are +150 American, 2.5 decimal and 3/2 fractional, an implied probability of 40%."
  },
  "examples": [
    {
      "given": {
        "format": "american",
        "odds": "+150"
      },
      "expect": {
        "american": "+150",
        "decimal": 2.5,
        "fractional": "3/2",
        "probability": 40,
        "against": 60
      },
      "source": "hand calculation in content.mdx: 1 + 150 ÷ 100 = 2.5; 1 ÷ 2.5 = 40%"
    },
    {
      "given": {
        "format": "american",
        "odds": "-110"
      },
      "expect": {
        "american": "-110",
        "decimal": 1.9090909090909092,
        "fractional": "10/11",
        "probability": 52.38095238095238
      },
      "source": "hand calculation in content.mdx: 1 + 100 ÷ 110 = 21/11; 11/21 = 52.380952…%"
    },
    {
      "given": {
        "format": "fractional",
        "odds": "5/2"
      },
      "expect": {
        "american": "+250",
        "decimal": 3.5,
        "fractional": "5/2",
        "probability": 28.571428571428573
      },
      "source": "hand calculation in content.mdx: 1 + 5/2 = 7/2; 2/7 = 28.571428…%"
    },
    {
      "given": {
        "format": "decimal",
        "odds": "1.8"
      },
      "expect": {
        "american": "-125",
        "fractional": "4/5",
        "probability": 55.55555555555556
      },
      "source": "hand calculation in content.mdx: 100 ÷ 0.8 = 125; 0.8 = 4/5; 1 ÷ 1.8 = 55.5…%"
    },
    {
      "given": {
        "format": "probability",
        "odds": "75%"
      },
      "expect": {
        "american": "-300",
        "decimal": 1.3333333333333333,
        "fractional": "1/3",
        "probability": 75
      },
      "source": "hand calculation in content.mdx: 100 ÷ 75 = 4/3; 4/3 − 1 = 1/3; −100 ÷ (1/3) = −300"
    },
    {
      "given": {
        "format": "decimal",
        "odds": "1.91"
      },
      "expect": {
        "american": "-109.89",
        "fractional": "91/100"
      },
      "source": "hand calculation in content.mdx: 100 ÷ 0.91 = 109.890…, rounded to 109.89"
    }
  ],
  "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): 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": [
    "implied-probability",
    "betting",
    "parlay",
    "no-vig"
  ],
  "changelog": [
    {
      "date": "2026-09-28",
      "note": "Each odds format has its own shape (American signed, fractional with a separator, probability with %); a decimal comma reads as a point in decimal odds and probabilities; odds typed in another format give a message with the same price (WP-70 QA)."
    }
  ]
}