{
  "id": "betting-odds",
  "version": "56e73725f9d3",
  "status": "published",
  "name": "Betting Odds Calculator",
  "question": "What is the odds payout on each side?",
  "summary": "Computes the payout and profit of a stake on each side of a two-way betting line (a moneyline), the implied probability of each side, and the bookmaker’s margin.",
  "category": "game",
  "subcategory": "betting",
  "url": "https://www.acalculator.org/game/betting-odds-calculator",
  "markdown": "https://www.acalculator.org/game/betting-odds-calculator.md",
  "kind": "function",
  "method": "Payout = stake × d and profit = stake × (d − 1) on each side; implied probability p = 100 ÷ d; overround = p₁ + p₂ − 100; hold = 100 − 10,000 ÷ (p₁ + p₂) percent.",
  "assumptions": [
    "The same stake goes on each side, shown side by side; each is a separate single bet.",
    "The line has exactly two outcomes (no draw). For three or more outcomes, use the no-vig calculator.",
    "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 both odds: American, decimal, or fractional.",
        "type": "string",
        "enum": [
          "american",
          "decimal",
          "fractional"
        ]
      },
      "odds1": {
        "title": "Odds on side 1",
        "description": "The odds offered on side 1 of the two-way line, in the chosen format.",
        "type": "string",
        "maxLength": 30
      },
      "odds2": {
        "title": "Odds on side 2",
        "description": "The odds offered on side 2 of the two-way line, in the chosen format.",
        "type": "string",
        "maxLength": 30
      },
      "stake": {
        "title": "Stake",
        "description": "The amount bet on one side.",
        "type": "number",
        "x-unit": "USD",
        "exclusiveMinimum": 0,
        "maximum": 1000000000
      }
    }
  },
  "outputs": {
    "payout1": {
      "label": "Payout on side 1",
      "description": "What the stake returns if side 1 wins: stake × decimal odds, stake included.",
      "format": "money"
    },
    "profit1": {
      "label": "Profit on side 1",
      "description": "Payout on side 1 minus the stake.",
      "format": "money"
    },
    "payout2": {
      "label": "Payout on side 2",
      "description": "What the stake returns if side 2 wins: stake × decimal odds, stake included.",
      "format": "money"
    },
    "profit2": {
      "label": "Profit on side 2",
      "description": "Payout on side 2 minus the stake.",
      "format": "money"
    },
    "prob1": {
      "label": "Implied probability, side 1",
      "description": "The win chance side 1’s odds imply: 1 ÷ decimal odds.",
      "format": "percent"
    },
    "prob2": {
      "label": "Implied probability, side 2",
      "description": "The win chance side 2’s odds imply: 1 ÷ decimal odds.",
      "format": "percent"
    },
    "overround": {
      "label": "Overround",
      "description": "How far the two implied probabilities add up past 100%.",
      "format": "percent"
    },
    "hold": {
      "label": "Bookmaker’s margin (hold)",
      "description": "The share of all money staked that the bookmaker keeps when bets on both sides pay out the same: 1 − 1 ÷ (sum of implied probabilities).",
      "format": "percent"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "format": "american",
      "odds1": "-150",
      "odds2": "+130",
      "stake": 100
    },
    "outputs": {
      "payout1": 166.66666666666666,
      "profit1": 66.66666666666666,
      "payout2": 230,
      "profit2": 130,
      "prob1": 60,
      "prob2": 43.47826086956522,
      "overround": 3.4782608695652186,
      "hold": 3.3613445378151283
    },
    "text": "A $100.00 bet pays $166.67 if side 1 (-150) wins and $230.00 if side 2 (+130) wins."
  },
  "examples": [
    {
      "given": {
        "format": "american",
        "odds1": "-150",
        "odds2": "+130",
        "stake": 100
      },
      "expect": {
        "payout1": 166.66666666666669,
        "profit1": 66.66666666666669,
        "payout2": 230,
        "profit2": 130,
        "prob1": 60,
        "prob2": 43.47826086956522,
        "overround": 3.4782608695652186,
        "hold": 3.361344537815128
      },
      "source": "hand calculation in content.mdx: d = 5/3 and 23/10; 3/5 + 10/23 = 119/115; hold 1 − 115/119 = 4/119"
    },
    {
      "given": {
        "format": "american",
        "odds1": "-110",
        "odds2": "-110",
        "stake": 110
      },
      "expect": {
        "payout1": 210,
        "profit2": 100,
        "prob1": 52.38095238095238,
        "overround": 4.761904761904773,
        "hold": 4.545454545454547
      },
      "source": "hand calculation in content.mdx: 22/21 − 1 = 1/21 = 4.76%; hold 1 − 21/22 = 1/22 = 4.55%"
    },
    {
      "given": {
        "format": "decimal",
        "odds1": "2",
        "odds2": "2",
        "stake": 50
      },
      "expect": {
        "payout1": 100,
        "payout2": 100,
        "overround": 0,
        "hold": 0
      },
      "source": "hand calculation in content.mdx: a fair even-money line has no margin"
    }
  ],
  "sources": [
    "Wikipedia, Fixed-odds betting (odds formats and overround): https://en.wikipedia.org/wiki/Fixed-odds_betting",
    "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",
    "National Council on Problem Gambling, help and treatment (1-800-MY-RESET): https://www.ncpgambling.org/help-treatment/"
  ],
  "related": [
    "betting",
    "no-vig",
    "implied-probability",
    "odds"
  ],
  "changelog": [
    {
      "date": "2026-09-28",
      "note": "Odds parser as on the odds calculator: shapes, decimal comma, same-price message (WP-70 QA)."
    }
  ]
}