Odds Payout Calculator and Converter

How It Works

Every odds format describes the same thing: how much a winning bet returns. Decimal odds are the total return per $1 staked, so payout is stake × decimal odds, as Ontario’s OLG PlaySmart guide puts it ($10 at 2.0 pays $20). A negative American price is the amount risked to win $100, so -110 becomes 1 + 100/110 = 1.9091; a positive price is the profit on $100, so +150 becomes 1 + 150/100 = 2.50. Fractional odds a/b are profit over stake, so 3/2 becomes 2.50 and 23/10 becomes 3.30 ($23 profit on $10).

Implied probability is 1 divided by the decimal odds: 1/1.9091 = 52.38%. It is the break-even win rate the price demands, not the book’s honest forecast, because it includes the margin. Fractions are reduced to lowest terms; American prices convert to exact fractions (-110 is 10/11, +150 is 3/2), while a decimal or percentage that is not an exact fraction is shown as the closest fraction with a denominator of 100 or less and marked ≈.

The second panel takes both sides of a two-way market. Adding the two implied probabilities gives more than 100%; the excess is the overround, or vig. Fair probabilities remove it by the multiplicative method, called basic normalisation in the forecasting literature: each implied probability divided by their sum. Other methods (Shin, power) split the margin differently and give slightly different fair prices for longshots.

Prices here are treated as data. This tool is informational only.

Worked Example

A price of -110 with a $10 stake. Decimal: 1 + 100/110 = 1.9091. Fractional: 100/110 reduced is 10/11. Implied probability: 110/210 = 52.38%. Payout: $10 × 1.9091 = $19.09, profit $9.09. With both sides of a market at -110, the implied probabilities add to 104.76%, so the overround is 4.76% and each side’s fair probability is 52.38/104.76 = 50.00%, or +100.

FAQ

Why does -110 on both sides add up to more than 100%?

Each side is priced so a bettor must win 52.38% of the time to break even. The extra 4.76% across both sides is the sportsbook’s margin; a fair coin would be priced +100 on each side.

What is the difference between overround and hold?

Overround is the sum of implied probabilities minus 100% (4.76% at -110/-110). Hold is the same margin expressed as a share of money wagered, 1 − 1/1.0476 = 4.55%. This tool reports overround.

Why is my fraction marked ≈?

Decimal odds such as 1.91 are usually rounded from a fraction. The tool searches every denominator up to 100 for the closest fraction and marks it ≈ unless it matches exactly.

Is basic normalisation the “right” way to remove vig?

It is the simplest and most common method, and it works well in the middle of the probability range. Research comparing methods finds that Shin’s model produces slightly better forecasts, mainly because books shade longshots more than favorites.

Can I enter a probability instead of a price?

Yes. Choose “Implied probability” and enter a percentage; the tool returns the equivalent American, decimal and fractional price. Prediction-market prices in cents map directly: a 63-cent share is 63%.

Sources

• OLG PlaySmart: Odds - Ontario Lottery and Gaming guide stating that decimal payouts are stake multiplied by the odds, with the American and fractional definitions (23/10 is 2.30 profit per $1)
• FanDuel Sportsbook House Rules, Massachusetts (Massachusetts Gaming Commission) - moneyline definitions: -120 risks $120 to win $100, +150 wins $150 per $100
• Mathematics of bookmaking (Wikipedia) - implied probability as the reciprocal of decimal odds and the overround as the sum of implied probabilities above 100%
• Štrumbelj, E. (2014). On determining probability forecasts from betting odds. International Journal of Forecasting, 30(4), 934–943 - defines basic normalisation (inverse odds divided by their sum) and compares it with Shin’s model