How to Convert Betting Odds to Implied Probability

The conversion formulas

• Negative American odds (−A): A ÷ (A + 100)
• Positive American odds (+B): 100 ÷ (B + 100)
• Decimal odds (D): 1 ÷ D
• Fractional odds (a/b): b ÷ (a + b)

Each formula answers the same question: what share of the total return is your own stake? At −110 you risk $110 to get back $210 on a win, and 110 ÷ 210 = 52.38%.

Worked conversions

The same price in any format gives the same answer: −250, 1.40, and 2/5 all imply 71.43%. If two formats of one quote disagree, one of them has been rounded. The implied probability calculator runs the conversion for any American price.

Implied probability is a break-even rate

An implied probability is the win rate at which a bet breaks even over time. Take 100 bets of $110 at −110. At a 52.38% win rate, that is 52.38 wins of $100 and 47.62 losses of $110 on average, and both sides come to about $5,238. Win more often than that and the bet makes money on average; win less often and it loses.

That makes the implied probability the bar your own estimate has to clear. If you believe a +150 underdog wins 43% of the time, the bet beats its 40% break-even rate. If you believe it wins 38% of the time, the price is too short.

Why both sides add up to more than 100%

Convert both sides of a market and the total almost always exceeds 100%. Two sides at −110 imply 52.38% each, or 104.76% combined. A −150/+130 moneyline implies 60.00% and 43.48%, or 103.48%. The excess is the book’s margin, also called the overround or vig, and it means quoted implied probabilities run slightly high on every side.

Dividing each side by the total removes the margin under a simple proportional assumption: 60.00 ÷ 103.48 = 57.98% and 43.48 ÷ 103.48 = 42.02%. The no-vig odds guide covers that method and its alternatives.

Turn a probability back into odds

To find the odds that match a probability p, decimal odds are 1 ÷ p. For American odds, a probability of 50% or more converts to −100 × p ÷ (1 − p), and anything below 50% converts to +100 × (1 − p) ÷ p. A 60% estimate is −150. A 35% estimate is +185.7, which you would round to about +186.

That gives you a fair price to hold against what books offer. Keep the two numbers distinct: an implied probability describes a price, while your estimate of the true chance has to come from somewhere else, such as a model, a no-vig market reference, or both.