Implied probability: turning odds into a percentage

Implied probability is the chance of winning that a price represents. For a minus price, divide the odds by the odds plus 100: −150 is 150 ÷ 250 = 60%. For a plus price, divide 100 by the odds plus 100: +130 is 100 ÷ 230 = 43.48%. For decimal odds, it is simply 1 ÷ the price. The number is also your break-even rate: the share of bets at that price you have to win just to not lose money. And because the book builds its margin into both sides, the implied chances of a real market always add up to more than 100%.

Why implied probability is your break-even rate

A price is a trade: you put up the stake, the book puts up the winnings. The implied probability is the win rate at which that trade is exactly even over many bets. At −110 you risk $110 to win $100, so you need to win 110 out of every 210 bets, 52.38%, to finish level. Win more often than that and the price is in your favor; win less often and it isn't, no matter how confident you felt about each game.

Why do both sides add up to more than 100%?

A fair coin flip would be priced +100 on both sides: 50% plus 50%, exactly 100%. A sportsbook prices it −110 on both sides instead, and each side then implies 52.38%, for a total of 104.76%. Those extra 4.76 points are how the book is paid. It doesn't need to know who wins; if it takes similar money on both sides, the winners are paid out of the losers' stakes with some left over. The margin goes by several names, including vig, juice, overround and hold, and hold and vig explained shows how to measure it on any market. Three-way markets such as a soccer result work the same way: add all three outcomes.

Getting the fair probability back

To estimate what the book actually thinks, remove the margin. The simplest way is to divide each side's implied probability by the total, so the two scale back down to 100%. That is called the multiplicative or proportional method. It is a reasonable first estimate, though on lopsided markets books tend to load more of the margin onto the underdog, and other methods handle that better; how to devig odds compares them. Better still is to start from the books whose prices are hardest to beat, which is how fair odds are built.

Turning a probability back into odds

Run the formulas backwards. If the chance p is 50% or more, the American price is −100 × p ÷ (1 − p): 57.98% becomes −100 × 0.5798 ÷ 0.4202 = −138. If p is under 50%, it is +100 × (1 − p) ÷ p: 42.02% becomes +138. In decimal it is just 1 ÷ p: 1 ÷ 0.4202 = 2.38. This is how you set your own price for a bet before you look at what the books are offering.

Where implied probability becomes an edge

Once you have a fair probability, compare it with the price on offer. If a bet truly wins more often than its price implies, it has positive expected value: you are being paid more than the risk is worth. That comparison is the whole of positive EV betting, which gets its own lesson. The hard part is not the arithmetic but having a probability estimate better than the market's, which is why most people who do this lean on sharp prices rather than their own opinion.

Doing it without the arithmetic

The free Hold Calculator takes the prices for every outcome of a market, two-way or three-way, in American or decimal, and returns the hold plus the no-vig fair price of each side, with a choice of devig method. Across the site you can also switch the odds display to percentage in Settings, which shows every price as its implied probability. The Odds Board's Fair column does the margin removal for every row, using the sharpest books quoting it; the walkthrough shows how to read it.