How to Convert American Odds to Implied Probability (and Remove the Vig)

Related book: The Sports Investing Blueprint by Ethan Cole · Amazon

An American price can be turned into a break-even win rate. That rate is the implied probability. Add the implied probabilities on every side of a market and the total is usually more than 100%. The amount above 100% is the bookmaker’s margin, also called the overround or the vig in probability terms. A simple way to remove that margin is to divide each side’s implied probability by the sum. This page uses that proportional method only. Other no-vig methods exist. They are not shown here.

Every price below is hypothetical. These are not odds from a book, not a game on today’s card, and not a suggestion to bet either side. This page is not an automatic calculator. A lower break-even rate is not an edge, and it is not a profit.

The two formulas

For a negative American price, drop the minus and call that number A. A price of -110 means A is 110.

Implied probability = A / (A + 100)

For a positive American price, call the posted number A. A price of +130 means A is 130.

Implied probability = 100 / (A + 100)

The result is a break-even win rate for that price alone. It is the share of bets that would have to win for wins and losses to balance at that price, before anything the price does not already show. It is not a forecast.

Percentages on this page are the exact result times 100, rounded half up to two decimal places. Where a sum of those rounded percentages is shown, it is the sum of the displayed figures.

A two-way market at -110 and -110

Both sides are -110. Each implied probability is 110 / 210.

Sum of the displayed rates: 104.76%. Overround: 4.76 percentage points.

Proportional no-vig price: divide each implied probability by the sum of the implied probabilities. Because the two prices match, each fair share is exactly one half. Displayed: 50.00% and 50.00%.

That 50% is not a prediction that either side wins half the time. It is what remains after this margin is split in proportion to the two equal prices.

A two-way market at -150 and +130

These are still made-up prices. -150 is the favorite in the example. +130 is the other side.

Sum of the displayed rates: 103.48%. Overround: 3.48 percentage points.

Divide each exact implied probability by the exact sum, then round half up to two decimals:

57.98% plus 42.02% is 100.00% after that rounding. Do not treat 57.98% as the chance the favorite wins. It is the -150 price with this margin removed, nothing more.

A three-way market, soccer style

A soccer-style result has three listed prices: home, draw, and away. The same addition works. Hypothetical prices: home -110, draw +240, away +260. They are not a match.

Sum of the displayed rates: 109.57%. Overround: 9.57 percentage points. Three prices often carry a larger displayed margin than a two-way -110 pair. That is arithmetic about these made-up numbers, not a claim about every soccer book.

Proportional no-vig shares, each exact implied probability divided by the exact sum of the three, then rounded half up to two decimals:

47.81 + 26.84 + 25.35 = 100.00 after rounding. Another method could split this 9.57 point margin differently. This page does not do that.

What this has to do with line shopping

Line shopping compares two prices for the same side. The break-even rate is one way to see the difference.

-105 is 1.16 percentage points lower than -110 on this display (52.38 − 51.22). The better price lowers the break-even rate. It does not make the bet a good one, and it does not remove the other side’s price from a two-way market. The margin examples above use both sides. A single shopped number does not.

The bankroll and line-shopping worksheet already holds the -110 and -105 pair as a flat stake and as a stake-to-win. Those rows are filled-in hypotheticals in a CSV. They do not calculate a new price for you, and they are not this no-vig table.

What this has to do with bankroll and variance

A break-even rate is not a unit size. Bankroll management and unit sizing is about how much of a separate bankroll one bet risks. Knowing that -110 corresponds to 52.38% does not say whether the stake is 1% of the starting bankroll or 1% of what remains after a loss. The worksheet shows that those two rules remove different amounts over twenty hypothetical losses.

Understanding variance is the other limit. A short winning or losing run does not show that results beat, or missed, the break-even rate on the price you took. The rate is a fact about the price. It is not a result.

Bottom line

Convert a negative price by dividing its absolute number by that number plus 100. Convert a positive price by dividing 100 by the price plus 100. Add every side in the market. The amount above 100% is the margin in this method. Divide each implied probability by that sum if you want the proportional no-vig share. Then stop. The number is still not a pick, not a promise of profit, and not a stake.

Educational content. Hypothetical prices only. No pick and no guarantee of profit. Break-even is not an edge. 18+/21+ where required. Only where legal. Responsible Gambling