Implied probability and how to work it out from any odds

Odds are a price, but every price also hides a percentage: how often the outcome would have to happen for that price to break even. That figure is the implied probability. Once you can work it out, odds in any format become easy to compare, and you can see how much margin a market carries.

The idea in one line

Implied probability is the share of your return that is your own stake. If a winning bet of 10 pays back 25 in total, your stake is 10 of that 25, so the price implies 10 ÷ 25 = 40%.

Each format below is just a different way of writing that same fraction.

Decimal odds

Decimal odds already show the total return per 1 staked, so the formula is the simplest:

Implied probability = 1 ÷ decimal odds

• 2.50 gives 1 ÷ 2.50 = 0.40, or 40%
• 1.80 gives 1 ÷ 1.80 = 0.5556, or 55.56%
• 2.00 gives 1 ÷ 2.00 = 0.50, or 50%

The higher the decimal price, the lower the implied chance. More on the format in decimal odds explained.

American odds

American odds use two formulas, one for each sign.

For a negative price (usually the favourite), use the number without its minus sign:

Implied probability = odds ÷ (odds + 100)

• -150 gives 150 ÷ 250 = 60%
• -110 gives 110 ÷ 210 = 52.38%

For a positive price (usually the underdog):

Implied probability = 100 ÷ (odds + 100)

• +150 gives 100 ÷ 250 = 40%
• +200 gives 100 ÷ 300 = 33.33%

A price of +100 (or -100) is exactly 50%. See American odds explained for how the signs work.

Fractional odds

A fractional price a/b means you win a for every b staked. Your stake is b out of a total return of a + b:

Implied probability = b ÷ (a + b)

• 3/2 gives 2 ÷ 5 = 40%
• 5/2 gives 2 ÷ 7 = 28.57%
• 4/6 gives 6 ÷ 10 = 60%
• Evens (1/1) gives 1 ÷ 2 = 50%

More in fractional odds explained.

One price, three formats

The same price written three ways always gives the same implied probability:

(Decimal 1.67 is rounded from 1.666… recurring, the exact decimal for 4/6, which implies exactly 60%; 1 ÷ 1.67 on its own gives 59.88%.)

Try any price in the converter:

From a probability back to odds

To turn a probability p (written as a decimal, so 40% is 0.40) back into odds:

• Decimal: 1 ÷ p. For 0.40 that is 2.50.
• American, p above 0.50: minus (p ÷ (1 − p)) × 100. For 0.60 that is −(0.60 ÷ 0.40) × 100 = -150.
• American, p of 0.50 or below: plus ((1 − p) ÷ p) × 100. For 0.40 that is (0.60 ÷ 0.40) × 100 = +150.
• Fractional: (1 − p) ÷ p, then simplified. For 0.40 that is 0.60 ÷ 0.40 = 1.5, or 3/2.

Why a market adds up to more than 100%

If you add up the implied probabilities of every outcome in one market, you will almost always get more than 100%. Take a two-way market priced at -150 and +130:

The extra 3.48 percentage points are the overround, the usual measure of the sportsbook's margin (the vig or juice), which the what the vig is guide measures in detail. Dividing each implied probability by the total takes it out again; fair odds shows the method and the no-vig calculator does it for you. OddsKeepr works out its fair prices the same way, from the median price across sportsbooks.

What implied probability is useful for

• Comparing prices. A lower implied probability for the same outcome means a better price for you. +150 (40%) pays more than +130 (43.48%).
• Knowing your break-even rate. A price's implied probability is how often a bet at that price has to win just to break even over time. At -110 that is 52.38%.
• Measuring margin. As in the table above, the total across a market shows the margin built into its prices.
• Thinking about value. If an estimate of a chance differs from the implied one, the expected value guide shows how to put a number on the gap. Any estimate can be wrong, and even a well-founded one does not make a single bet more likely to win.

Implied probability describes a price, not the future. It never tells you what will happen.

Betting always carries a risk of losing money, so if you bet, set a limit you are comfortable with and check that the sportsbook is licensed where you are. If gambling stops feeling like entertainment, free and confidential help is listed for every country under where to get help.