Implied Probability Calculator

By Alex Thornton · author of the MIT-licensed teachersbettextbook library · Last reviewed 24 July 2026

A price is a percentage in disguise. This converts it — both directions — and then says the part most calculators leave out: that percentage still has the house’s cut inside it.

Implied probability is a posted price restated as a percentage: the win rate a bet has to exceed for the price to break even. It is a property of the price rather than a forecast of the event, and it carries whatever margin the venue built in, which is why the two sides of a market always sum to more than 100%.

From decimal odds the conversion is one division. From American odds it splits by sign:

q = \dfrac{1}{d}, \qquad q = \dfrac{100}{100 + m}\ \ (m > 0), \qquad q = \dfrac{|m|}{|m| + 100}\ \ (m < 0)

and running it backwards turns a probability into the price that implies it:

d = \dfrac{1}{p}, \qquad m = -\dfrac{100\,p}{1 - p}\ \ (p \ge 0.5), \qquad m = \dfrac{100\,(1 - p)}{p}\ \ (p < 0.5)

where:

$m$ — the posted American moneyline, unitless (−110, +240).
$d$ — decimal odds: total return per $1 staked, stake included.
$q$ — the implied probability of the posted price, between 0 and 1. Vig-inclusive: it is the break-even rate, not an estimate of the outcome.
$p$ — a probability you supply, used in the reverse direction to produce the fair price that would exactly break even at that rate.

Worked example — the price in the form below

At −110 a bet risks $110 to win $100, so a win returns $210 — the stake back plus the profit:

q = \dfrac{110}{110 + 100} = \dfrac{110}{210} = 52.38\%

The bet has to win 52.38 times in 100 to break even — not 50. Those extra 2.38 points above even money are the sportsbook’s margin on that side of the market.

The reverse: a probability into a price

The same arithmetic run backwards answers a different question — what price would exactly break even at a given win rate. That is the fair price for that probability, with no margin attached.

Why −110 implies 52.38%

The arithmetic is short enough to do in full. A $110 stake at −110 returns $210 when it wins: the $110 back plus $100 profit. Over a long run of identical bets at win rate $q$ , the money in has to equal the money out:

110 = q \times 210 \quad \Longrightarrow \quad q = \dfrac{110}{210} = 0.5238

Which is the same as the general rule, since decimal odds here are $210/110 = 1.909$ and $1/1.909 = 0.5238$ . Both routes land on 52.38%.

The number is often written as 52.4%. The extra digit matters more than it looks: 0.025 probability points is exactly what separates decimal 1.91 from −110 at two venues quoting in different formats, and edge estimates are built by subtracting numbers of that size from each other.

Implied probability is a vig-inclusive number

This is the part that most implied probability calculators stop short of, and it is the part that changes what the number means.

Both sides of a standard −110 / −110 market imply 52.38%. Added together:

q_A + q_B = 52.38\% + 52.38\% = 104.76\%

Probabilities of mutually exclusive, exhaustive outcomes sum to 100%. This pair sums to 104.76%, so at least one of the two is not a probability. In fact neither is: both are inflated by the same margin. The 4.76-point surplus is the overround, and it is the sportsbook’s built-in edge on that market.

Removing it — rescaling the pair back to 100% — leaves the fair, no-vig probabilities. On a symmetric −110 market that is exactly 50% / 50%. The panel below runs that step on any two-sided price, using the same engine as the no-vig calculator:

Two numbers, two jobs. 52.38% is what the price demands. 50.00% is what the market, stripped of its margin, is estimating. Comparing a de-vigged probability from one venue against a raw implied probability from another invents edge out of the vig alone — a 2.38-point mirage on this market, and larger on a market with a heavier hold. The vig calculator measures that hold directly.

Implied probability is also the break-even win rate

Same number, second name. The probability a price implies is exactly the rate at which betting it forever returns zero:

\mathrm{EV} = q \cdot b - (1 - q) = 0 \quad \text{when} \quad q = \dfrac{1}{b + 1} = \dfrac{1}{d}

So a −110 bettor needs 52.38% to tread water, and a +150 bettor needs 40%. This is why comparing raw win rates across bettors is meaningless without their prices: 55% at −150 is losing money, and 45% at +150 is making it. The break-even win rate calculator takes that further, into how many bets it takes before a record means anything.

Conversion table

Common prices and the probability each one demands.

American	Decimal	Implied probability	Break-even record	Contract price
−300	1.333	75.00%	75 in 100	75.0¢
−200	1.500	66.67%	66.7 in 100	66.7¢
−150	1.667	60.00%	60 in 100	60.0¢
−120	1.833	54.55%	54.5 in 100	54.5¢
−110	1.909	52.38%	52.4 in 100	52.4¢
+100	2.000	50.00%	50 in 100	50.0¢
+120	2.200	45.45%	45.5 in 100	45.5¢
+150	2.500	40.00%	40 in 100	40.0¢
+200	3.000	33.33%	33.3 in 100	33.3¢
+300	4.000	25.00%	25 in 100	25.0¢

Full five-format coverage, including fractional odds, is on the odds converter.

Implied probability on a prediction market

Event contracts make the conversion disappear. A Kalshi contract settles at $1 if the event happens and $0 if it does not, so a contract trading at 52¢ is a 52% market — no formula required.

What replaces the conversion is a fee. The standard Kalshi taker fee is $0.07 \times C \times P \times (1-P)$ , rounded up to the cent, which pushes the break-even above the purchase price:

A 52¢ contract, 100 lots, taker

\text{fee} = \lceil\,0.07 \times 100 \times 0.52 \times 0.48\,\rceil_{\text{cent}} = \$1.75

p_{\text{break-even}} = \dfrac{\$52.00 + \$1.75}{100} = 53.75\%

The implied probability is 52.00%; the break-even is 53.75%. On an exchange the price and the break-even are different numbers, in the same way that a sportsbook’s price and its fair value are different numbers — the fee replaces the vig. The Kalshi fee calculator runs the full schedule.

Where implied probability shows up outside sports

Any fixed payout implies a probability, which is what makes house edge computable in games where nobody posts odds at all.

Roulette. An even-money bet on an American wheel pays 1 to 1, implying 50%. The actual chance is 18 in 38, or 47.37%. Expected value on a $1 bet is $2p - 1 = -5.26\%$ — twice the 2.63-point gap, because every point is a win gained and a loss avoided. The roulette page has the full table.
Blackjack. Insurance pays 2 to 1, implying 33.33%. With only the dealer’s ace exposed in an eight-deck shoe the actual chance is 128 ten-value cards among 415 unseen, or 30.84%. Blackjack strategy works through it.
Craps. The pass line and the odds bet behind it have famously different implied-versus-true gaps; craps odds shows both.
Slots and keno. The payout table implies a probability the game never states. Slot machine odds and keno odds reconstruct it.

The arithmetic is identical in every case: a payout implies a break-even probability, and the gap between that and the real chance is the operator’s margin.

Common mistakes

Reading it as a forecast. 52.38% at −110 is what the price demands. The market’s own estimate, after its margin comes out, is 50%.
Expecting the two sides to sum to 100%. They never do at a real book. The surplus is the hold, and it is the only reason a book runs the market.
Mixing de-vigged and raw numbers. Comparing a 58.94% fair probability against a 60.32% raw implied probability produces a 1.4-point gap made entirely of vig.
Averaging implied probabilities across books. Averaging vig-inclusive numbers averages the vig too. Each venue’s pair is de-vigged first, then pooled — the method is on the methodology page.
Rounding to whole percentages. 52% and 52.38% are different prices: −108 and −110. On repeated bets that difference is the whole margin.
Assuming an exchange price needs no adjustment. It needs a fee adjustment instead of a vig adjustment, and at a 5¢ price the fee is 6.7% of the money at risk.

Check this number yourself

Implied probability is one function in the MIT-licensed teachersbettextbook package, and the overround is one more:

pip install teachersbettextbook

>>> from teachersbettextbook import moneyline_to_prob, overround, devig
>>> moneyline_to_prob(-110)
0.5238095238095238
>>> overround(-110, -110)       # the two sides sum to 104.76%
0.04761904761904767
>>> devig(-110, -110, method='proportional')
(0.5, 0.5)

Same inputs, same digits, no account required. More on what is open and what is not: open source.

Implied probability is the pivot every other calculation turns on: de-vigging cleans it, expected value compares two of them, Kelly sizes the gap between them, and closing line value grades it after the fact. How to de-vig odds is the long-form version of the middle step.

Frequently asked questions

What is implied probability in betting?

Implied probability is a posted price restated as a percentage: the win rate a bet must exceed for the price to break even. It is a property of the price, not a forecast of the event, and it includes whatever margin the venue built into that price.

How do you calculate implied probability from odds?

From decimal odds it is 1 divided by the price. From American odds it is 100 / (100 + m) for a positive price and |m| / (|m| + 100) for a negative one. A prediction-market contract needs no conversion at all: its price in cents is already the probability in percent.

Why does −110 imply 52.38%?

At −110 you risk $110 to win $100, so the bet returns $210 when it wins. Break-even requires winning often enough to cover the $110 risked out of that $210: 110 ÷ 210 = 52.38%. The extra 2.38 points above an even-money 50% is the sportsbook’s margin on that side.

Do implied probabilities add up to 100%?

No, and that is the point. Both sides of a −110 / −110 market imply 52.38%, which sums to 104.76%. The 4.76 points of surplus is the overround — the sportsbook’s margin. Removing it, which is what a no-vig calculation does, is the step that turns a price into an estimate.

Is implied probability the same as the chance of winning?

No. It is the break-even rate the price demands, inflated by the venue’s margin. A market’s actual estimate is closer to the de-vigged probability, and even that is an estimate rather than a fact. Comparing a de-vigged probability from one venue against a raw implied probability from another manufactures edge that does not exist.