Calculator

Implied Probability Calculator

About this calculator

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

Every price is a percentage wearing a disguise. This converts it in both directions.

Implied probability is a betting price restated as a percentage: how often the bet has to win just to break even. It describes the price, not the game, and the venue’s vig is still inside it.

What it does and does not tell you

Implied probability is the win rate a bet has to clear for the price to break even. It is a fact about the price, not a forecast about the game.

It also carries the venue's margin, which is why both sides of a real market add up to more than 100%. To get an honest probability out, you have to take that margin out first.

Same number, two names. The implied probability of a price and its break-even win rate are one figure looked at from opposite ends.

The reverse: a probability into a price

Backwards, the same arithmetic answers a different question: what price breaks even at a given win rate. That is the fair price for that probability, no margin attached.

Want more math?the Nerd Corner

From decimal odds it 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 backwards, a probability becomes 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, 0 to 1. Vig-inclusive: a break-even rate, not an estimate of the outcome.
$p$ : a probability you supply, used in reverse to produce the fair price that breaks even at exactly 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.

Implied probability is a vig-inclusive number

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

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

Mutually exclusive, exhaustive outcomes sum to 100%. This pair sums to 104.76%, so neither is a probability: both are inflated by the same margin. That 4.76-point surplus is the overround, the book’s edge on the market.

Rescaling the pair back to 100% leaves the fair, no-vig probabilities: on a symmetric −110 market, exactly 50% / 50%. Same engine as the no-vig calculator:

Two numbers, two jobs. 52.38% is what the price demands; 50.00% is what the market estimates once its margin is out. Comparing a de-vigged probability at one venue against a raw one at another invents edge out of the vig alone. The vig calculator measures that hold.

Also the break-even win rate

Same number, second name: the probability a price implies is 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}

A −110 bettor needs 52.38% to tread water; a +150 bettor needs 40%. A win rate means nothing without its price: 55% at −150 loses money, 45% at +150 makes it. Break-even win rate carries that further.

Conversion table

Common prices and the probability each demands.

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

All five formats, fractional included, are on the odds converter.

Implied probability on a prediction market

Event contracts remove the conversion: a Kalshi contract settles at $1 or $0, so one trading at 52¢ is a 52% market.

A fee replaces it, $0.07 \times C \times P \times (1-P)$ for a standard taker, rounded up to the cent, which lifts 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\%

Implied probability 52.00%, break-even 53.75%. The fee plays the part the vig plays at a book. The Kalshi fee calculator runs the full schedule.

Implied probability outside sports

Any fixed payout implies a probability, which is what makes house edge computable where nobody posts odds. An even-money roulette bet on an American wheel implies 50% against a true 47.37%; blackjack insurance pays 2 to 1, implying 33.33% against roughly 30.84%. The gap is the operator’s margin, worked through on roulette, blackjack, craps, slots and keno.

Common mistakes

Averaging implied probabilities across books. Averaging vig-inclusive numbers averages the vig too. Each venue’s pair is de-vigged first, then pooled. See 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 rather than a vig one, and at 5¢ the fee is 6.7% of the money at risk.

Check this number yourself

One function in the MIT-licensed teachersbettextbook; the overround is another:

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. More: open source.

Implied probability is the pivot the rest turns on: de-vigging cleans it, expected value compares two, Kelly sizes the gap, closing line value grades it afterwards.

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.