Expected Value Calculator for Any Betting Odds Price

How expected value works

Expected value is the average result of a bet if it could be repeated many times at the same price with the same true probability. It has two terms. The first is how often you win multiplied by what you win. The second is how often you lose multiplied by what you lose. Subtract the second from the first and the answer is the expected value per bet.

At +150 a $100 bet wins $150 and loses $100. If it wins 45% of the time, the first term is $67.50 and the second is $55.00, so the expected value is $12.50. That is $12.50 per bet on average across a long run, not $12.50 on the next one. The next one pays $150 or costs $100 and nothing in between.

The break-even rate is the other half of the picture. It is the implied probability of the price, and it is the rate at which expected value is exactly zero. At +150 that is 40%. Any estimate above 40% gives a positive figure, any below gives a negative one, and the size of the gap drives the size of the number.

The number this calculator cannot supply

Everything above rests on the probability, and the probability comes from you. There is no model here, no data feed, no rating system. You type in how often you think something happens and the arithmetic prices it. If that estimate is off by five points the expected value is wrong by a wide margin, and it will still be displayed to the cent, looking exactly as authoritative as a correct one.

This is worth stating because expected value is the most misused figure in betting. A confident probability estimate with no track record behind it produces confident arithmetic and no information. The honest use is comparative: run several prices against the same estimate and see which one the market is charging least for, or run the same price against a range of estimates and see how quickly the answer flips sign.

That second test is the more revealing one. A bet that stays positive across a plausible range of probabilities is different from one that turns negative if your number is two points optimistic. The calculator makes that fragility visible in about ten seconds, and it is a better question than what the expected value happens to be at one estimate.

Reading the fair price line

The last output converts your probability back into a price. If you think something happens 45% of the time, the fair price for that view is +122. Seeing your own opinion expressed in the same units as the market's is usually more informative than a dollar figure, because it makes the disagreement concrete: the market says +150 is generous enough, you say the true price is +122, and the distance between them is what you are being paid for the view.

It also exposes how small the disagreements usually are. Five percentage points sounds like a lot until it is converted to a price, and a handful of points is often the difference between a bet worth making and one worth passing. Prices move in units far smaller than most people's confidence in their own estimates.

One limitation applies to every figure on this page. Expected value says nothing about variance. A positive number describes the centre of a distribution, not its width, and the width is what decides whether a run of results feels like anything at all. A string of losses is entirely consistent with a positive expected value, and no amount of arithmetic on this page changes that. If the question is how much to stake rather than whether a price is fair, the bankroll calculator answers it through risk of ruin instead, which is the right tool for a different question.

A last point about the sign of the answer. Because the market price already contains the book’s margin, the break-even rate is always worse than the fair probability of the outcome. On a standard spread the fair rate is 50% and the break-even rate is 52.38%, so an estimate that matches the market exactly still produces a negative expected value. Getting to zero means being right about something the price is not; getting above it means being right by more than the margin. That is a higher bar than it looks, and it is why the figure comes out negative far more often than positive.