Expected Value Calculator

Expected value is the average result of a bet across every possible outcome, and it is the only defensible reason to place one. It has nothing to do with whether this particular bet wins.

Give the calculator a price and your own honest win probability. It returns what the bet is worth per dollar risked, the win rate the price requires, and how far your opinion sits from that requirement.

The Formula

Expected value is the probability of winning times the amount won, minus the probability of losing times the amount lost.

EV = (p × profit) − ((1 − p) × stake)

Worked example. You rate an outcome at 55% and it is priced at -110, so $100 risked wins $90.91.

EV = (0.55 × 90.91) − (0.45 × 100) = 50.00 − 45.00 = +$5.00

Every $100 risked returns $5 in expectation, a 5% return on turnover. Across a hundred such bets that is +$500, and across a season of them it is the entire difference between a winning bettor and a losing one.

The same opinion at a worse price. At -130, $100 wins $76.92.

EV = (0.55 × 76.92) − (0.45 × 100) = 42.31 − 45.00 = −$2.69

Identical view of the game, negative expectation. Nothing about the teams changed. This is why chasing a bet up through a worse number is so expensive: the opinion that justified it at -110 does not justify it at -130.

Edge In Probability Points

The dollar figure depends on your stake, so the portable measure is the gap between your probability and the break-even rate the price demands.

At -110 the break-even rate is 52.38%. A 55% estimate is +2.62 percentage points of edge. That is a strong, realistic number: professional bettors operate on two to four points, not on twenty.

Which is the uncomfortable part. If your process estimates probabilities to within three points — better than most — then a two-point edge is inside your own error bars, and the honest description is "no demonstrable edge" rather than "small edge". Require a disagreement bigger than your own measurement error before betting.

Pushes Change The Break-Even Rate

On a whole-number spread or total, a tie returns the stake. That is neither a win nor a loss, and it lowers the win rate you need.

The break-even rate becomes (1 − push probability) ÷ decimal price. At -110 with a 5% chance of a push, that is 0.95 ÷ 1.9091 = 49.76% instead of 52.38%. A 50% opinion is a small positive bet rather than a small negative one, purely because a slice of the outcomes gives your money back.

Push probability is not a guess to wave at: on an NFL game a spread of exactly 3 lands on the number roughly 9 to 10% of the time, while a spread of 7 is nearer 5%. Those are the key numbers, and they are the reason buying off 3 costs so much.

A Winning Bet Can Be A Bad Bet

Expected value and outcome are separate things, and holding them apart is the mental shift that distinguishes a bettor from a gambler.

Take a -400 favourite in a game you project at 75%. The price implies 80%. Profit on $100 is $25.

EV = (0.75 × 25) − (0.25 × 100) = 18.75 − 25 = −$6.25

Negative, and it wins three times out of four. A bettor placing that bet repeatedly feels successful nearly every week and loses money steadily. The reverse is just as true: a +250 underdog you rate at 33% has positive expectation and loses two times in three, so it feels wrong constantly while being correct throughout.

Because the feedback is this misleading, expectation has to be judged before the bet and never revised afterwards on the strength of the result. That is what closing line value is for in the short run, and once a bet clears this calculator, Kelly or a flat unit size decides how much of the bankroll it deserves.

Frequently Asked Questions