How do you calculate expected value on a bet?

Multiply your profit if the bet wins by the chance of winning, then subtract your stake multiplied by the chance of losing. At +150 with a 45 percent chance, a $100 bet gives 0.45 x $150 minus 0.55 x $100, which is +$12.50.

What is break-even probability?

It is the chance an outcome needs in order for a price to be worth exactly what it costs, calculated as 1 divided by the decimal odds. Odds of +150, or 2.50, break even at 40 percent.

Does positive expected value mean I will win?

No. Expected value is an average across many repeated bets. A positive EV bet can lose many times in a row, and a single bet says nothing about whether the estimate behind it was right.

Where should the true probability come from?

Most bettors take a sharp sportsbook's price and remove the margin with a no-vig calculation, then use that as the probability. Guessing at probabilities tends to produce edges that are not there.

Expected Value Calculator: Is This Bet Worth It?

Expected value is an average over many repetitions, not a forecast for one bet. A positive number can still lose several times in a row.

How expected value works

Expected value weighs what you win against what you lose, by how often each happens. Multiply your profit by the chance of winning, subtract your stake multiplied by the chance of losing, and the result is what the bet is worth on average.

At +150 with a 45 percent chance, a $100 bet wins $150 nearly half the time and loses $100 the rest. That comes to +$12.50 per bet on average, or 12.5 percent of the stake.

The break-even number

Every price has a chance it needs in order to break even, and that is simply 1 divided by the decimal odds. At +150, or 2.50, the number is 40 percent. Anything above that is positive EV, anything below is negative, so the whole question becomes whether your estimate beats it.

Where the estimate comes from

This is the hard part, and it is where most EV betting goes wrong. Guessing produces confident nonsense. The usual approach is to take a sharp sportsbook’s price, strip the margin out with a no-vig calculation, and use that as the probability, on the theory that a tightly priced book is close to right.

Once you have an edge worth backing, Kelly handles how much to stake. And if you would rather not rely on an estimate at all, arbitrage works from the prices alone. Our guide on closing line value covers how to tell whether your estimates are any good.

Expected value calculator

Positive EV starts with a real price

How expected value works

The break-even number

Where the estimate comes from