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Expected Value Calculator

Compute the expected value of any wager

How it is calculated

The win probability is entered as a percentage from 0 to 100 and converted to p = prob ÷ 100. The expected value is EV = p × win − (1 − p) × loss, where win is the amount you gain if the bet wins and loss is the amount you give up if it loses. The result is the average profit per bet over many repetitions.

Enter the loss as a positive number: the tool subtracts it itself, so typing a negative loss would add to the result instead. Probabilities outside 0 to 100 give no result. A negative EV is shown with the minus sign after the currency symbol, for example -$49.20. The tool handles one win outcome and one loss outcome; it does not model several payouts, taxes, fees or the effect of betting a large share of your bankroll.

Worked example

A bet wins 40% of the time. A win pays 150 and a loss costs 50.

p = 40 ÷ 100 = 0.4, so the loss probability is 0.6. Win part: 0.4 × 150 = 60. Loss part: 0.6 × 50 = 30. EV = 60 − 30 = $30.00 per bet. Over 100 identical bets you would expect about $3,000 of profit, though any single bet either wins 150 or loses 50.

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Common mistakes

  • Entering the probability as a decimal. Type 40 for 40%, not 0.4; 0.4 is read as 0.4% and gives a large negative value.
  • Entering the loss as a negative number. The loss is the amount lost, as a positive figure; a negative value turns the loss into a gain.
  • Entering the total returned on a win, including the stake, as the win amount. Use the profit only, since the stake is counted in the loss.
  • Using a probability implied by odds without removing the bookmaker's margin. The implied figure overstates the real chance.
  • Treating a positive EV as a guaranteed result. It describes the average over many bets; short runs vary widely.

Sources

About this calculator

Expected value combines every possible outcome of a wager weighted by its probability, computed here as EV = P(win) × amount won − P(lose) × amount lost; a positive EV means the bet is profitable on average over many repetitions, while a negative EV means it loses money in the long run even if any single try can still win.

Poker players and sports bettors use expected value to separate genuinely favorable bets from lucky short-term wins, since a single win says nothing about whether a bet was mathematically sound. Actuaries and insurers use the same principle in reverse to price policies profitably, and decision theorists apply it more broadly to any choice involving uncertain payoffs, from business investments to everyday risk decisions.

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Comments (1)

  • Editorial team

    Use it to find the break-even point. With a win of 150 and a loss of 100, a 40 percent chance gives exactly 0, since the break-even probability is loss divided by win plus loss. At 50 percent the value is 25. Enter the loss as a positive amount. A positive value describes the long-run average, not what any single attempt will do. What decision are you weighing?

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