The short version
Expected value (EV) is the average net result implied by a set of outcomes and their probabilities. For a wager with one win payout and one full-loss outcome, multiply the profit if you win by the chance of winning, then subtract the amount lost times the chance of losing.
The answer is an average under your assumptions. A positive EV does not mean a wager is likely to win, and a negative EV does not mean the next result must lose.
The formula
For a two-outcome wager, the calculation is:
The probabilities should add to 100% when the only possible results are a win and a loss. Odds formats describe payout; they do not supply your estimate of the true chance to win.
Work through the +140 example
Suppose you stake $100 at +140. A win earns $140 in profit, while a loss costs the $100 stake. If your estimated chance to win is 45%, your chance to lose is 55%.
Expected value is (0.45 × $140) − (0.55 × $100) = +$8. In this example, that is an expected net profit of $8 per $100 staked, or 8% of the stake, across many comparable wagers if the probability estimate holds.
Compare your estimate with break-even
At +140, the break-even probability is 41.67%. That comes from $100 divided by the $240 total return on a winning $100 stake. At exactly 41.67%, the expected value is zero before other costs. Above it, EV is positive under the estimate; below it, EV is negative.
Entering the odds’ own break-even probability as your win estimate will therefore produce an EV of about zero. To show a different result, you need a separate estimate of the true probability. The calculator cannot determine whether that estimate is sound.
Positive EV can still lose
In the +140 example, a 45% chance to win also means a 55% chance to lose. The wager can have positive expected value and still be more likely to lose than win. EV describes the average across many comparable outcomes; it does not predict the next one or guarantee the average will appear over a small sample.
Estimates can also be wrong. If your probability is too high, a result that looks positive on paper can actually be negative. Be conservative and make clear where the estimate came from.
Expected value applies to casino wagers too
Consider a $1 bet on black in European roulette. There are 18 black pockets and 19 non-black pockets out of 37. The bet pays 1-to-1 profit on a win and loses $1 otherwise.
Its EV is (18/37 × $1) − (19/37 × $1) = −$0.027, or about −2.70 cents per $1 bet. That is the same as a 2.70% house edge for this wager. A particular spin can still win; the expected loss describes the average over many spins under the same rules.
FadeIt’s expected value calculator can model one win payout and one loss amount. It can also be used for a binary casino wager when the chance and payout are known. For games with several different payouts, calculate each possible net result and weight it by its probability. OpenStax explains this probability-weighted method in more detail ↗
How EV relates to house edge and Kelly
House edge is a casino-focused way of describing a game’s expected cost as a share of the amount wagered. The house edge calculator applies that idea to common games and total wagers.
Kelly uses a probability estimate and a price to calculate a bankroll fraction when the estimate shows an edge. It does not create an advantage or verify the estimate. Read Kelly criterion, explained for how that sizing formula differs from expected value.
What this calculator includes
The calculator handles a single win outcome at fixed odds and assumes the full stake is lost on the other outcome. It does not include pushes, partial losses, commissions, taxes, or multiple payout tiers. Those cases need each possible outcome represented separately.
Use the expected value calculator to see the net average implied by your inputs, then read the result as a model of assumptions—not a promise about what will happen.