Expected Value Calculator

In short Expected value is the sum of each outcome multiplied by its probability — a weighted average of what happens. A bet that wins 10 one time in ten and loses 1 the other nine times has an expected value of +0.10 per play, so it is profitable in the long run. What that number does NOT tell you is anything about a single play, and it is often a value that cannot actually occur: a coin flip paying +1 or −1 has an expected value of exactly 0, which is not a possible result of any flip. That is why the standard deviation is printed beside it. Two bets with the same expected value and very different spreads are not the same bet, and the spread decides how long the long run takes to arrive. The average of n plays has a standard deviation of σ divided by the square root of n, so a high-variance edge needs a great many repetitions before the observed result resembles the expectation. And a positive expected value with a large spread can still ruin you before that happens — the gap between "profitable on average" and "survivable" is exactly what bankroll management exists to close. Probabilities can be entered as percentages, decimals or raw weights; if they do not sum to 1 they are scaled, so 10 and 90 mean the same as 0.1 and 0.9.