How this calculator works
Expected value weights each possible outcome by its probability and adds the results. For a simple win-or-lose decision, the winning branch contributes the chance of winning multiplied by the profit, and the losing branch contributes the chance of losing multiplied by the loss. A positive expected value means the decision makes money on average; a negative one loses money on average. It says nothing about a single hand, because variance can produce a win from a bad decision or a loss from a good one. The break-even chance is the win probability at which the expected value is exactly zero: if you win more often than that, the call is profitable.
Formula
expected value = chance to win x profit if you win - chance to lose x amount lost. With a two-outcome decision the chance to lose is 1 minus the chance to win. break-even chance = loss / (profit + loss).
Worked example
A 30 percent chance to win $200 against a 70 percent chance to lose $100 has an expected value of 0.30 x 200 - 0.70 x 100 = 60 - 70 = -$10. The call loses $10 on average, so folding is better if those are the only options. The break-even chance is 100 / (200 + 100) = 33.33 percent: at a 33.33 percent win chance the expected value is zero.
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Frequently asked questions
Does positive EV mean I will win this hand?
No. Expected value is a long-run average. A positive EV decision can lose the current pot, and a negative EV decision can win it. The point of using EV is to make the same good decision repeatedly, not to predict one result.
Should I include the money already in the pot?
Use the amount you can still win and the amount you must still put in. Money already committed is sunk: it belongs to the pot, not to you. The profit if you win is the pot you collect minus the call you make now, and the loss if you lose is the call itself.
What about ties?
A tie returns your share of the pot, which is usually close to breaking even. For a precise calculation, split the outcome into win, tie and lose and weight all three. This page uses a simple two-outcome model, which is accurate when ties are rare.
How does this relate to pot odds?
Pot odds compare the call you must make with the pot you can win and give the break-even chance directly. This page goes a step further by letting you enter any win chance and see the money expectation. If your estimated chance exceeds the break-even chance shown here, the call has positive expected value.