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EV calculator.
Expected value is what a decision is worth on average, made a thousand times. Two versions matter at the table: what a call is worth given your chance of winning, and what a bluff is worth given how often it gets through. Both are one line of arithmetic, and both are here with the working shown.
the calculator
your honest estimate, not a number you can look up
Expected value
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Break even point
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Over 100 spots like this
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the same numbers, spelled out
A flush draw facing a half pot bet is in the fields. It wins less than half the time and it makes money anyway, which is the whole idea in one example.
the two formulas
Both fit on one line.
A call is a purchase with two outcomes. You win the pot with probability p, and you lose what the call cost the rest of the time, so the value is p times the pot minus one minus p times the call. Nothing else belongs in that line, and in particular the money you already put in the pot does not, because it is not yours any more.
A bet has three. They fold and you take the pot, they call and you win the bigger pot with your equity, or they call and you lose your bet. Written out: f times the pot, plus one minus f times your equity times the pot plus twice the bet, minus the bet. Set that to zero with no equity at all and you get the break even fold percentage, which is the bet divided by the pot plus the bet.
Take the example in the fields. Calling 50 into 100 with a flush draw worth 35.0 percent is worth 2.50, and the break even point is 33.3 percent. You lose that pot roughly two times in three, and it is a call anyway, by a margin of 1.7 points. Over a hundred spots like it the difference is about 250, which is the only frame in which the number means anything. Notice how thin it is: get the equity wrong by two points and the edge is gone. If you want the price side of that same decision on its own, the pot odds calculator does it without the equity estimate.
break even points by bet size
These two columns are the whole of betting theory compressed into a table. The middle one is how often a bluff has to work; the right one is how much equity the person facing it needs to call. Choosing a size is choosing both of those numbers at once, which is why the size is a decision and not a habit.
| Bet size | A bluff has to work | They need to call |
|---|---|---|
| A quarter of the pot | 20.0% | 16.7% |
| A third of the pot | 25.0% | 20.0% |
| Half the pot | 33.3% | 25.0% |
| Two thirds of the pot | 40.0% | 28.6% |
| Three quarters of the pot | 42.9% | 30.0% |
| The size of the pot | 50.0% | 33.3% |
| Twice the pot | 66.7% | 40.0% |
both columns worked out at build time from the same two formulas the calculator uses
where the inputs come from
An EV is only as good as the equity you feed it, and that is the hard part. With a draw you can count it exactly: counting your outs gives the number straight from the deck, and the probability tables show what a flop typically does to a hand. With a made hand it is a judgement about what your opponent holds, and no calculator will do that for you.
The fold percentage in bluff mode is worse still: nobody can measure it in the moment. It is worth typing in the number you actually believe rather than the one that makes the bet look good, and then checking what would have to be true for the bet to break even. If a pot sized bluff needs 50 percent folds and you would guess forty, the bet is a loser and the table just told you so.
One more thing this arithmetic cannot see. It assumes you can absorb the swings, and a positive EV is worthless if a bad month takes your whole roll off the table. What a bankroll has to be for your win rate is a separate sum, and it is the one that decides whether you get to keep making these decisions long enough for them to pay.
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A positive EV is invisible for a long time.
Every number on this page is an average over a run of hands you have not played yet. The uncomfortable part is how long that run has to be before your results start to resemble it, and the answer is longer than almost anyone assumes.
questions about expected value
How do you calculate EV in poker?
Multiply each outcome by how often it happens and add the results. For a call it is one line: your chance of winning times the pot you win, minus your chance of losing times what the call costs. Calling 50 into a pot of 100 with 35 percent equity is 35 percent of 100 minus 65 percent of 50, which comes to 2.50.
What does a positive EV actually mean?
That the decision makes money if you keep making it, not that this particular hand will win. A call worth 2.50 loses the pot 65 percent of the time. Made a hundred times it is worth about 250, and that is the only sense in which it is profitable. Judging a call by whether the card came is the single most common way players talk themselves out of good decisions.
How often does a bluff need to work?
The bet size decides it, and nothing else. Betting half the pot needs to work 33.3 percent of the time, a pot sized bet 50.0 percent, and a quarter pot stab only 20.0 percent. That is why small bluffs are cheap and large ones are a commitment: you are setting your own break even point every time you choose a size.
What is the difference between EV and pot odds?
Pot odds tell you the break even point, EV tells you how far past it you are. They are the same arithmetic rearranged: pot odds ask what equity a price demands, EV asks what a given equity is worth at that price. Pot odds are quicker at the table; EV is better for comparing two different lines afterwards.
Should I include the money I might win later?
Only if it is genuinely likely to arrive. Implied odds are real, and they are also where wishful thinking hides. The honest test is whether your opponent has both a hand that can pay you and a stack deep enough to do it. If either is missing, the extra money is a story rather than a number.
Why does a winning decision still lose so often?
Because equity below fifty percent still makes money when the price is right. A flush draw calling a half pot bet is profitable and loses roughly two thirds of the time. That gap between being right and being paid is what a poker bankroll is for, and it is why results over a few hundred hands say almost nothing about how well you played.
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