EV in poker: how to work out whether a play makes money

EV in poker stands for expected value: the amount a decision wins or loses on average if you could repeat it thousands of times. A call, a bet, a raise and a fold each have their own EV. A play with positive EV (+EV) makes money in the long run, a play with negative EV (−EV) loses it, and folding is the zero you measure everything else against.

The idea comes straight from probability theory, and the arithmetic is short. What makes EV useful is that it turns “I had a feeling” into a number you can check after the session. Below, you’ll find the formula, worked examples for calls, bluffs and all-ins, the tournament twist that changes the maths near the money, and quick versions you can use while a hand is still running.

What EV means (and what it doesn’t)

Think of EV as a long-run average. If a play has an EV of +$12, you won’t win exactly $12 the next time you make it. You’ll win the pot or lose your bet, but over a large number of identical spots the results average out to $12 a time.

• +EV: the play earns money on average. Making it again and again is how winning players win.
• −EV: the play loses money on average, even if it works this time.
• 0 EV: break-even. Folding is the standard example, because once you fold you put in nothing more and win nothing more.

A common mix-up treats EV as a chance of winning. It isn’t. A hand can win only 20% of the time and still be a profitable call, if the pot is big enough. Another can win 60% of the time and lose money, if winning pays little and losing costs a lot. Probability is only one of the two inputs; the other is how much money moves in each outcome.

EV is not how often you win. It’s how much you win on average, counting the times you lose.

The EV formula

Every EV calculation follows one rule: take each possible outcome, multiply what it pays by how often it happens, and add the results.

EV = (chance of outcome 1 × money won or lost) + (chance of outcome 2 × money won or lost) + …

Before the poker examples, here’s the rule on a coin. A friend offers a game: heads, you win $2; tails, you pay $1. Each side comes up half the time, so EV = 0.5 × $2 + 0.5 × (−$1) = +$0.50. You’d lose some flips and win others, but you’d make about fifty cents a flip.

In poker, most decisions have two outcomes, so the formula shrinks to:

EV = (chance you win × what you win) − (chance you lose × what you lose)

“What you win” means the money already in the pot plus your opponent’s bet, not counting your own call. “What you lose” is the amount you’re about to put in. Money you invested on earlier streets doesn’t count either way: it already belongs to the pot.

EV in different spots

The same formula covers every decision in a hand. What changes is where the chances come from: your cards against the opponent’s cards, how often the opponent folds, or both.

The EV of a call

Calls are the easiest place to start, because the chance of winning comes almost entirely from your cards. Here’s a turn spot with a flush draw:

Nine hearts complete your flush, and 46 cards are unseen, so you hit on the river 9 ÷ 46 = 19.6% of the time. If the opponent has a king, nothing else helps: a jack or a ten gives you a pair that still loses.

• You win: the $100 pot plus the $50 bet, $150 in total, 19.6% of the time.
• You lose: your $50 call, 80.4% of the time.
• EV of calling = 0.196 × $150 − 0.804 × $50 = $29.35 − $40.22 = −$10.87.

Each time you make this call you give away about eleven dollars on average, so folding is better. The break-even point is easy to find: you’re paying $50 to win a final pot of $200, so you need to win 50 ÷ 200 = 25% of the time. That matches what pot odds tell you, because pot odds are just EV with the answer set to zero.

Future streets can rescue the call. If the opponent will pay you more on the river when the flush comes in, that extra money goes into the “what you win” side. Here it would take about $56 more, on average, to bring the call up to break-even. Players call this implied odds. It cuts both ways: when your draw can complete and still lose to a bigger hand, you’re facing reverse implied odds, and the real EV is lower than the simple sum.

The EV of a bluff

A bluff has no showdown value. It wins when the opponent folds and loses the bet when he calls. That makes the calculation even shorter. On the river, the pot is $100 and you have nothing; you’re thinking about a $75 bet.

• If the opponent folds half the time: 0.5 × $100 − 0.5 × $75 = +$12.50.
• If he folds 35% of the time: 0.35 × $100 − 0.65 × $75 = −$13.75.

The break-even fold rate is the bet divided by the bet plus the pot: 75 ÷ 175 = 42.9%. Here’s that number for common bet sizes:

Bigger bluffs need more folds, but they also get more folds, because hands that would call a small bet give up against a large one. The right size depends on how the opponent reacts to each, which is where reads and bluffing strategy come in.

The EV of a semi-bluff

A semi-bluff combines the two previous cases. You bet with a draw, so you win when the opponent folds and you also win some of the time when he calls. Here both stacks started the flop with $100, and you’re up against top pair:

With the nut flush draw and an ace that pairs to win, A♥ J♥ has 45.6% equity against K♣ Q♦ with two cards to come.

• If the opponent folds, you win the $40 pot and his $20 bet: +$60.
• If he calls, the pot holds $240 and you win 45.6% of it: 0.456 × $240 − $100 = +$9.33.
• If he folds 30% of the time: 0.3 × $60 + 0.7 × $9.33 = +$24.53.

Even when he never folds, the shove makes money, because 45.6% is more than the 41.7% you need to break even (100 ÷ 240). Every fold on top of that adds profit. This is why draws are the favourite hands for aggression: they have two ways to win. Our guide to fold equity works through more of these spots.

The EV of a call against a range

The examples so far assume you know what the opponent holds. At the table you don’t, so you estimate a range: all the hands he could have, weighted by how many card combinations each one has. On the river, the pot is $100 and the opponent bets $100. Your hand beats his bluffs and loses to everything else.

Say his betting range has 20 combinations: 12 strong hands and 8 bluffs. Calling $100 to win $200 needs 100 ÷ 300 = 33.3%. Bluffs make up 8 ÷ 20 = 40% of his range, so:

EV of calling = 0.4 × $200 − 0.6 × $100 = +$20.

Take away half the bluffs and the answer flips. With 4 bluffs out of 16 combinations (25%), the call is worth 0.25 × $200 − 0.75 × $100 = −$25. The cards in your hand didn’t change, only your read of his range. Counting combinations is covered in our guide to equity, and your own cards can remove some of his combinations, which is the idea behind blockers.

The EV of a preflop all-in

Preflop all-ins show the range effect even more clearly. In a cash game with 100-big-blind stacks, you open to 2.5 big blinds from the cutoff with A♠ K♦, and the big blind moves all-in.

Calling costs 97.5 more big blinds and makes a final pot of 200.5 (the folded small blind left 0.5 behind). You need 97.5 ÷ 200.5 = 48.6% equity. Against single hands, A♠ K♦ has about 42.7% against queens, 44.5% against sevens and 74.1% against ace-queen. But the shover won’t show you one hand, so what matters is his whole range:

Against a tight player who only shoves premiums, ace-king is a fold. Against a wider shover, calling is worth 14 big blinds. Notice also what the table ignores: the 2.5 big blinds you opened with. That money is already in the pot, and counting it as “yours to protect” is a classic way to talk yourself into −EV calls.

EV in tournaments: chips are not money

Everything above measures EV in chips or cash, and in a cash game chips are money. In a tournament they aren’t, because prize money is paid by finishing position, not by chip count. Doubling your stack doesn’t double your share of the prize pool, while busting takes your share to zero. The model players use to turn chips into money is called ICM, the Independent Chip Model.

To see what that does to a decision, take four players left in a small tournament that pays $50, $30 and $20, so the bubble is one elimination away. All four have 2,500 chips, so each holds a quarter of the chips and, by ICM, a quarter of the remaining money: $25. An opponent moves all-in and you must decide whether to call with a hand that wins 55% of the time.

• In chips, the call is +250 on average: 55% of the time you double to 5,000, 45% of the time you lose 2,500.
• In money, winning moves you from $25 to $38.33, and losing sends you out in fourth with nothing. EV of calling = 0.55 × $38.33 = $21.08. Folding keeps your $25, so the call loses about $3.92.

To make this call profitable in money, you’d need to win about 65% of the time, not 50%. That gap is why players tighten up near the money, and why the shorter stacks get pushed around on the bubble. Early in a big field, when the pay jumps are far away, chip EV and money EV are close, and you can play mostly by chips. The closer you get to a pay jump, the more the money version should decide. Our guide to tournament strategy covers the stages.

ICM assumes every player is equally skilled and ignores future blinds. It’s still the standard model for final tables and bubbles, and most tournament study tools are built on it.

EV and variance: why results lie

A +EV decision guarantees nothing about the next hand, the next session or even the next month. Variance is the spread of real results around the expected one, and in poker it’s wide. The chart below shows how wide it can be when the decisions are perfect:

Each simulated player makes the same +$10 decision 500 times, so each one’s EV is +$5,000. Their actual results ended anywhere from +$2,800 to +$12,000, and one of them was $1,600 down at his worst point before recovering. Nobody made a mistake. That’s what the luck of the cards looks like over a few hundred big pots.

This is why most tracking software can show all-in adjusted winnings, also called the EV line. When an all-in happens before the river, the software replaces what you actually won with your equity share of the pot. If your real results sit well below that line, you’ve run under expectation; if they sit above it, you’ve been lucky. GGPoker’s built-in stats tool, PokerCraft, draws this line for its players. Our article on variance explains how big these swings get and how to live with them.

Review hands by the decision, not the result. If a call was +EV with the information you had, it was a good call, even when the river went the other way.

Using EV at the table

You won’t multiply decimals in the middle of a hand, and you don’t need to. At the table, EV comes down to one comparison: the price of a play against how often it works. Here are three quick versions, one for each kind of decision.

Facing a bet with a draw. On the turn the pot is $60 and the opponent bets $15. You’re paying $15 to win a $90 pot, so you need 15 ÷ 90 = 16.7%. Multiply your outs by 2 for a quick estimate of one card to come. With a flush draw, 9 × 2 ≈ 18%: call. With a gutshot, 4 × 2 ≈ 8%: fold, unless you’re sure to win a lot more when you hit. The method behind the shortcut is in our guide to counting outs.

Thinking about a bluff. On the river the pot is $80 and you consider a $40 bet. It needs to work 40 ÷ 120 = 33% of the time, one time in three. So the question to ask is simple: will this player fold one time in three here? Against someone who never folds a pair, no. Against a player who checked twice with a hand that’s weak and hopes to see a free showdown, often yes.

Facing a river bet with a medium hand. The pot is $100 and the opponent bets $50. You need 50 ÷ 200 = 25%. Instead of guessing, list what he could have. If you can name three value hands for every bluff, you’re right at break-even; if bluffs are more common than that, call.

After the session, go back to the hands that felt close and do the full calculation. A few weeks of that and your estimates at the table get noticeably better.

Common EV mistakes

Most EV errors aren’t arithmetic. They come from feeding the formula the wrong inputs:

Judging a play by how the hand ended. A call that lost can be +EV and a bluff that worked can be −EV; one result says almost nothing about either.

Counting money you’ve already put in. Chips from earlier streets belong to the pot. Only the amount you’re about to add goes on the “lose” side.

Putting the opponent on one hand. Calculate against his range: one call can be −20 or +14 big blinds depending on how wide he plays.

Treating tournament chips like cash near the money. A call that wins chips on average can still cost you prize money on a bubble or a final table.

Ignoring future streets is the last big one. Simple EV sums assume the hand ends after this decision; when there’s more betting to come, implied odds can make a call better than the sum shows, and reverse implied odds can make it worse. Our guide to value betting covers the other side: getting paid when you’re the one with the best hand.

EV in poker FAQ