Poker Expected Value (EV) Calculator

Expected value, the foundation of winning poker

Expected value (EV) is the most important concept in poker math. It tells you whether a decision is profitable in the long run, regardless of what happens in any single hand.

The reality of poker:

• Any individual hand outcome is random
• Even the best decision can lose
• Even the worst decision can win
• Skill compounds over thousands of hands
• EV is the only metric that matters

Winning poker is not about winning every hand. It is about consistently making decisions with positive expected value. The math is the same whether you’re playing $1/$2 NL Hold’em at the local card room or $25/$50 online.

The EV formula

Expected Value = (Probability of winning × Amount won) − (Probability of losing × Amount lost)

For a call decision:

EV = (Equity × Amount won) − ((1 − Equity) × Amount lost)

Where:

• Equity = your probability of winning the hand (decimal, 0 to 1)
• Amount won = total you win if you win (typically pot + opponent’s contribution)
• Amount lost = your call/bet amount

Worked example

A flush draw on the turn:

• Current pot: $100
• Opponent bets: $25
• Your equity to hit flush: 19.6% (9 outs × 2.2%)
• To continue, you must call $25

EV calculation:

• Amount won if you hit: $100 (pot) + $25 (their bet) = $125
• Amount lost if you miss: $25 (your call)
• EV = (0.196 × $125) − (0.804 × $25)
• EV = $24.50 − $20.10
• EV = +$4.40

This is a profitable call long-term. Over 1,000 such situations, you’d win an average of $4.40.

Pot odds and break-even equity

Break-even equity is the point where the EV formula returns exactly zero. Set it to zero and solve:

0 = E × (Amount won) − (1 − E) × (Amount lost)

Equity needed = Call ÷ (Amount won + Call)

For the example above: $25 ÷ ($125 + $25) = $25 ÷ $150 = 16.7%

Your 19.6% clears that comfortably, which is why the EV came out at +$4.40. Check it the other way if you like: at exactly 16.7%, EV = (0.167 × $125) − (0.833 × $25) = $20.83 − $20.83 = $0.

The denominator is the trap. It is the whole pot AFTER your call, meaning everything you would win plus the chips you are putting in. Use the pot before your opponent’s bet and you will get 20% here instead of 16.7%, a threshold that is nearly a fifth too high and will have you folding profitable draws.

The quick sanity check: if a number you are calling “break-even” gives a non-zero EV when you run it through the EV formula, it is not the break-even. At 20% in this spot, EV = $25 − $20 = +$5.00, which is a long way from zero.

Pot odds as a ratio. The same thing said the way players say it at the table: you are risking $25 to win $125, so the pot is laying you 5-to-1. Turn a ratio of X-to-1 into required equity with 1 ÷ (X + 1), so 5-to-1 needs 1/6 = 16.7%. Same number, same idea.

If your equity exceeds the threshold, call. If it is below, fold, unless implied odds change the amount you stand to win.

Common pot sizes and required equity

The fractions are of the pot before the bet, which is how bet sizes are always quoted. These percentages are the minimum equity needed to call profitably.

Common hand equities

Useful equity numbers to memorize:

Suited draws on turn (one card to come):

• Flush draw (9 outs): 19.6%
• Open-ended straight (8 outs): 17.4%
• Inside straight (4 outs): 8.7%
• Pair + flush (3 outs): 6.5%
• Two pair to set: 4.3%

Suited draws on flop (two cards to come):

• Open-ended straight + flush (15 outs): 54.1%
• Flush draw alone (9 outs): 35%
• Open-ended straight alone (8 outs): 31.5%
• Inside straight (4 outs): 16.5%
• Two pair (4 outs): 16.5%

Common pre-flop equities:

• AA vs random hand: 85%
• AA vs KK: 81%
• AA vs underset: 80%
• AKs vs QQ: 46%
• AK vs QQ: 43%
• Pocket pair vs underpair: 80%

Implied odds, looking past the current street

Implied odds extend EV calculation to consider future betting:

Implied odds = Money you expect to win on later streets if you hit

If you call $25 with a flush draw expecting to win $50 more if you hit:

• Effective amount won: $125 + $50 = $175
• Break-even equity: $25 / ($25 + $175) = 12.5%

This makes more draws profitable to chase. But:

• Don’t overestimate implied odds
• Consider opponent skill and tendencies
• Stack sizes matter (can’t win more than you have)

Reverse implied odds

The opposite scenario: when hitting your draw still loses or wins less than expected:

• You hit a non-nut flush, opponent has higher flush
• You make middle pair, opponent has top pair already
• You complete a straight, but board pairs

Reverse implied odds reduce effective amount won. Skilled players factor this in.

EV in different decisions

EV applies to all poker decisions:

Calling: EV = (Equity × Amount won) − (Equity-lost × Call)

Betting/Raising: EV = (Fold equity × Pot) + (Equity × Amount won when called) − (Equity-lost × Bet when called)

Bluffing: EV = (Fold equity × Current pot) − ((1 − Fold equity) × Bet)

Slow-playing: Compare EV of betting now vs betting later

Multi-street planning: EV of entire hand from current position

The role of variance

EV is a long-run average, and single-hand results vary enormously:

• Pocket aces lose pre-flop 15% of the time
• Even a 90% favorite loses 1 in 10 times
• A 10-stack swing can be normal variance
• Bankroll management is essential

For tournament poker:

• 100+ buy-ins for any specific tournament
• Variance dominates short-term results
• Long-term winners need substantial bankroll

For cash games:

• 25-50 buy-ins typical recommendation
• More stable than tournaments
• Easier to evaluate skill over short term

EV vs ICM (Independent Chip Model)

In tournaments, chip EV differs from monetary EV:

Chip EV: based on chip stack changes Monetary EV: based on actual money won (considers prize structure)

In a tournament, doubling your chips doesn’t double your equity in the prize pool. ICM corrects for this. Most casual tournament players use chip EV; professionals use ICM.

Common EV mistakes

1. Tilting after bad beats: variance is inevitable
2. Ignoring fold equity: not just about equity when called
3. Overvaluing implied odds: opponents fold often
4. Underestimating ranges: opponents have more hands than you think
5. Wrong equity calculations: rough estimation when math matters
6. Bankroll-blind decisions: making +EV moves that risk bankruptcy
7. Failing to consider position: out-of-position decisions are harder
8. Tournament vs cash confusion: different formats different math
9. Not accounting for rake: house takes some on every pot
10. Misjudging opponent skill: better players reduce your edge

The path from beginner to winning

Levels of EV thinking:

Level 0 (beginner): “I have a flush draw, I’ll call” Level 1: “Does pot give me odds for my draw?” Level 2: “EV of call vs fold, considering implied odds” Level 3: “Whole-hand EV considering opponent ranges” Level 4: “EV considering opponent tendencies + meta-game” Level 5: “Game theory optimal play considering all hands”

Each level requires more study and experience.