Expected value is the long-run average result of a decision if you could repeat it many times. In poker it answers the only question that really matters: does this call, bet or fold make money over time? A play with positive EV is profitable even if it loses this particular hand; a negative-EV play loses money in the long run even when it happens to win.
To use EV you need two things: probabilities (your equity, the chance of winning the hand or of your opponent folding) and amounts (how much you win when it works, and how much you lose when it does not). Multiply each outcome by its chance and add them up. The result is measured in chips or money per play.
Variance matters too. Two plays with the same EV can have very different swings – a big all-in with 40% equity fluctuates wildly from hand to hand. The calculator shows the standard deviation per play and the expected profit over a number of plays so you can see how quickly the edge appears through the noise.
How to use the Poker EV Calculator
- Chance to win (P win)
- Profit if you win
- Chance to lose
- Chance to lose (P lose)
- Loss if you lose
- Number of plays
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Enter the probability of winning and the net amount won, and either let the calculator use 100% − P(win) as the losing chance or enter it separately (any remaining probability is a tie worth zero). EV is the probability-weighted sum; the break-even probability is where EV = 0.
Worked example
You win $100 with probability 40% and lose $50 with probability 60%. EV = 0.4 × 100 − 0.6 × 50 = $10 per play. Break-even needs 50 ÷ 150 = 33.3% wins. The standard deviation is √(0.4 × 100² + 0.6 × 50² − 10²) = √5,400 = $73.48, so over 100 plays you expect +$1,000 with a typical swing of ±$735.
A dice example
Win $5 on a roll of 5 or 6 (1/3), lose $2 otherwise (2/3): EV = 5/3 − 4/3 = $0.33 per roll – a small but positive edge.
Inputs explained
| Field | What to enter |
|---|---|
| Chance to win (P win) | In % |
| Profit if you win | Amount in your currency |
| Chance to lose | Choose one: 100% minus the chance to win, Enter it myself (the rest is a tie worth 0) |
| Chance to lose (P lose) | In % |
| Loss if you lose | Amount in your currency |
| Number of plays | A number |
What each result means
- Expected value per play = [Chance to win (P win)]÷100×[Profit if you win] – [Chance to lose used]÷100×[Loss if you lose]
- Break-even chance to win = [Loss if you lose]÷([Profit if you win] + [Loss if you lose])×100
- Standard deviation per play = sqrt(max([Chance to win (P win)]÷100×[Profit if you win]^2 + [Chance to lose used]÷100×[Loss if you lose]^2 – [Expected value per play]^2, 0))
- Expected profit over all plays = [Expected value per play]×[Number of plays]
- Typical swing over all plays (±1 σ) = [Standard deviation per play]×sqrt([Number of plays])
Example values
How the main result changes when Chance to win changes and everything else stays at the example values above:
| Chance to win (P win) (%) | Expected value per play |
|---|---|
| 20 | -20 |
| 30 | -5 |
| 40 | 10 |
| 50 | 25 |
| 60 | 40 |
| 80 | 70 |
Formula
EV = P(win) × amount won − P(lose) × amount lost · break-even P(win) = loss ÷ (win + loss) · σ = √(P(win)·win² + P(lose)·loss² − EV²)
Worked example
Inputs — Chance to win (P win): 40 %; Profit if you win: $100; Chance to lose: 100% minus the chance to win; Loss if you lose: $50; Number of plays: 100.
Results — Chance to lose used = 60 %; Expected value per play = $10.00; Verdict = Profitable in the long run (+EV); Break-even chance to win = 33.33 %; EV per unit risked = 20 %; Standard deviation per play = $73.48; Expected profit over all plays = $1,000.00; Typical swing over all plays (±1 σ) = $734.85.
Key terms
- Expected value (EV)
- The probability-weighted average of all outcomes.
- Equity
- Your share of the pot based on your chance of winning at showdown.
- Variance
- How widely results scatter around the expected value; its square root is the standard deviation.
- +EV / −EV
- A decision that wins / loses money on average.
Frequently asked questions
What is EV in poker?
The average amount a decision wins or loses per play over the long run. A call with +$10 EV makes $10 per hand on average, even though each hand is won or lost.
How do I calculate the EV of a call?
EV = equity × (pot + call) − call. With a $150 pot, a $50 call and 25% equity: 0.25 × 200 − 50 = $0.
What is the difference between equity and EV?
Equity is your share of the pot (your chance of winning); EV is money. Equity of 40% only becomes +EV if the pot pays you more than 1.5 times your risk.
Can a +EV play lose?
Yes, often. In our example you lose 60% of the time but still make $10 per play on average because wins are twice as large as losses.
What is the break-even probability?
The win chance at which EV is zero: loss ÷ (win + loss). Winning $100 or losing $50 breaks even at 33.3%.
Why look at standard deviation?
It shows how much results swing. With σ ≈ $73 per play, 100 plays have an expected profit of $1,000 but a typical swing of ±$735.