Expected Value (EV)

What Is Expected Value?

Every poker decision has an expected value under the probabilities and costs used in the model. Positive EV means a positive average net result, not a promise about the next hand. Compare legal alternatives on the same basis, including fees where relevant.

A positive-EV call can lose this hand. A negative-EV call can win it. Variance separates expectation from the result of any finite sample; a larger sample does not guarantee a profit. An EV estimate is useful only to the extent that its probabilities and costs are credible.

Understanding EV also provides emotional resilience. When you know a decision was +EV, a bad outcome is just variance, not a mistake. This separation between decision quality and outcome quality is what keeps professional players grounded through inevitable losing stretches.

How It Works

The EV formula is straightforward:

EV = (Probability of Winning x Amount Won) – (Probability of Losing x Amount Lost)

Simple Example:

Hypothetical all-in call: the pot already contains $200, including the opponent’s bet, and you must call $100. The final pot would be $300. Assume 60% equity, no ties, no rake and no later bets.

EV = 0.60 x $300 – $100 = +$80. Equivalently, 0.60 x $200 net won – 0.40 x $100 lost = +$80.

The model gives an average net gain of $80 per repetition under those assumptions. An individual call still loses $100 when it fails.

Calling a River Bet:

The pot is $150. Your opponent bets $50. You believe you have the best hand 35% of the time.

EV of calling = (0.35 x $200) – (0.65 x $50) = $70 – $32.50 = +$37.50

Calling is clearly +EV. You only need to be right 20% of the time to break even (based on your pot odds of $50 / $250), and you estimate 35%.

Bluffing EV:

You are considering a $75 bluff into a $100 pot. You estimate your opponent folds 55% of the time.

EV of bluffing = (0.55 x $100) – (0.45 x $75) = $55 – $33.75 = +$21.25

The bluff is profitable even though it gets called almost half the time, because the pot you pick up when it works is large relative to the cost when it fails.

Example

You are playing $1/$2 online. On the river, the pot is $120. You hold As Ks on a board of Ad 8c 5h 3s 2d. Your opponent shoves all-in for $60.

You must call $60 to win a pot of $180. Your pot odds require 25% equity. Your opponent could be value betting a weaker Ace, two pair, or a set, but they could also be bluffing missed draws.

You estimate you are ahead 55% of the time. EV = (0.55 x $180) – (0.45 x $60) = $99 – $27 = +$72. This is a clear call.

Common Mistakes

• Confusing a single bad outcome with a bad decision and abandoning +EV lines that happen to lose
• Ignoring EV on small decisions like calling small bets without thought, since many small -EV leaks compound into significant losses
• Using EV calculations with inaccurate probability estimates, making the output unreliable
• Only thinking about EV in all-in situations when it applies to every single decision

Related Terms

• Pot Odds — the immediate mathematical framework that feeds into EV calculations
• Implied Odds — adjusts EV by incorporating expected future winnings
• Fold Equity — the EV component created by the chance your opponent folds
• Equity — your probability of winning, a core input to the EV formula
• Variance — why +EV decisions can produce short-term losses

FAQ

How do I calculate EV quickly during a hand?

Compare your estimated equity with the price of a call using our pot odds and call EV calculator. Supply your own equity estimate; the tool does not evaluate cards or hand ranges.

Can a -EV play ever be correct?

In pure chip-value terms, no. But in tournaments, ICM considerations can make a chip-EV positive play negative in dollar-EV terms. For example, folding a marginally +EV spot near a pay jump can be correct because the risk of elimination outweighs the chip gain. In cash games, always choose the highest EV line.

What is the relationship between EV and long-term profit?

Expected results and realised results are different. In a hypothetical model with an average net EV of $5 per hand, 100,000 hands have total expected net value $500,000: $5 x 100,000. Actual results can differ, and this is not a measured win rate or income forecast. Include rake and other costs before calling an estimate net EV. Related reading: bankroll management guide.