What Is Expected Value (EV) in Poker? Understanding the True Definition
Expected Value (EV) in poker is the expected payoff of one strategy against another specific strategy. Learn the correct definition of EV, how it differs from equity, what EV loss means, and how variance affects your results.
📝 Prerequisites: This article assumes you understand pot odds, alpha, and MDF. If not, please read MDF (Minimum Defense Frequency) first.
The Basics of Expected Value (EV) — Determined by Strategy
Pot odds, alpha, MDF — you've learned many numbers so far. But all of these calculations lead to a single concept: Expected Value (EV). EV is "the expected payoff of one strategy against a specific strategy." In poker, you can't calculate EV precisely because you don't know your opponent's strategy, but understanding the concept of EV forms the foundation of every decision you make.
What You'll Learn
- The correct definition of EV
- When EV can and cannot be calculated
- The difference between EV and equity
- What EV loss means
- How to think about variance
🎯 EV Is Determined by "Strategy vs. Strategy"
📝 Expected Value (EV): The expected payoff of one strategy against a specific strategy. When you repeat that strategy against a given strategy, EV represents how much you gain (or lose) on average per iteration.
A strategy here doesn't mean a single action choice. It refers to the complete set of actions across your entire range — for example, "raise with AA, call with KQs, fold 72o." The way you color every cell of a range chart is your "strategy."
The most important thing to understand about EV is that it's determined by the combination of your strategy and your opponent's strategy. If your opponent's strategy changes, the EV of the same strategy on your end also changes.
Coin Flip Example — When EV Can Be Calculated
Let's start with a simple example to calculate EV. A coin flip has no "opponent strategy" — probabilities are fixed, so we can calculate EV precisely.
EV = Σ (probability of each outcome × payoff of that outcome)
Flip a coin: heads you win 200 chips, tails you lose 100 chips.
- Probability of heads: 50%
- Probability of tails: 50%
- EV = (0.5 × 200) − (0.5 × 100) = 100 − 50 = +50 chips
This game earns an average of 50 chips per play. Since the probabilities are fixed, EV can be calculated precisely.
🃏 In Poker, You Can't Calculate EV Precisely
We could calculate EV for a coin flip. But poker is fundamentally different.
| Coin Flip | Poker | |
|---|---|---|
| Opponent's strategy | None (probabilities are fixed) | Unknown (you don't know how they'll play) |
| Outcome resolution | Completes in one round | Multiple streets (flop → turn → river) |
| EV calculation | Possible | Not possible because opponent's strategy is unknown |
Poker EV is determined by "your strategy × opponent's strategy." But in practice:
- You don't know your opponent's strategy: Whether they bet, check, call, or fold with each hand — those action choices completely change EV
- A hand doesn't end in one street: Turn and river developments also affect EV
- Either player can fold: Many hands never reach showdown
In poker, calculations like "my equity is X% so calling has an EV of +Y chips" don't work. As long as you don't know your opponent's strategy, you cannot determine exact EV.
Does this mean EV is useless? Not at all. Even though you can't calculate it precisely, understanding the concept of EV itself forms the foundation of every decision. Tools like pot odds and alpha help you estimate the direction of EV and make better decisions.
💡 "But solvers can calculate EV, right?" Solvers like GTO Wizard calculate EV by fixing (assuming) the opponent's strategy. In real poker too, if you knew exactly which action your opponent takes with every hand, you could calculate EV. Solvers operate under precisely that assumption.
🔄 The Difference Between EV and Equity
EV and equity are often confused, but they are determined in fundamentally different ways.
| Equity | EV | |
|---|---|---|
| Meaning | Win rate at showdown (share of the pot) | Expected payoff of one strategy against a specific strategy |
| Unit | % (percentage) | Chips (monetary amount) |
| Determined by | Hand and board | The combination of your strategy and opponent's strategy |
- Equity is a measure of "hand strength" and is just one ingredient for thinking about EV
- Equity alone isn't enough for decisions. Even with the same equity, EV changes depending on the opponent's strategy and bet sizing
💡 Equity = hand win rate. EV = expected payoff determined by strategy vs. strategy. Even with high equity, depending on how you respond to your opponent's strategy, EV can be negative.
📉 EV Loss
"EV loss" is a commonly used term in poker theory.
📝 EV loss: When comparing two strategies against a given strategy, if one strategy has a higher EV than the other, the strategy with the lower EV is said to have "EV loss."
📌 The EV of Folding
The EV of folding is 0.
This is because EV is measured from that moment forward. Once you fold, you neither lose nor gain any more chips. Chips already in the pot don't come back (sunk cost), but EV only considers "what happens from here."
Folding is optimal when all other actions (call, raise) have negative EV.
💡 Variance — Don't Be Misled by Short-Term Results
Even when EV is known, short-term results will fluctuate. This is called variance.
📝 Variance: The fluctuation of results. Even with an EV of +50 chips, the first trial might be −150 chips, the second +200 chips, the third −100 chips, and so on. But as you repeat the process, results gradually converge toward the EV.
Understanding Through Coin Flips
Say you repeat the coin flip from earlier (EV = +50 chips) 10 times.
- Heads (+200 chips): about 5 times
- Tails (−100 chips): about 5 times
But in reality, heads might only come up 3 times, or it might come up 7 times.
| Pattern | Heads | Tails | Total |
|---|---|---|---|
| Unlucky run | 3 times (+600) | 7 times (−700) | −100 |
| Average run | 5 times (+1,000) | 5 times (−500) | +500 |
| Lucky run | 7 times (+1,400) | 3 times (−300) | +1,100 |
With only 10 trials, results vary widely. But over 100 or 1,000 repetitions, the average result per trial converges toward +50 chips.
⚠️ You can't judge a decision by a single result. Even if losses continue in the short term, that may just be within the range of variance. Evaluate your decision-making process, not the outcome.
🎓 Practice
Q1: Flip a coin — heads you win 300 chips, tails you lose 200 chips. What's the EV? Should you play this game?
See Answer
EV = (0.5 × 300) − (0.5 × 200) = 150 − 100 = +50 chips. Since EV is positive, you should play. In a coin flip, probabilities are fixed, so EV can be calculated precisely.
Q2: Why can't EV be calculated in poker the way it can for a coin flip?
See Answer
Because poker EV is determined by "your strategy × opponent's strategy," and you don't know your opponent's strategy. Furthermore, hands span multiple streets making the situation complex, and either player may fold. Unlike a coin flip where probabilities are fixed, precise EV calculation is not possible.
🎯 Summary
- EV is the expected payoff of one strategy against a specific strategy
- In poker, you can't calculate EV precisely because you don't know your opponent's strategy
- Solvers can calculate EV because they fix the opponent's strategy
- Equity is just one ingredient of EV — equity alone isn't enough for decisions
- EV loss is the difference in expected value compared to a better strategy
- Due to variance, you can't judge a decision's quality by short-term results
In poker, EV can't be calculated precisely — but in a simplified toy game, it can. In the next article, we'll use the AKQ Game, a mini-poker played with just three cards, to actually calculate EV. We'll also put the concepts you've learned so far — pot odds, alpha, and more — to use.
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