What Is Expected Value (EV)?
Expected Value (EV) is the average amount of money (or chips) you can expect to win or lose on a specific bet or decision if that exact situation were repeated hundreds or thousands of times.
- $+EV$ (Positive Expected Value): A decision that makes money in the long run. Even if you lose this specific hand due to a bad beat, making this play repeatedly will generate steady profit.
- $-EV$ (Negative Expected Value): A decision that loses money in the long run. Even if you get lucky and win the pot this time, continuing to make this play will guarantee long-term losses.
- $0 EV$ (Neutral Expected Value): A break-even decision with no expected profit or loss.
The Fundamental EV Formula
In any poker decision where you are facing a call or making a bet, EV is calculated using this core formula:
\[EV = (P_{\text{win}} \times \text{Amount Won}) - (P_{\text{lose}} \times \text{Amount Lost})\]Where:
- $P_{\text{win}}$ = Probability of winning (your hand equity as a decimal).
- $\text{Amount Won}$ = Total pot you stand to collect (excluding your call).
- $P_{\text{lose}}$ = Probability of losing ($1 - P_{\text{win}}$).
- $\text{Amount Lost}$ = The amount of chips you must risk/call.
Practical Example: Calling an All-In on the Flop
Imagine this common tournament scenario:
- Current Pot: $600
- Opponent goes all-in for: $200
- Total pot after their bet: $800
- Cost for you to call: $200
Step 1: Calculate Your Hand Equity ($P_{\text{win}}$)
Suppose you hold the Nut Flush Draw with two cards to come (Turn and River). You have 9 outs to complete your flush, giving you approximately 35% equity ($P_{\text{win}} = 0.35$). Therefore, your chance of losing is 65% ($P_{\text{lose}} = 0.65$).
Step 2: Plug Numbers into the Formula
\(EV = (0.35 \times \$800) - (0.65 \times \$200)\) \(EV = \$280 - \$130 = +\$150\)
The Verdict:
Because the result is $+$150$, calling this bet is a massively $+EV$ decision. Every time you make this call in this situation, you average a profit of $150, regardless of whether you hit your flush on this particular run-out.
Pre-Flop EV in the River Pairs Matchup Database
Throughout our heads-up matchup articles, you will see an Expected Value rating listed in the hand ratings table.
In pre-flop limit hold’em, EV reflects the average number of big bets won or lost per hand when dealing that specific holding against random opponents:
- Pocket Aces (AA): $+0.75$ to $+0.80$ EV (The most profitable starting hand in poker).
- Pocket Twos (22): $-0.09$ to $-0.05$ EV in early position; positive EV on late position steal spots.
- 7-2 Offsuit (72o): $-0.35$ EV (The least profitable starting hand in the game).
Pot Odds vs. Required Equity Quick Reference
To quickly assess if an in-game call is $+EV$, compare your Hand Equity against your Pot Odds:
\[\text{Required Equity} = \frac{\text{Cost to Call}}{\text{Total Pot After Your Call}}\]| Bet Faced Relative to Pot | Pot Odds Offered | Minimum Equity Needed to Call |
|---|---|---|
| Half Pot | 3 : 1 | 25.0% |
| Two-Thirds Pot | 2.5 : 1 | 28.6% |
| Full Pot | 2 : 1 | 33.3% |
| Double Pot | 1.5 : 1 | 40.0% |
If your hand’s mathematical equity (which you can check across all our matchup guides) is greater than the required equity, calling is strictly $+EV$!
The Key to Mental Mastery in Poker
Professional poker players separate decision quality from outcomes:
- A bad decision that gets lucky is still a $-EV$ error.
- A great decision that loses to a river card is still a $+EV$ triumph.
By understanding expected value and reviewing precise hand equities in our database, you align your strategy with mathematical reality.
