Expected Value
Expected Value
It is calculated as the sum of the products of all possible outcomes' probabilities and their respective payoffs. In practice, players use it to determine whether an action is profitable: a positive expected value +EV indicates long-term profit, a negative expected value -EV indicates loss, and an expected value of zero EV=0 means breakeven. For example, when drawing to a flush on the flop, if the pot is 100 chips and the opponent bets 20, the call costs 20. The probability of hitting the flush is about 36%, and if hitting it wins 200, then the expected value of the call is 200 × 0.36 - 20 × 0.64 = 72 - 12.8 = +59.2, indicating that calling is profitable in the long run.
Overview
Expected Value (EV) is a core mathematical concept in poker strategy used to quantify the average outcome of an action over the long run. Positive expected value (+EV) indicates long-term profit, while negative expected value (-EV) indicates long-term loss. Players aim to maximize profit by choosing +EV actions.
Calculation Method
The formula for expected value is:
EV = (Probability of Winning × Amount Won) - (Probability of Losing × Amount Lost)
Example: On the flop, you have a flush draw with approximately 36% equity. The pot is 100 yuan, and your opponent bets 50 yuan. You call.
- Probability of winning: 36%, amount won = pot 100 + opponent's bet 50 = 150 yuan
- Probability of losing: 64%, amount lost = call 50 yuan
- EV = (0.36 × 150) - (0.64 × 50) = 54 - 32 = 22 yuan (+EV)
Application Scenarios
- Betting and Raising: When your bet is called, you need to calculate EV against your opponent's calling range.
- Calling: Determine whether a call is +EV based on pot odds and equity.
- Bluffing: Calculate the EV of a bluff by considering opponent's fold probability and pot size.
- Range vs. Range: Analyze EV for an entire range rather than a single hand, used in GTO strategy.
Notes
- EV is a long-term concept; individual results may deviate, but it holds over the long run.
- In actual gameplay, you must estimate opponent ranges and probabilities, which introduces error.
- In tournaments, combine ICM adjustments with EV calculations because chip values are non-linear.
Related Terms
- Pot Odds: The basis for calculating the required equity to call.
- Implied Odds: Potential future winnings from later betting rounds.
- GTO: Game Theory Optimal strategy, aiming for balanced EV.