Expected Value
期望值
Context: Poker term: Expected Value Expected Value is a mathematical metric in Texas Hold'em that measures the long-term average profitability of a decision. 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.
Context: Poker term article: Expected Value
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.