Expected Value (EV)

Overview

Expected Value (EV) is one of the most important mathematical concepts in Texas Hold'em. It is used to evaluate the long-term average result of an action (such as calling, raising, or folding). EV is calculated based on the probabilities of all possible outcomes and their corresponding gains or losses. Positive EV (+EV) means the decision is profitable in the long run, while negative EV (-EV) means it is a long-term loser. Skilled players consistently choose +EV actions and avoid -EV actions.

How to Calculate

EV = Σ (Probability of each outcome × Gain or loss of that outcome)

Example:

The pot is $100, and your opponent bets $50. You estimate you have a 20% chance of winning the pot and an 80% chance of losing.

• Win: 20% probability, gain $150 (pot $100 + opponent's bet $50)
• Lose: 80% probability, lose $50 (your call) EV = 0.2 × 150 + 0.8 × (-50) = 30 - 40 = -$10 The EV of this call is -$10, which means it is a losing play in the long run; you should fold.

Applications

• Calling Decisions: Calculate the EV of calling and compare it to folding (EV = 0).
• Bluffing: Evaluate whether the success rate of a bluff is high enough to make EV positive.
• Range vs. Range: Compute overall EV by considering your opponent's range.
• Tournament ICM: In tournaments, EV must account for ICM factors because chips have diminishing marginal value.

Common Misconceptions

• Short-term results ≠ EV: Even if a decision is +EV, you may lose money in the short run, and vice versa.
• EV is not actual profit: It is a long-term average; a single result can deviate.

Relationship with GTO

GTO strategy aims to make it impossible for opponents to gain +EV from any adjustment, while exploitative strategies take advantage of opponents' -EV mistakes. Understanding EV is the foundation for executing both approaches.