Expected Value (EV)

Expected Value (EV)

What EV Means for Your Decisions

Expected value (EV) measures the average money you expect to win or lose from a specific action over the long run. A play that returns more than zero on average is +EV; less than zero is -EV; zero is breakeven. Folding has 0 EV; you risk no further money after folding.

Key terms: equity is your probability of winning the pot; pot odds are the immediate price to call now; implied odds are the likely future money you can win if your hand improves; fold equity is the chance an opponent folds to your bet.

Think of EV as the scoreboard that shows which decisions profit over thousands of hands.

Calculating EV - The Basic Formula

The core formula is: EV = (%W × $W) - (%L × $R)

Where:

• %W = your win probability (equity)
• $W = amount you win when you succeed (usually the pot after you act)
• %L = 1 - %W
• $R = amount you risk by making the call or bet

Quick steps to apply it at the table:

1. Estimate %W (use an equity calculator off-table, or assign a range and estimate equity).
2. Calculate $W (current pot + opponent’s bet if you call) and $R (what you must put in).
3. Plug values into the formula. If EV > 0, the action is +EV.

Concrete check: if a shove requires about 33% equity to break even, and your hand’s equity versus the opponent’s range is 43%, calling is +EV.

Applying EV Across the Hand (preflop -> river)

Preflop: build opening and calling ranges that are +EV given stack sizes and opponent tendencies. A tight preflop raise that folds out better hands can be +EV even if it wins fewer showdowns.

Postflop: weigh your current equity against the pot and expected future bets. A marginal flop call can be +EV if implied odds or later value bets justify it. Conversely, calling repeatedly into large pots with little equity will erode EV.

Always ask how future streets change the amounts won ($W), the risked amount ($R), and your win probability (%W).

Pot Odds and Implied Odds: Comparing Odds to EV

Pot odds compare the cost to call now with the current pot size to give a break-even equity percentage. Implied odds add expected future bets you can win if your draw hits. Use both: if your estimated equity exceeds the pot-odds break-even point or is justified by implied odds, the call is likely +EV.

Range-based thinking matters: compare your hand’s equity against the opponent’s likely range, not just a single hand.

Value Betting & Bet Sizing to Maximize EV

Bet sizing changes the EV equation by altering $W and $R and by changing opponents’ folding frequencies (which affects realized wins). Evaluate sizings by how they shift these three EV inputs.

• Small bets: extract thin value from worse hands and keep opponent calling ranges wide.
• Larger bets: increase fold equity, protect against draws, and charge opponents more to chase.

Choose sizes that maximize the net EV of your line given opponent tendencies.

Practical Limits, Range Uncertainty, and Game Theory

You never know exact holdings, so assign opponent ranges and compute a weighted EV across that range. Overestimating folding frequencies or implied odds can turn a theoretical +EV play into a losing one.

EV evaluates strategies; combine it with range-based and game-theory thinking to develop lines that are both profitable and hard to exploit.

Checklist

• Use the EV formula on every contested decision.
• Always compare your hand equity to pot odds and consider implied odds.
• Assign opponent ranges and calculate weighted EVs, not single-hand EVs.
• Choose bet sizes that improve the net EV of your line (value vs protection).
• Think long term: small +EV edges compound across many hands.