Expected Value
Expected value (EV) tells you how much an action wins or loses on average when the same decision is repeated many times. Compare actions from the decision you face now. Chips already in the pot are gone; folding invests nothing more, so folding has an EV of 0 from this point.
What you will be able to do
- Build probability-weighted win and loss branches.
- Use net outcomes consistently rather than mixing final pots and profits.
- Judge the decision independently of one observed runout.
DECISION, NOT RESULT
EV is what an action earns on average
This hand produces one result. Expected value asks what the same decision would earn or lose on average if the situation were repeated many times.
START WITH A COIN FLIP
A fair coin flip has an EV of zero
Heads wins 100 chips and tails loses 100 chips. Each happens 50% of the time, so the wins and losses cancel out and the EV is zero per flip. But if the game pays more for a win—or charges more for a loss—the EV changes. Try it below.
(50% × +100) + (50% × −100) = 0
Break-even: no average gain or loss over timeEV IS NOT A GUARANTEE
Positive EV can still lose in the short term
Suppose you can choose to play a fair-coin game that wins 120 chips on heads and loses 100 on tails. The EV of choosing to play is +10 chips per flip. Tails can still appear several times in a row, producing a short-term loss.
This short-term movement above and below the long-run average is called variance. EV describes the long-run value of a decision; it does not promise what happens this time.
NOW CONNECT IT TO POKER
The same equity can produce different EV
The river pot is 100 BB and Hero must call or fold after Villain bets. Assume Hero wins 30% of the time and loses 70%. A larger bet does not change that 30% equity, but it does increase what Hero loses when the call is wrong.
The hand’s pot share stays fixed
Wins the existing 100 BB pot plus Villain’s bet
Loses the additional chips paid to call
EV is not +150 or −50. It is the weighted average: multiply each result by how often it happens, then add the two amounts.
Call price ÷ final pot after calling
30% exceeds the required 25%, so calling is +EV
Hero wins only 30% of the time and loses 70%. When the bet grows, Hero gains the extra chips in the 30% winning branch but pays that same extra amount in the more frequent 70% losing branch. That is why the EV of calling falls—and why pot odds matter. Without comparing your equity with the equity required by the price, you can make a negative-EV call or fold when calling would be positive EV.
River. Pot 75. Villain bets 25. Hero may call 25 or fold.
No more chips are invested from this decision point. Chips already in the pot are sunk and do not return.
Assume Hero has 28% equity against Villain’s betting range.
WIN
Net result +100
0.28 × 100 = +28LOSE
Net result −25
0.72 × −25 = −18ADD THE WEIGHTED BRANCHES
+28 − 18
= +10TEST THE IDEA
A positive-EV decision can lose this time
Choose either result. The call remains +10 EV; one outcome does not change the quality of the decision.
ONE THING TO REMEMBER
A positive-EV call can lose this hand. Outcome quality and decision quality are different questions.
TRY IT
This is a 2-question test. Start when you are ready.
Takeaway
Expected value combines every outcome with its probability and measures the average result from the current decision point.