3 · LEARN THE USEFUL MATH · LESSON 14 OF 29 · 6 min
Good decisions can lose
Expected value, or EV, asks what a decision would return on average across repeated comparable spots. Variance explains why one outcome can be far from that average. You judge the decision using the information available when it was made, not solely whether the river card was kind.
A call that wins 35% of the time at a 25% price can still lose this particular hand. That loss does not turn the original call into a mistake.
Score the choice separately from the result
Expected value asks what a decision earns on average if comparable situations repeat. In a simplified call with no future betting, suppose you pay 6 chips for a final pot of 24 and win 35% of the time. The call's average net return is 0.35 × 18 minus 0.65 × 6, or 2.4 chips. You still lose the entire 6-chip call in 65 of every 100 such outcomes. A favorable decision can lose most individual attempts.
The calculation depends on the 35% estimate. If that estimate was based on a range that missed many strong hands, the decision might not be profitable at all. If more betting remains, a simple one-street calculation leaves out future costs and winnings. EV is a way to compare choices under stated assumptions, not a guarantee that one session will go well.
Variance is the spread of actual results around the long-run average. Poker has a lot of it because the cards are uncertain and pots differ in size. After a loss, record the pot, call price, board, action, and range you thought you faced. Revisit the decision you controlled rather than trying to explain the river card after it appeared.
Review one trainer hand that you lost. Hide the outcome, calculate the price at your uncertain decision, and decide whether the call was reasonable from the information then available.
Winning a hand is not proof that a call was profitable, and losing is not proof that it was wrong.
MAKE THE CALL
A sound call loses this time. What follows?
Start with a prepared decision, then play the rest of the hand with practice chips. Turn on guidance to see the trainer's reasoning.