Part 1 · Lesson 1 of 25 · Free
Poker expected value (EV): how to evaluate a call
You call 10 bb on the river and lose. Was the call a mistake? One hand cannot tell you. Expected value (EV) can: it is the average result a decision would produce if you could repeat it many times, each outcome weighted by how likely it is.
The hand
River. You have middle pair. The Loose-aggressive player bets 10 bb into 20 bb, so the pot with his bet in it is 30 bb and you must call 10 bb. Against the hands he bets here, you win 30% of the time.
Predict first
You win 30% of the time. Is calling 10 bb to win this 30 bb pot right?
- Yes: it makes money on average
- No: you lose more often than you win
- Only if you win this time
Show the answer
Answer: Yes: it makes money on average
You lose 7 times in 10, but each win collects 30 bb and each loss costs only 10 bb: 0.30 × 30 − 0.70 × 10 = 9 − 7 = +2 bb per call.
Working it out
Repeat the call ten times. You win 3 and collect 30 bb each, 90 bb; you lose 7 and pay 10 bb each, 70 bb. That is +20 bb over ten calls, +2 bb per call: 0.30 × 30 − 0.70 × 10 = +2. The call is right even though it loses most of the time, because a win pays three times what a loss costs.
Every option gets a number. Folding is the zero point: it neither wins nor loses from here on. Calling is worth +2 bb, so you call. The same EV can be written with your equity and the pot after your call: 0.30 × (30 + 10) − 10 = +2. The two forms always agree, as long as the pot includes his bet.
Formula
EV = Σ probability × result. Calling: EV = equity × pot − (1 − equity) × call = equity × (pot + call) − call, with his bet in the pot
Check your understanding
The pot is 40 bb with his bet in it. You must call 20 bb, and you win 25% of the time. What is the EV of calling, in bb?
Show the answer
Answer: −5 bb
0.25 × 40 − 0.75 × 20 = 10 − 15 = −5 bb, so folding (0) is better. The other form agrees: 0.25 × (40 + 20) − 20 = 15 − 20 = −5.
You call with 40% equity at a good price and lose the hand. What should you conclude?
- Nothing new: a right call loses part of the time
- The call was a mistake
- Your equity must have been lower than 40%
Show the answer
Answer: Nothing new: a right call loses part of the time
A call with 40% equity loses 60% of the time by design. One loss says nothing about the decision; its EV does.