Module 4 · Lesson 19 of 39 · Free
Why acting last wins money
From the button you act last on the flop, the turn and the river: on three of the four betting rounds you see what everyone else did before you decide. In position you choose with that information; out of position you choose first, without it. On the river below, that is worth 1.5 bb in a 10 bb pot.
The hand
The river, heads-up, with 10 bb in the pot. You hold K♦ J♣, a pair of kings. Say he could hold ten hands: three beat yours, four are worse but would call a bet of 5 bb, and three are worse and would fold.
Predict first
Same cards, same pot: who earns more on average, you acting first or you acting last?
- Acting first: you can bet before he does
- Acting last
- Neither: the cards decide who wins
Show the answer
Answer: Acting last
Acting last you bet only after he checks, so your bet meets only worse hands: 9 bb per hand on average. Acting first, the best you can do is 7.5 bb.
Working it out
Here is the model in full. He plays honestly: he bets his three better hands and checks the others, and he calls a bet with his better hands and his four worse callers. Acting last, three times he bets and you fold; four times he checks, you bet 5 bb and he calls, and you win 10 + 5 = 15 bb; three times he checks and folds to your bet, and you win 10 bb. On average: (4 × 15 + 3 × 10) ÷ 10 = 9 bb. Acting first you must choose before he moves. A bet also pays off his three better hands: (4 × 15 + 3 × 10 − 3 × 5) ÷ 10 = 7.5 bb. A check wins only the pot from his seven worse hands: 7 × 10 ÷ 10 = 7 bb. Acting last earns 9 − 7.5 = 1.5 bb more.
Real players also bluff and trap, as the game-theory lessons of the Mathematics track show, but the player who acts last still decides with more information on every round after the flop. He can check behind to take a free card, bet when the others show weakness, and stop when they show strength. That is why the cutoff and the button can play more hands than the early seats.
Formula
Edge of acting last = bet × the smaller of (his better hands, his worse callers) ÷ his hands: 5 × 3 ÷ 10 = 1.5 bb
Check your understanding
Three players see the flop: the big blind, the hijack and the cutoff. Who is in position?
- The cutoff
- The big blind
- The hijack
Show the answer
Answer: The cutoff
After the flop the action runs from the small blind round to the button, so of these three the cutoff acts last on every round.
In the lesson's model the pot is 20 bb and you bet 10 bb. Of his ten hands, 2 beat yours, 5 are worse and call, and 3 are worse and fold. Acting last, what do you win per hand on average, in bb?
Show the answer
Answer: 21 bb
Acting last you bet only when he checks: (5 × 30 + 3 × 20) ÷ 10 = 21 bb.
Same spot, but you act first. What is the most you can win per hand on average, in bb?
Show the answer
Answer: 19 bb
Betting: (5 × 30 + 3 × 20 − 2 × 10) ÷ 10 = 19 bb. Checking: 8 × 20 ÷ 10 = 16 bb. Betting is better, and it still earns 2 bb less than acting last.