Module 5 · Lesson 24 of 39 · Free
Why we bet: value and bluffs
A bluff of 10 bb into a pot of 20 bb only has to work one time in three to break even. Making a better hand fold is one of the two reasons to bet; the other is getting called by a worse hand. When a bet can do neither, check.
The hand
The river: the board is K♠ 8♥ 4♥ 2♣ T♦, you hold 9♣ 9♦, and 20 bb are in the pot. The Loose-aggressive player holds a king, K♦ Q♣, or a missed heart draw, 7♥ 6♥, as often one as the other, and he will call a bet with the king and fold the draw.
Predict first
You can bet 10 bb or check. What should you do with your pair of nines?
- Bet for value: a pair of nines is a good hand
- Bluff: a bet can make the king fold
- Check: only the king would call a bet
Show the answer
Answer: Check: only the king would call a bet
The king calls a bet and beats you: you lose 10 bb more. The draw folds, and your nines would have beaten it anyway. Half the time the bet costs 10 bb and half the time it changes nothing, 5 bb lost on average. Check, and you still win the pot every time he has the draw.
Working it out
Sort his hands by what a bet does to them. With 9♣ 9♦, the king calls and wins, and the draw folds a hand you were beating: check. Hold K♣ T♣ instead, two pair, and the king calls and pays you 10 bb more while the draw folds: the bet gains 10 bb half the time, a value bet. Hold 5♣ 3♣, a missed straight draw that loses to both of his hands, and the bet wins the 20 bb pot when the draw folds and loses 10 bb when the king calls. A bluff risks 10 bb to win 20 bb, so it must work 10 ÷ (20 + 10) = 1 time in 3. This one works 1 time in 2, and earns (20 − 10) ÷ 2 = 5 bb a hand on average.
Before you bet, sort the hands he can hold into four groups: better hands that call, better hands that fold, worse hands that call and worse hands that fold. Your bet loses to the first group, wins the pot from the second, wins the bet from the third and changes nothing against the fourth. Bet for value when more worse hands than better ones will call. Bluff when better hands fold more often than bet ÷ (pot + bet), the share a bluff needs. Otherwise, check.
Formula
A bluff must work bet ÷ (pot + bet) of the time: 10 ÷ (20 + 10) = 1 in 3 = 33.3%
Check your understanding
You bluff 30 bb into a pot of 40 bb. How often must he fold for the bluff to break even, in %?
Show the answer
Answer: 42.9%
The bluff risks 30 bb to win 40 bb: 30 ÷ (40 + 30) = 42.9%.
On the river he calls a bet with any pair and folds anything less. Your hand loses to every hand he can hold, and half of his hands have no pair. Is a bet of half the pot a good bluff?
- Yes: it works half the time and needs to work only 1 time in 3
- No: you lose every time he calls
- No: a bluff must work more than half the time
Show the answer
Answer: Yes: it works half the time and needs to work only 1 time in 3
A bet of half the pot risks 1 to win 2, so it must work 1 ÷ (2 + 1) = 1 time in 3. Half of his hands fold, so the bluff works more often than it must, even though it loses every time he calls.
Which of these river bets has no reason?
- A bet with a middle pair that only better hands call
- A bet with a set that worse pairs call
- A half-pot bet with nothing that better hands fold half the time
Show the answer
Answer: A bet with a middle pair that only better hands call
With the middle pair, no worse hand calls and no better hand folds: the bet only loses when he is ahead. The set is a value bet, and the half-pot bet with nothing is a bluff that needs folds a third of the time and gets them half the time.