Part 2 · Lesson 9 of 25 · Free

Adaptive play: exploiting a distribution

Course by Hernan Alejandro Gajardo Morales

Same river, same pot-sized bet, same hand. Against the Maniac, calling earns +21 bb; against the Nit, it loses 33 bb. When you know how an opponent deviates, the most profitable answer is often extreme: fold every bluff catcher against a player who bluffs too little, and call with all of them against one who bluffs too much.

The hand

River. You hold second pair, which beats only bluffs. The Maniac bets 60 bb into 60 bb, so the pot with his bet in it is 120 bb and you must call 60 bb. In this spot, 45% of his bets are bluffs.

Predict first

Call or fold?

1. Call
2. Fold
3. Raise

Working it out

Calling 60 bb wins the 120 bb pot when he bluffs and loses 60 bb when he does not. It breaks even when bluffs make up bet ÷ (pot before his bet + 2 × bet) = 60 ÷ (60 + 2 × 60) = 33% of his bets: lesson 4's price. The Maniac bluffs 45%: 0.45 × 120 − 0.55 × 60 = +21 bb. The Nit bluffs 15%: 0.15 × 120 − 0.85 × 60 = −33 bb. Same cards, opposite answers.

Exploiting has a cost: it moves you away from balance and can be counter-exploited if your read is wrong or the opponent adapts. Bigger, more reliable reads justify bigger adjustments. The next part asks what to play when you have no read at all.

Formula

Break-even bluff share for a bluff catcher = bet ÷ (pot before his bet + 2 × bet)

Check your understanding

1. He bets half the pot. What share of his bets must be bluffs for a bluff catcher to break even, in %?

   Show the answer

   Answer: 25%

   bet ÷ (pot + 2 × bet) = 0.5 ÷ (1 + 2 × 0.5) = 0.5 ÷ 2 = 25%.

2. A Loose-aggressive player bets the pot on the river, and 30% of his bets are bluffs. With a bluff catcher, you:

   1. Fold
   2. Call
   3. Call half the time
   Show the answer

   Answer: Fold

   A pot-sized bet needs 33.3% bluffs and he has 30%: 0.30 × 2 − 0.70 × 1 = −0.1 pots per call. Close, but a fold.