Part 3 · Lesson 13 of 25 · Pro
The AKQ game: poker game theory with three cards
In a game with only three cards, the queen should bluff exactly one time in three when the pot is 2 bets, and no opponent can punish it. The AKQ game: A, K and Q, one card to each player and one left over. The first player may bet; the second calls or folds.
The hand
You hold the Q. The Tight-aggressive player holds the A or the K, equally likely. The pot is 2 bets; you may bet 1 or check.
Predict first
Your Q never wins a showdown. How often should you bet it as a bluff?
- Never: it always loses
- One time in three
- Always: it is your only way to win
Formula
Pot P (more than 1 bet), bet 1: bluff the Q with frequency 1 ÷ (P + 1); call with the K with frequency (P − 1) ÷ (P + 1)
This lesson is part of Pro. Above are its opening, its question and the idea it leads to; the worked numbers, the common mistake, the interactive tool and the check are in the app.