#1: Kuhn Poker | Rules

Kuhn Poker Rules

Kuhn Poker is the simplest nontrivial version of poker. Here is the setup:

  • 3 card deck: Queen, King, Ace (in ascending order, so Ace is highest)

Any deck of 3 ranked cards works. For example:

  • The python game engine that we’ll use in later challenges uses {0, 1, 2}.

  • Wikipedia’s description uses {Jack, Queen, King}.

  • Kuhn Poker is played with 2 players. For this exercise, they’ll be and .

  • Each player starts with 2 chips and both players ante 1 chip.

  • Deal 1 card to each player (discard the third).

  • There is one street of betting in which players can take these actions:

    • ↑Up (putting a chip into the pot)

    • ↓Down (not putting a chip into the pot)

↑Up and ↓Down in traditional poker terms

  • ↑Up actions indicate a Bet or Call.

  • ↓Down actions indicate a Check or Fold.

Example game

  • Players ante and cards are dealt.

  • sees a A and plays ↑Up (1 more chip into pot).

  • sees a K and plays ↑Up (1 more chip into pot).

  • Both cards are revealed in a 2-chip showdown. has an A and has a K.

  • has the better hand and wins +2 chips (+1 from the ante, +1 from ’s ↑Up).

The betting (and the game) can go in three ways:

  1. One player plays ↑Up, then the other player plays ↓Down. The player who played ↓Down folds. The winner wins the loser’s ante (and gets their own chip back). The players’ cards are not revealed. Note that this happens if the action is :
  • ↑Up, ↓Down, or
  • ↓Down, ↑Up, ↓Down.

  1. Both players play ↓Down. They go to a showdown and the winner wins the one chip that the loser anted (and their own back).

  2. A player plays ↑Up, then the other player plays ↑Up. They go to a showdown and the winner wins the two chips the loser has put in the pot (and gets their own chips back). Note that the game will proceed to a 2-chip showdown if the action is:

  • ↑Up, ↑Up or - ↓Down, ↑Up , ↑Up.

Here is a list of all possible betting sequences:

Winner
↑Up ↓Down (+1)
↑Up ↑Up Higher Card (+2)
↓Down ↓Down Higher Card (+1)
↓Down ↑Up ↓Down (+1)
↓Down ↑Up ↑Up Higher Card (+2)
Partner Exercise: Get started with Kuhn Poker

  • Get cards, chips, paper, pen

  • Play 3 hands of Kuhn Poker and get used to how the game runs

  • Use the pen and paper to start writing down all deterministic situations in the game (situations where there is clearly a correct move that you should take 100% of the time)

  • Play more hands as you think helpful

  • Once you have what you think is a full list of the deterministic states, you can stop and review the optional reading