(C) Dirk Hanneforth, Ravensburger Spieleverlag 1994, Play the game

[In Deutsch]


At the beginning of the game each of both players gets 15 chips.
Each round consists of betting up to 3 chips: Both players simultaneously choose a number from 0 up to 3 of their remaining chips. A player who selects more chips than his opponent wins the round. 
A player who has won 3 rounds more than his opponent wins the whole game.

Some comments concerning the game:

QUAAK! is a very simple game of bluffing (the publisher created it for childs in the age from 7 to 12 years).

The computer is using a (randomized) mixed minimax strategy. The general existence of such strategies for all two-player zero-sum games was first proved by the famous mathematician John von Neumann in 1928. The strategy was computed recursively using the so called simplex algorithm for each round. Details are described in chapter 44 of my book "Luck, Logic and White Lies: The Mathematics of Games" (preface and contents).

The strategy is optimal in the sense that you don't have any  bluffing strategy which is favourable against the computer in the long term.

Jörg Bewersdorff