Hexapawn

A simple game in which the computer learns to play well from its mistakes.

This is a deterministic game invented by Martin Gardner, who presented it as a simple demonstration of computer adaptation. Originally designed to be played against a mechanical computer made out of matchboxes and jelly beans. As you play and win, the computer will "learn" from its mistakes, until eventually, it can win every time. To start over you must reset the computer's skill level.

More info:

http://en.wikipedia.org/wiki/Hexapawn