I remeber implementing a version of this in basic about ten years ago. What I remember being really fun was telling the program to play itself.

Intitially the two robots played randomly, but then a trend would start to emerge. However, as soon as it did, the feedback would cause the opponent to change his strategy, and the trend would shift or disappear. Gradually the robots learned that there was no 'winning move' and each assigned an equal probability to each move.

I'm sure I was inspired by WOPR's tic-tac-toe game in the classic movie 'Wargames'. Unfortunately, my robots weren't as smart as WOPR, they never realised the sisyphean futility of their game ;)