I read recently of an invincible checkers-playing program call Chinook. Apparently this computer can never be beaten because a bunch of scientists sat down and literally mapped out a metric crap load of moves and combinations (39 trillion) that would lead to a tie or a win for Chinook.
What is amazing here is that it took 18 years to solve what appears to be one of the simplest board games on the planet. Do not get me wrong this is an amazing landmark for computer science, I find the topic fascinating and I always wish that I had done more with neural networks and fuzzy logic while at University.
Ultimately I feel a little sorry for all the real word games that can/will be mathematically resolved to win, lose or draw. I think it takes away from the mystery of competition. Even the success of IBM's Deep Blue falls way short of invincibility. The complexity of chess, or should I say the variations of chess, make mapping every move almost impossible. Resolving chess "would require an effort so massive that the world’s fastest computers would need eons to play out every possible move".
"Brain: an apparatus with which we think we think." - Ambrose Bierce