Game Analysis

As a mathematician, I can't resist thinking about the best strategy for a game. Some games yield easily to analysis, other are impenetrable.  More details to follow, but here are some initial comments . . .

Noughts & Crosses (aka Tic Tac Toe)
Great game to teach kids, but experience soon leads to near perfect play.
A computer can run through the tree of all possible games, so the game is completely solved.  See my OXO article for a downloadable file giving the game result (with best play) from all possible positions (allowing for rotations and reflections).

Nim (take away game)
Single or multiple pile games have an easy mathematical strategy.  See Nim - Single Pile and Nim - 3,4,5.
Nim variants might be a bit trickier.

Hex
It is easy to prove that the first player has a winning strategy, but no-one knows it!
More detail in the Hex article.

Chess
Computers now play better than any human, but that does not mean there is a known winning strategy.

Lots of apparently simple abstract games have a search tree which grows exponentially to a ginormous size, so cannot be solved by computer.