And other mathematical games. I'm going to be teaching an elective this semester on How to Win Games, and I thought it's start out with more deterministic games like Tic Tac Toe and later in the semester do games that involve chance. Or move along the spectrum of skill/chance as I go. I'm not really sure which games I want to go over, though. Any suggestions?
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"To truly live, one must first be born." ~ Evan [aX]
Paper Mario Social: The Safe Haven of GameFAQs. (Board 2000083)
The annoying thing about abstract-strategy games is that, given sufficiently large game trees, mathematics tends to be useless for improving one's own play. It's only good for programming computer players. So the deepest questions on this topic are computer-sciency questions of how to get the best play out of finite memory and computation time.
Two games that are especially noteworthy from this perspective are Arimaa, which was specifically designed to be easy for humans and hard for computers, and backgammon, for which (I read in an AI textbook) expert-level play is currently beyond the reach of software but the way that existing software plays has influenced the human metagame. It's also interesting to compare chess, which computers are now better at than humans, and Go, which remains very difficult for computers.
If you want to stay away from computer science, games of chance with smaller game trees than backgammon, like card games, are probably your best bet. Then you can leverage probability and statistics.
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What atrocities have been committed in the name of backwards compatibility!
Well, I definitely want to start with games where you can develop a winning strategy, or at least a non-losing strategy, so Nim-based games will also probably be up in the course. But yeah, I don't want to stray into computer science too much.
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"To truly live, one must first be born." ~ Evan [aX]
Paper Mario Social: The Safe Haven of GameFAQs. (Board 2000083)