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Why are games fun? In part, because they challenge our ability to think. Even simple games like Tic-Tac-Toe, Nim and Kalah, or puzzles like the Eights Puzzle, are challenging to children. More complex games like checkers, chess, bridge, and Go are difficult enough that it takes years for gifted adults to master them. Nearly all games require seeing patterns, making plans, searching combinations, judging alternative moves, and learning from experience, all being skills which are also involved in many daily tasks.
It's no surprise that Alan Turing proposed chess playing as a good project for studying computers' ability to reason. In many ways, games have provided simple proving grounds for many of AI's powerful ideas.