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JGWeissman comments on Explaining vs. Explaining Away - Less Wrong
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I'd be surprised if a chess program weren't easily re-adapted to playing Checkers just by adding rules for the pieces; checkers even has a similar "transformation" rule as pawns in Chess, whereby pieces which reach the opposing side of the board can turn into pieces with different abilities. Backgammon, on the other hand...
The hard parts of make chess and checkers AI would not translate well, like evaluating the strength of a position, and strategies for pruning the search tree.