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We describe two unexpected applications of game theory to recreational mathematics. The first, which is joint work with Scrabble expert Nick Ballard, is a Scrabble position in which the best strategy is mixed (i.e., randomized). Although it is not theoretically surprising that such positions should exist, ours is the first provably correct explicit example, and even elite Scrabble players find it striking. The second concerns an old but little-known lateral-thinking "poison puzzle" by Michael Rabin, which turns out to have several alternative solutions to the intended solution. We are led to consider a two-player game with three distinct Nash equilibria, which is difficult to analyze theoretically and begs for experimental investigation