Abstract: We develop an approach to combinatorial games (e.g., chess, Go, checkers, Chomp, Nim) that unveils connections between such games and nonlinear phenomena commonly seen in nature: scaling behaviors, complex dynamics and chaos, growth and aggregation processes. Using the game of Chomp (as well as variants of Nim) as prototypes, we show that the game possesses an underlying geometric structure that "grows" (reminiscent of crystal growth), and show how this growth can be analyzed using a probabilistic renormalization procedure. This approach allows us to answer some open questions about the game of Chomp and opens a new line of attack for understanding (at least some) combinatorial games more generally through their underlying connection to nonlinear science.

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