Jenga

Abstract

Jenga is a popular block game played by two players. Each player in her turn has to remove a block from a stack, without toppling the stack, and then add it the top of the stack. We analyze the game mathematically and describe the optimal strategies of both players. We show that 'physics', that seems to play a dominant role in this game, does not really add much to the complexity of the (idealized) game, and that Jenga is, in fact, a Nim-like game. In particular, we show that a game that starts with n full layers of blocks is a win for the first player if and only if n = 2, or n = 1,2 (mod 3) and n ≥ 4. We also suggest some several natural extensions of the game.