The vertex picking game and a variation of the game of dots and boxes

Meyniel, H.; Roundneff, Jean-Pierre

doi:10.1016/0012-365x(88)90007-6

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2021

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“…Later, Berlekamp [5] wrote an entire book The Dotsand-Boxes game: Sophisticated Child's Play about the game, in particular discussing winning strategies in particular positions. Since then, the mathematics of Dots & Boxes and variants has been discussed in many papers and books [1,2,7,12,16,21,22,26,30,31,33,34]. There is also a rich body of work on solvers for Dots & Boxes [3,4,11,27,35].…”

Section: Introductionmentioning

confidence: 99%

Dots & Boxes is PSPACE-complete

Buchin,

Hagedoorn,

Kostitsyna

et al. 2021

Preprint

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Exactly 20 years ago at MFCS, Demaine posed the open problem whether the game of Dots & Boxes is PSPACE-complete. Dots & Boxes has been studied extensively, with for instance a chapter in Berlekamp et al. Winning Ways for Your Mathematical Plays, a whole book on the game The Dots and Boxes Game: Sophisticated Child's Play by Berlekamp, and numerous articles in the Games of No Chance series. While known to be NP-hard, the question of its complexity remained open.We resolve this question, proving that the game is PSPACE-complete by a reduction from a game played on propositional formulas.

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