Efficient Winning Strategies in Random-Turn Maker–Breaker Games

Asaf Ferber, Michael Krivelevich, Gal Kronenberg

Research output: Contribution to journalArticlepeer-review


We consider random-turn positional games, introduced by Peres, Schramm, Sheffield, and Wilson in 2007. A p-random-turn positional game is a two-player game, played the same as an ordinary positional game, except that instead of alternating turns, a coin is being tossed before each turn to decide the identity of the next player to move (the probability of Player I to move is p). We analyze the random-turn version of several classical Maker–Breaker games such as the game Box (introduced by Chvátal and Erdős in 1987), the Hamilton cycle game and the k-vertex-connectivity game (both played on the edge set of Kn). for each of these games we provide each of the players with a (randomized) efficient strategy that typically ensures his win in the asymptotic order of the minimum value of p for which he typically wins the game, assuming optimal strategies of both players.

Original languageEnglish
Pages (from-to)446-465
Number of pages20
JournalJournal of Graph Theory
Issue number2
StatePublished - Jun 2017


  • Maker-Breaker games
  • positional games
  • random graphs


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