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Biased weak polyform achievement games

Abstract : In a biased weak (a,b) polyform achievement game, the maker and the breaker alternately mark a,b previously unmarked cells on an infinite board, respectively. The maker's goal is to mark a set of cells congruent to a polyform. The breaker tries to prevent the maker from achieving this goal. A winning maker strategy for the (a,b) game can be built from winning strategies for games involving fewer marks for the maker and the breaker. A new type of breaker strategy called the priority strategy is introduced. The winners are determined for all (a,b) pairs for polyiamonds and polyominoes up to size four.
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Ian Norris, Nándor Sieben. Biased weak polyform achievement games. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2014, Vol. 16 no. 3 (3), pp.147--172. ⟨10.46298/dmtcs.2098⟩. ⟨hal-01188912⟩

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