Biased Positional Games for Which Random Strategies are Nearly Optimal

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and natural numbers n and q let G(G; n, q) be the game on the complete graph in which two players, Maker and Breaker, alternately claim 1 and q edges respectively. Maker's aim is to build a copy of G while Breaker tries to prevent it. Let . It is shown that there exist constants and such that Maker has a winning strategy in G(G; n, q) if , while for the game can be won by Breaker.