On Biased Positional Games
Małgorzata Bednarska · Combinatorics Probability Computing · 1998
Let TBin( N , n , q ) be the game on the complete graph K N in which two players, the Breaker and the Maker, alternately claim one and q edges, respectively. The Maker's aim is to build a binary tree on n 0, there exists n 0 such that, for every n [ges ] n 0 , the Breaker has a winning strategy in TBin( N , n , q ) if q >(1+ε) N /log n , while, for q <(1−ε) N /log n , the game TBin( N , n , q ) can be won by the Maker provided that n = o ( N ).