Almost optimal pairing strategy for Tic-Tac-Toe with numerous directions

Padmini Mukkamala, Dömötör Pálvölgyi

We show that there is an $m=2n+o(n)$, such that, in the Maker-Breaker game played on ${\mathbb{Z}}^d$ where Maker needs to put at least $m$ of his marks consecutively in one of $n$ given win…