Sách Asymptotically optimal pairing strategy for Tic-Tac-Toe with numerous directions

Abstract
We show that there is an m = 2n + o(n), such that, in the Maker-Breaker game
played on Z
d
where Maker needs to put at least m of his marks consecutively in one
of n given winning directions, Breaker can force a draw using a pairing strategy.
This improves the result of Kruczek and Sundberg [15] who showed that such a
pairing strategy exists if m > 3n. A simple argument shows that m has to be at
least 2n + 1 if Breaker is only allowed to use a pairing strategy, thus the main term
of our bound is optimal.