Introduces the (m,n)_q-game on affine spaces F_q^m and proves existence of a finite threshold T(n,q) separating draw and first-player-win regimes, with explicit bounds including T(n,2) ≤ 2^{n+1}.
Positional games.Combinatorics, Probability and Computing, 14:649–696
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Thresholds for Tic-Tac-Toe on Finite Affine Spaces
Introduces the (m,n)_q-game on affine spaces F_q^m and proves existence of a finite threshold T(n,q) separating draw and first-player-win regimes, with explicit bounds including T(n,2) ≤ 2^{n+1}.