Parameters $a,b,c$ are given such that $c\leq\max(a,b)$. In an $a\times b$ board, two players take turns putting a mark on an empty square. Whoever gets $c$ consecutive marks horizontally, vertically, or diagonally first wins. (Someone must win because we use only one mark type.) For each triple $(a,b,c)$, who has a winning strategy?

For $a=b=c=3$ (tic-tac-toe size), the first player can win by first going on the middle square and winning in the next turn.

In the one-dimensional case ($a=1$), this may well be a known game, but I also cannot find a reference. I asked the question on math.SE but it has not been solved.

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