In an $a\times b$ board, two players take turns putting a mark on an empty square. Whoever gets $c\leq \max(a,b)$ 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. A generalization is that for $a,b,c$ are all odd, the first player can go on the middle square, then reflect the second player's move across the middle square. (He also needs to keep his eyes open in case the second player marks the $(c-1)$st square of a $c$-in-a-row, so that he can win immediately.)
In the one-dimensional case ($a=1$), this may well be a known game, but I also cannot find a reference.