# Parallelogram boards

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Hex is usually played on a rhombic n×n board, but one can also try playing it on n×m parallelogram boards, where n is the number of rows, m the number of columns, and n ≠ m. However, there is a simple symmetry winning strategy for the player with the shorter distance between his sides, even when he moves second. To mitigate this, one can allow the player with the greater distance between his sides to begin the game and place a certain number of pieces at once in her first move. In particular, it has been found that Hex on a 7×9 board is a rather fair game, when the vertical player may start the game with two pieces at once.

Number of pieces head start the vertical player needs to force a win:

× 1 2 3 4 5 6 7 8 9 10 11 12
1 1 2 3 4 5 6 7 8 9 10 11 12
2 0 1 2 2 3 4 4 5 6 6 7 8
3 0 0 1 2 3 3 4 (≤)5
4 0 0 0 1 2 2 3 (≤)4
5 0 0 0 0 1 2 2 (≤)5
6 0 0 0 0 0 1 2 2 (≤)5
7 0 0 0 0 0 0 1 2 2
8 0 0 0 0 0 0 0 1 2 2?