Difference between revisions of "Parallelogram boards"
From HexWiki
(Added 3x9; the lower bound is 3x8, and 5 is easily achievable.) |
(Resolved 4x9. Lower bound is 4x8, and 4 pieces is easily achievable.) |
||
| Line 17: | Line 17: | ||
|- | |- | ||
! scope="row" | 4 | ! scope="row" | 4 | ||
| − | | 0 || 0 || 0 || 1 || 2 || 2 || 3 || 4 || | + | | 0 || 0 || 0 || 1 || 2 || 2 || 3 || 4 || 4 || || || |
|- | |- | ||
! scope="row" | 5 | ! scope="row" | 5 | ||
Revision as of 04:46, 12 October 2020
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 | 5 | |||
| 4 | 0 | 0 | 0 | 1 | 2 | 2 | 3 | 4 | 4 | |||
| 5 | 0 | 0 | 0 | 0 | 1 | 2 | 2 | 3 | (≤)5 | |||
| 6 | 0 | 0 | 0 | 0 | 0 | 1 | 2 | 2 | 3 | (≤)5 | ||
| 7 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 2 | 2 | |||
| 8 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 2 | 2? |
