What is Four in a Row on other board sizes?
Four in a Row works on any grid with enough room for a line of four, so it can be played on boards other than the classic one of 7 columns and 6 rows. Here you can choose a 6×5, 8×7, 9×7 or 10×7 grid in the table setup. Sizes are written as columns × rows, the way the classic board is described as 7 × 6.
Every rule stays the same. Red drops first, discs fall to the lowest free space in their column, and the first player with four discs in a row horizontally, vertically or diagonally wins. A full grid without a four is a draw.
The 6×5 grid holds 30 discs and plays quickly, with little room to build threats before the grid fills. The 8×7, 9×7 and 10×7 grids hold 56, 63 and 70 discs. Each extra column gives more ways to make a line across the board, and the seventh row adds room for threats stacked higher in a column, so games last longer and the fight over who keeps the last useful threat matters even more.
Rule changes
| Rule | Standard Four in a Row | Four in a Row on other board sizes |
|---|---|---|
| Board | Standard Four in a Row7 columns × 6 rows, 42 spaces. | Four in a Row on other board sizes6×5 (30 spaces), 8×7 (56), 9×7 (63) or 10×7 (70), chosen in the table setup. |
| How to win | Standard Four in a RowFour of your discs in a row horizontally, vertically or diagonally. | Four in a Row on other board sizesThe same four in a row on every size. |
| Game length | Standard Four in a RowAt most 42 drops. A full grid without a four is a draw. | Four in a Row on other board sizesAt most 30, 56, 63 or 70 drops. A full grid without a four is a draw. |
| First move | Standard Four in a RowRed drops first and the players alternate. | Four in a Row on other board sizesThe same. On 9×7, the only grid with an odd number of spaces, Red makes the last drop of a full grid. |
| Perfect play | Standard Four in a RowSolved in 1988: the first player wins with perfect play by starting in the middle column. | Four in a Row on other board sizesIn John Tromp's computer results 6×5 is a draw and 8×7 a win for the first player. 9×7 and 10×7 are not in his table. |
History
The classic game is played on a grid of 7 columns and 6 rows, and that is still by far the most common size. Board sizes such as 6×5, 8×7, 9×7 and 10×7 are listed among its common size variations, and many of them are studied more in game theory and computer research than played at the table.
The 7×6 game was solved in 1988, first by James D. Allen, who announced his solution on 1 October, and then independently by Victor Allis, who announced his 15 days later. With perfect play the first player wins by starting in the middle column. John Tromp later solved the game by brute force, beginning with a database of all positions after eight moves.
Tromp's solver has since worked through many other sizes, and his table of results lists 6×5 as a draw and 8×7 as a first-player win. His 9×6 result took about 2,000 hours of computation and was finished in November 2005, and in late 2015 he solved 8×8 as a win for the second player.