Kaplansky's game

Kaplansky's game or Kaplansky's n-in-a-line is an abstract board game in which two players take turns in placing a stone of their color on an infinite lattice board, the winner being the player who first gets k stones of their own color on a line which does not have any stones of the opposite color on it.^[1][2][3][4] It is named after Irving Kaplansky.

General results

• k ≤ 3 is a first-player win.
• 4 ≤ k ≤ 7 is believed to be draw, but this remains unproven.
• k ≥ 8 is a draw: Every player can draw via a "pairing strategy" or other "draw strategy" of m,n,k-game.

See also

• m,n,k-game
• Hex (board game)
• Harary's generalized tictactoe