Kaplansky's game

Updated on Oct 26, 2023

Edit

Comment

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 unmarked n stones of their own color in a row, horizontally, vertically, or diagonally. It is named after Irving Kaplansky.

General results

k ≤ 3 is a first-player win.

k = 4 : unknown. but it is probably a tie.

5 ≤ k ≤ 7 is believed to be draw. But it is not known if this suspicion is true.

k ≥ 8 is a draw: Every player can draw via a "pairing strategy" or other "draw strategy" of m,n,k-game.

References

Kaplansky's game Wikipedia

(Text) CC BY-SA