Kaplansky's game or Kaplansky's ''n''-in-a-line is an
abstract board game
A board game is a type of tabletop game that involves small objects () that are placed and moved in particular ways on a specially designed patterned game board, potentially including other components, e.g. dice. The earliest known uses of the ...
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.
It is named after
Irving Kaplansky
Irving Kaplansky (March 22, 1917 – June 25, 2006) was a mathematician, college professor, author, and amateur musician.O'Connor, John J.; Robertson, Edmund F., "Irving Kaplansky", MacTutor History of Mathematics archive, University of St And ...
.
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)
Hex (also called Nash) is a two player abstract strategy board game in which players attempt to connect opposite sides of a rhombus-shaped board made of hexagonal cells. Hex was invented by mathematician and poet Piet Hein in 1942 and later r ...
*
Harary's generalized tictactoe
References
{{Tic-Tac-Toe
Abstract strategy games
In-a-row games