Kaplansky's game

Kaplansky's game, also called Kaplansky's n-in-a-line, is an abstract strategy board game played by two people on an infinite lattice board. Players alternate placing a stone of their own color at any open point on the grid, and the first player to arrange k of their own stones in an unbroken line, with no opposing stone anywhere on that line, wins the game. Because the board has no fixed boundary, the game can in principle continue indefinitely if neither side completes a qualifying line. The game takes its name from the American mathematician Irving Kaplansky, reflecting its origin as a subject of mathematical study of combinatorial games rather than a commercially manufactured product. Its appeal lies less in physical equipment than in the strategic and combinatorial questions it raises about achieving an unbroken line under contested conditions on an unbounded surface.