Imagine a grid of squares, like a tic-tac-toe board, that goes on infinitely in all directions.
Players alternate taking turns marking the board with X's and O's. The winner is the first player to get four marks in a row (horizontally, vertically, or diagonally).
On each turn, a player may either:
A: Place two of his/her marks on the board, or
B: Remove one of the other player's marks, and then place one of their own.
With optimal play, does either player have a forced win, or will this game continue on infinitely?
The first player has a forced win by his/her third move at most (with optimal play).
Like a simplified Pente.
Anyone care to explain? X should always place two marks for optimal play. O should either surround X's marks, or remove one and place the other one adjacent for optimal play. X tries to form an L shape, or a box shape (2x2), or a diamond shape (2x2), and will win on the third turn.
Posted by Ryan
on 2006-06-09 16:30:31