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?

(In reply to my thoughts by dylan)

you forgot one blocking position for:
XXX

the other option for O would be:
XOX
the follow up move is:

  X
XOX
  X

Now O is screwed. What ever O's move, X has a wining position.

And for turn 2
OXXO is a valid position too
then
OXXX or XXXO gives X a forced win.

Posted by Pascal Gelinas on 2007-04-27 17:46:33