Imagine a grid of squares, like a tictactoe 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 game should be over after the player who goes first, makes her third move.
X's first move. Two X's next to each other.
Option A:
O's first move. Block both ends if the string of X's with an O. Anything else and the next two X's win.
X's second move. Two new X's adjacent to the first two (forms a 2x2 grid) At this point there are 10 spots for O to block. Can't cover them all, so X will win on her third turn.
Option B:
Lets say that O wiped one of the X's from the board during her first turn.
O's first move. Place the O anywhere. (it doesn't matter)
X's second move. Two X's on a different row, one adjacent to the first X and one diagonal. At this point there are 6 points to block. If O does not erase an X. X will win on the third turn.
If O erases one X, there will remain two X's adjacent to one another and only one O available to block. X's third move will complete the string of 4.

Posted by Leming
on 20060609 16:43:21 