Tic Tac Toe is a game that can end in a draw. So in any Tic Tac Toe game state, either one of the two players can force a win or both players can force a draw. On an empty tic tac toe board, both players can force a draw, so the game is a theoretical draw.

In the game of Nim, there are no ties, so there is always one player in a position capable of forcing a win. I should have made it clear in my last statement that i was refering specifically to non-tie games, such as Pearls/Nim.

In addition, his argument was about the complexity involved in determining safe states, not the existence of them,

Yeah, sorry, i misread that.


By the way, in John's posts where he uses [ code ], some of his post is cut off.

I think we should all collaborate and devise a strategy for forcing wins in Chess.

Tic Tac Toe is a game that can end in a draw.

Sorry. I misread your original post as ``any game's state''.

Regardless, it's still untrue, as any game's initial position has neither side in an indefensible state. If it did, it wouldn't be a very good game.

Regardless, it's still untrue, as any game's initial position has neither side in an indefensible state. If it did, it wouldn't be a very good game.

I beg to differ. Pearls II starts out with the 2nd player in a winning position. That means player 1 cannot win no matter how he plays as long as player 2 plays perfectly.

Chess perhaps may start out with player 1 in a winning position. Nobody knows. But if it does, then the first player can win every single time as long as he knows how to go about forcing his win. And you're right, once you have a game solved, it's no fun playing - I suppose that's why most adults don't bother playing Tic Tac Toe, since with a little a practice you can force a draw every single game.

If you're interested, I have a math book that has a proof of the theorem that in games of this nature either one of the two players must be in a position to force a win or both players must be in a postion to force a tie.