- #1

- 655

- 3

EG,

x wins:

X O ..

.. O X

.. X ..

o wins:

X .. X

O O O

X .. ..

- Thread starter maze
- Start date

- #1

- 655

- 3

EG,

x wins:

X O ..

.. O X

.. X ..

o wins:

X .. X

O O O

X .. ..

- #2

- 664

- 3

It seems that if you go first, you can always force a win. You could lose if you tried to (while going 1st), but you can always win if you go first. And actually, I think you're destined never to have a tie game, either.If you play tic-tac-toe on a torus (the board wraps around), would you prefer to move first or second, or does it matter?

DaveE

- #3

Hurkyl

Staff Emeritus

Science Advisor

Gold Member

- 14,916

- 19

The proof goes as follows: suppose player 2 has a winning strategy. Then player one has a winning strategy as follows:

1. Place his first piece randomly (this will now be called the 'extra' piece)

2. Pretend the extra piece doesn't exist

Note that, when pretending this, he becomes player 2 in his pretend game

3. Use player 2's winning strategy to win

Note that if the winning strategy ever asks him to play a piece where he's already put his extra piece, then he just stops pretending it's extra, and makes a random play, now considering *that* piece the extra piece

Since both players cannot win, we have a contradiction. Therefore, there exists a player 1 strategy that guarantees player 2 cannot win.

Of course, there are variations you can make to defeat this technique... but you didn't make one.

Since both players cannot win, we have a contradiction. Therefore, there exists a player 1 strategy that guarantees player 2 cannot win.

Of course, there are variations you can make to defeat this technique... but you didn't make one.