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cubedbee
04-07-2004, 05:25 PM
Game is played on a normal 3X3 tic tac toe board, with X going first. The goal of the game is not to place three in a row. The game is drawn if both players are sucessful, the game is won by a player who forces their opponent to place three in a row.

In regular tic tac toe, X can force a draw from any opening position with perfect play. I'm trying to figure out if the same is true for this game.

4sigma
04-07-2004, 06:25 PM
Can't X just take the middle square and then place an X opposite wherever O places his O's?

RedSoxFan
04-07-2004, 06:40 PM
Game is played on a normal 3X3 tic tac toe board, with X going first. The goal of the game is not to place three in a row. The game is drawn if both players are sucessful, the game is won by a player who forces their opponent to place three in a row.

In regular tic tac toe, X can force a draw from any opening position with perfect play. I'm trying to figure out if the same is true for this game.

Technically in tic tac toe, O can force a draw from any opening position (since X goes first and has the advantage). In toe tac tic, X is the one that can force the draw, despite the disadvantage of going first, using 4sigma's strategy.

4sigma
04-07-2004, 06:46 PM
An interesting toe-tac-tic problem:

X goes first and takes an edge (not the center or a corner).
O then takes the center.

Can either player now force a win, or with best play should a draw result?

Hummer
04-07-2004, 07:02 PM
Does it have to play through to the ninth move?

thing
04-07-2004, 07:03 PM
| X |
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4sigma
04-07-2004, 07:10 PM
Does it have to play through to the ninth move?

A good question. I understand the game to end if anyone completes 3 in a row. However, you could consider the problem under both sets of rules, I suppose.

BC
04-08-2004, 11:44 AM
If X plays first in a corner, O can force a win by playing adjacent to X.
There are 7 cases (based on X's next move) but all are fairly easy to solve.

If X plays first in the center, X can force a tie by playing opposite O.

This only leaves the "X places first on an edge" case.

Still working...

3rookie
04-08-2004, 11:56 AM
An interesting toe-tac-tic problem:

X goes first and takes an edge (not the center or a corner).
O then takes the center.

Can either player now force a win, or with best play should a draw result?
I don't think X can force a win regardless of the board setup after each has moved once. And O cannot force a win with the given setup. X's strategy is to not ever get 2 in a row with the 3rd unoccupied, as O can usually force X to play there for the final move. I think that no matter where X plays first, O will win.

Editing to agree with BC about X starting in the center always being able to force a draw.

BC
04-08-2004, 12:34 PM
An interesting toe-tac-tic problem:

X goes first and takes an edge (not the center or a corner).
O then takes the center.

Can either player now force a win, or with best play should a draw result?
I don't think X can force a win regardless of the board setup after each has moved once. And O cannot force a win with the given setup. X's strategy is to not ever get 2 in a row with the 3rd unoccupied, as O can usually force X to play there for the final move. I think that no matter where X plays first, O will win.

Editing to agree with BC about X starting in the center always being able to force a draw.

Actually, if X starts on an edge, O can start on the adjacent edge to force a win. Usually, O's second move is to place on the opposite edge; i.e. if the squares are numbered 1-9 in the normal way, and X places first in square 2, then O should play in square 4. And unless X places next in square 6, O should. If X's second move is square 6, then O should play in square 1 to force a win.

All this assumes I haven't made a mistake...

BC
04-08-2004, 01:24 PM
An interesting toe-tac-tic problem:

X goes first and takes an edge (not the center or a corner).
O then takes the center.

Can either player now force a win, or with best play should a draw result?

X Should Win. X takes the opposite edge from what it originally took.

If O takes any corner, X takes its "mirror" (i.e. if the first three moves were 2,5,8, and then O takes 1, X takes 3). Conversely, if O takes one of the two remaining edges, X takes a corner on the other side of the mirror (i.e. after 2,5,8,4, X takes either 3 or 7).

Note that I have not considered ALL possible winning strategies; in my analysis, once I found that either player could force a win, I stopped looking down that tree.

Lemma: If O can get two opposite edges, O can win with optimal play.

Corollary: In order for X to have any chance of forcing a tie, X must prevent O from getting two opposite edges. It turns out that this is not sufficient for X to force a tie (the only way for that to happen is if X starts in the middle) but it helps rule out a lot of "strategy branches" in the tree.

This lemma helped me in analyzing many of the cases. I leave proof to the interested reader.

4sigma
04-08-2004, 08:02 PM
This is correct. X forces a win by taking the opposite edge.

| X |
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| O |
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| X |

No matter how O plays, X can now force him to complete a row of 3 on his 4th move.

I thought it was interesting that X, supposedly at such a disadvantage at toe-tac-tic, can force a win from this early stage.

3rookie
04-09-2004, 10:02 AM
Not what I expected.

Ebenezer Kohl
10-28-2004, 02:41 PM
| X |
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