Toe Tac Tic

[cubedbee]

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]

Can't X just take the middle square and then place an X opposite wherever O places his O's?

[RedSoxFan]

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]

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]

Does it have to play through to the ninth move?

[thing]

| X |
-----------
| |
-----------
| |

Your move.

[4sigma]

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]

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]

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]

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]

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]

This is correct. X forces a win by taking the opposite edge.


| X |
-----------
| O |
-----------
| 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]

Not what I expected.

[Ebenezer Kohl]

| X |
-----------
| |
-----------
| |

Your move.

| X | O
-----------
| |
-----------
| |