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What are some ways in which you can force a win? Do you have an advantage as the first or second player?

Consider the following strategy: As the first player, take the center of the middle board first. Whatever move the other player makes, you can make a move that requires the other player to block a 3-in-a-row in a place that cannot be in the same 3-in-a-row as their first move. Then you can choose a spot which gives you two possible 3-in-a-rows. Then the other player must block one but you still win -- in a total of 7 moves.

For example,

1. you move in the center (X)

2. the other player moves anywhere (O)

3. you move so that they have to block you where it won't give them 2 in the same row

(This is possible since every space other than the center is not a 3-in-a-row with some other space -- those around the outsides are not in a row with the center square in a different level and those in the center cannot be used in a 3-in-a-row except within the level since you already hold the center space.)

4. the other player moves to block you

5. you move to have two possible 3-in-a-rows

(This is possible since you had moved to have two in a row earlier -- one of which was the center; and because of the three levels you can move so you have two potential 3-in-a-rows, one within a level and one using the center space.)

6. the other player blocks you

7. you win

Another interesting question to explore would be to find the expected length of a game if players are just playing randomly.