## Nov 12 Meta Tic-Tac-Toe

This isn't the first time that noughts and crosses has come up on this website. However the game is so enduring because the rules are simple and it has been independently invented at various times in history. In this article I'm going to look at one of the more imfamous variations of it, Meta Tic-Tac-Toe.

Each of the 9 squares of the grid are filled out with a smaller noughts and crosses game. The first player may play anywhere on any of the grids for their first move. Letâ€™s say that they play here:

X went first

After the first move each subsequent turn must be played in the same large square that corresponds with the position of the smaller square from the previous move. For example our turn two has to be in the middle right large square like this:

O is forced to play in the right middle large square

If I play a few more moves you can see it evolve. X played on the left of the middle square, then when O sent her back to the middle she played in the bottom left. O claimed the centre of the bottom left, but this will allow X to win the middle large square on the next move:

The game unfolds. Each move dictates which large square the opponent must play their next move in

Although moves can still be played in the middle it is now owned by X and so I've drawn a large marker in it to claim it:

The game is won by a player getting a line of three on the large board. Lines of 3 on the smaller board are only used to claim large squares.

There is an opening gambit which is sometimes used by the first player and in the only two games I've ever played it worked successfully. The idea is to play in the centre centre square as your first move. The other player now has to play in the same large square. Whichever square they send you to you repeatedly pick the centre square again. For example, the first 3 moves could look like this:

The first three moves

But every move the second player is forced back into the centre large square. They quickly win it, but that becomes redundant. They have to force you, the first player, into a new square each time where you can claim the centre of each.

After sending the second player back to the centre for the last time they have no more mores and so get a turn of free play. For the price of one large square you get a hefty advantage in the other 8.

Claiming the middles of 8 of the large squares at the cost of the entire centre large square. A possibly good strategy.

Despite having a search space bounded at around 10^50 (actually far lower because lots of games end early) computers have solved Meta Tic-Tac-Toe as a win for the first player.