Meta Tic Tac Toe

Meta Tic Tac Toe with Monte Carlo Tree Search (without neural networks).

+-1-2-3-+-4-5-6-+-7-8-9-+
1       | o o o |       |
2       | o o o |       |
3     o | o o o | o   o |
+-------+-------+-------+
4 x x x |     x |   x   |
5 x x x |   x   | x     |
6 x x x |     o |       |
+-------+-------+-------+
7 x     |   o   | . x x |
8   o   |       | . . . |
9       |       | . . . |
+-------+-------+-------+
        x to move
        
Choose your move!
> 77

This graphic analyzes the winning prediction (probability) of the first player dependent on their first move.

The central sub-board is evidently the preferred choice. The central square within both the central and corner sub-boards has the highest probability of winning.
However, in the edge sub-boards, the preference shifts to the edge squares. Even the least favorable move still provides a winning chance of more than 50%.

Rollouts play an important role in the Monte Carlo Tree Search Algorithm, particularly when not a neural network isn't used. When reaching a leaf node at the constructed tree, a game is played to the end by rolling it out using random moves. This heuristic gives a hint which player is likely to win the game from the specific leaf node position of the game.

The graph illustrates the correlation between the rolled out winnings chances and the actual value Q of a position.