here are still two optimizations left that we haven’t tried. The first is using the symmetry of the board to help us: for example, there are really only three first moves that can be made in...

here are still two optimizations left that we haven’t tried. The first is using the symmetry of the board to help us: for example, there are really only three first moves that can be made in Tic-Tac-Toe: a corner, the middle of the board, and the middle of a side. The second optimization is to truncate the tree when there’s a winner. These are both a bit tedious to track by hand, but it’s manageable with a small program. (programming required) We can cut the size of the game tree down to less than a third of the original size—actually substantially more!—by exploiting symmetry in plays. (We’re down to a third of the original size just within the first move.) Write a program to compute the entire Tic-Tac-Toe game tree, and use it to determine the number of unique boards (counting as equivalent two boards that match with respect to rotational or reflectional symmetry) in the game tree. How many boards are now in the tree