You could run a very long search from the starting position, and save some fraction of the resulting tree. That

would speed up the first few moves in some circumstances; but consider that you can only save a very small part

of the precomputed tree, both as a practical matter, and because it would be mostly useless.

The problem is that a successful search tree is full of holes, corresponding to the nodes that were pruned out

by alpha-beta. As soon as your opponent steps off a path that you actually investigated, your saved tree is

irrelevant. So even if your search took 24 hours, reached 20 ply, and evaluated billions of terminal nodes,

saving the entire result is almost pointless.

For the same reason, keeping the search tree and using it to seed the search tree for the next move,

after the opponent responds, is mostly useless. You have to discard 99% of the saved tree, and save

only 1% of the time in the new search.