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> From start of game to 50 squares left is enumerable.

A nitpick, but I don't think you meant to say "enumerable" here

"enumerable" means "able to be enumerated, or counted"

"innumerable" means "unable to be numbered, or counted"

Enumerable as in "computationally enumerable", or "able to be enumerated in a reasonable amount of time x cpu x memory"

The beginning and end of the game have less possibilities to consider. The midgame has the most possible moves = hardest to calculate.

If you read carefully, the midgame is the bit the author avoids explaining how to solve ;)