[qntm]

Alpha-beta pruning sounds like a reasonable route forward. In this case, each "well" is a state in the game and placing a new piece in the well constitutes a move to a new state. Since the "heuristic value" of a move is absolute (player wins or AI wins), I already have stuff in place to exit early from an exhaustive evaluation of all possible landing points if a definitive answer is found. But I don't have anything in place to put those landing points into an optimal order for evaluation purposes. A Tetris-playing AI which can quantify the "goodness" of a move would be useful here, and that's entirely possible.

Intelligent caching is possible but I think it would be difficult for me to implement and I'm not certain that it would yield much benefit.

Actually, the procedure for identifying all the possible player moves is very fast already and I think making it prioritise "easier" moves would slow it down. In particular, ruling out or de-prioritising simple things like "tucking" a piece under another is very counterproductive.