One thing that is on my (way too long) list of things to try is n-gram chess. 1-gram chess would, for every move from black, have a dictionary of (following move, win probability) pairs, and it would pick one that is legal using the win probabilities to generate a distribution (if there is a sure win, almost always pick it; if there is a move that always lost before, pick it very rarely)

You can start this of with empty dictionaries, and have the thing learn after each game (let two copies play for a few days to get let them teach each other how to play chess)

2-gram chess would improve on this by using (white move, black's reply) as the key in such a dictionary.

I think that would make for better chess than this. For some N, N-gram chess might even superficially look like the real thing at times.