Null move pruning

The null move heuristic has been added and yielded another pretty solid increase in Elo.

For the uninitiated, a “null move” isn’t a real over-the-board move of course, it’s just a heuristic that can be used to terminate a line of search early, before any moves are even generated. The heuristic is based on the “Null Move Observation,” which says that it is almost always better to do something rather than nothing.

The basic idea is to actually try “doing nothing” and seeing if that would allow the opponent to improve their position. If they can’t, odds are that when you really do make a move your position will be too good (the opponent will do something else which prevents this entire line anyway). An example might be capturing the opponent’s queen with a pawn, leaving none of my pieces hanging (en-prise). No matter what the opponent does in response, he’s probably losing, so he’ll make a move which avoids leaving his queen hanging in the first place.

For this to actually save time, the search that is done after “doing nothing” (allowing the opponent a second move) is done to a reduced depth. How much to reduce is the big question – too much and you will make some very unsafe and risky cutoffs. Too little and you’re not really saving much time. A very conservative value would be R=2 or R=3, but with increasing processor speeds and greater and greater search depths many programmers push this value to extremes. It should all be backed by testing. Currently I am using R=3 but I do plan to revisit this in the future.

I am also reducing that reduction towards the leaves to ensure there is at least one ply of full width depth search remaining before dropping into the quiescence search. The idea here is to give the search an opportunity to resolve checks (the qsearch is currently capture only). My programs also avoid using this heuristic in positions that are likely zugzwang, meaning any move could potentially be harmful (which violates the Null Move Observation the heuristic is based on).

You’d have to know a little about the alpha-beta algorithm for a more technical description to make sense, but there’s really no reason for me to do that when you can read all about it on CPW – https://www.chessprogramming.org/Null_Move_Pruning or on this old-but-excellent description by Bruce Moreland – http://web.archive.org/web/20070708232843/http://www.brucemo.com/compchess/programming/nullmove.htm .

The important question – how much is it worth?

WinsLossesDrawsPctEloError
78051670456.6%+46.13+/- 12.29
81250468457.7%+53.93+/- 12.41
chess4j self play match, with null move vs. without, 5+0.25

… and …

WinsLossesDrawsPctEloError
237111864528.0%-164.29+/- 13.13
Prophet 4 vs Prophet 3, 10+0.5

So once again a pretty large jump, and of course I’m very pleased. Prophet4 is now within 200 elo of Prophet3 and there is still a pretty good list of enhancements to implement.

The next four planned changes are going to be smaller and perhaps more difficult to measure: (1) stopping the iterator early if less than half the allotted time remains, (2) proper treatment of mate scores in hash (rather than the “cheat” that’s in place now), (3) aspiration windows within the iterative deepening function, and (4) re-examination of the three-fold rep: is a two-fold repetition good enough? I don’t expect any of those will be big changes on their own, but I’m hoping that cumulatively they’ll be worth a few points. But, you never know, which is why we test.

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