Author: Dann Corbit
Date: 13:04:13 03/29/04
Go up one level in this thread
On March 29, 2004 at 15:59:59, Uri Blass wrote: >On March 29, 2004 at 15:50:10, Dann Corbit wrote: > >>On March 29, 2004 at 10:17:18, martin fierz wrote: >> >>>aloha! >>> >>>i was discussing this somewhere in a thread, but thought i'd like to make this >>>question more visible in the hope of getting a good answer: >>> >>>everybody knows that with plain alpha-beta, a fixed number of moves N per node, >>>and perfect move ordering a search to depth D needs >>> >>>nodes(depth) = sqrt(N)^(D/2) nodes. >>> >>>with absolutely imperfect move ordering it needs >>> >>>nodes(depth) = N^(D) nodes. >>> >>>a typical chess program gets something like 90% move ordering in the sense that >>>if a cutoff move exists, it will search it as first move in 90% of all cases. >>>here's my question: >>> >>>can anybody give an estimate for nodes(depth) as function of this move ordering >>>parameter? obviously, this would also depend on when you find the best move in >>>those cases where you don't find it first. any kind of model is acceptable, e.g. >>>you always find it on 2nd, always on sqrt(N)th, always last, at a random number, >>>whatever. i'm just interested in the general behavior of nodes(depth) as a >>>function of the cutoff-%age. >>> >>>i'd be extremely surprised if nobody ever estimated this, so: has any of you >>>ever seen or calculated such numbers, and if yes, what do they look like? >>> >>>and is there any theory how this would apply to a modern chess program with >>>nullmove and extensions instead of the plain A/B framework above? >>> >>>basically this question of course means: do you really gain anything tangible >>>when improving your MO from say 90% to 92%? >> >>I have not done the math, but I am guessing no matter what king of move ordering >>you have (purely randome or the pv move every time) you will get something like >>this: >> >>nodes = some_constant * sqrt(mini_max_nodes) >> >>If you have random move ordering, then the constant will be very large. >>If you have perfect move ordering, then the constant will be very small. >> >>You will never get worst case unless you try very hard to achieve it. >>It might be possible to degenerate to mini-max (or very close to it) but you >>will have to choose the worst possible move at every single turn except the >>leaves. I doubt if anyone can do it. >>;-) > >doing it is not enough because the worst move can cause fail high. But even that case might go perverse if each subsequent node also failed high (e.g. some zugzwang position and you go from the least bad for the opponent to the most bad) and you have to do a full width research for every node. I doubt in real life if minimax type behavior can ever be created. But it might be closely approximated if you tried really hard. Not sure why you might want to do that.
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