Author: Dann Corbit
Date: 01:37:31 07/13/02
Go up one level in this thread
On July 13, 2002 at 04:02:49, Uri Blass wrote: >On July 13, 2002 at 03:39:06, Dann Corbit wrote: > >>On July 13, 2002 at 03:36:54, Uri Blass wrote: >> >>>On July 13, 2002 at 01:38:49, Russell Reagan wrote: >>> >>>>I have a question about alpha-beta. My understanding is that with perfect move >>>>ordering, you can get your branching factor down to the square root of the >>>>min-max branching factor. I did a few walk throughs of small trees using >>>>alpha-beta because I wanted to "see" what the tree looked like (where cutoffs >>>>occured), and I don't find this to be the case. I did a simple ternary tree walk >>>>through, and these are my numbers: >>>> >>>>Depth=1 : 4 nodes >>>>Depth=2 : 9 nodes >>>>Depth=3 : 49 nodes >>>>Depth=4 : 132 nodes >>>> >>>>Using a min-max search the branching factor should be 3. The branching factor >>>>for each of these depths was 2.22, 2.45, and 2.69 (which looks to be approaching >>>>3 with added depth). The square root of 3 is 1.73, so am I misinterpreting what >>>>I heard about the branching factor and alpha-beta? >>>> >>>>In other words...If your min-max branching factor is N, then does using >>>>alpha-beta with perfect move ordering give you the square root of N as the >>>>branching factor, or is that the lowest possible limit of the branching factor? >>>> >>>>If I understand this all correctly, that means that in chess a branching factor >>>>below about 6 is not possible without using forward pruning (using alpha-beta)? >>> >>>You need to assume also that hash tables are not used to prune the tree. >>> >>>I believe that pruning is very important and I exepct 2M nodes per second with >>>recursive null move pruning(R=3) to beat 200M nodes per second with no pruning >>>if you use 120/40 time control. >>> >>>I believe that programs practically can get good branching factor mainly thanks >>>to pruning and not thanks to hash tables(at least I do because I still do not >>>use hash tables to prune the tree). >> >>But you order your moves from the hash table! >>;-) >> >>Which came first, the chicken or the egg? > >This is only better order of moves and we assume perfect order of moves >for calculating the branching factor. I was talking of trying to actually achieve it. Without a hash table, you will have to have some sort of genius evaluation to approach it. >It is clear that hash tables with no pruning means beanching factor of at least >5 in the opening position and 6 in the middle game. I wonder what the best branching factor for a program is. I think Pepito and Chess Tiger are both impressive in that regard.
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