Author: Uri Blass
Date: 00:36:54 07/13/02
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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). Uri
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