Author: Robert Hyatt
Date: 07:19:09 08/11/99
Go up one level in this thread
On August 11, 1999 at 07:31:10, Vincent Diepeveen wrote: >On August 11, 1999 at 06:29:22, David Blackman wrote: > >>Start with an ACTUAL branching factor B (ie number of legal moves in each >>position). >> >>For depth N, minimax needs B ** N, apparent branching factor B. >> >>Plain alpha-beta with perfect move ordering needs k * B ** (N/2) where k is some >>small constant. So apparent branching factor is SQRT(B). >> >>With alpha-beta, nullmove pruning factor R, assume perfect move ordering, and >>every move that fails low gets cut by null move pruning, k * B ** (N/(R+2)) so >>apparent branching factor is B ** ( 1/(R+2) ) . For R=3 that is fifth root of B. >>With B=32 (probably a bit low for a midgame) that would be branching factor 2. > >B=32 is a bit high, see earlier posts of my: >lots of pieces get of the board, and lots of transpositions. > >So B is a lot less than that. No it isn't, and this is an easy hypothesis to test: search a few positions for an hour each, no null move, no hashing. Turn on hashing and see what that does to reach the same depth. Then turn on null-move and see what that does. Then you can compute exactly what the two things do to shrink the overall tree. In my testing, I generally find null-move is worth 2 extra plies over non-null move, using R=2. Stripping out my eval _might_ get another ply as my eval is 50% of total search time. Stripping out move ordering will lose that ply right back due to less efficient move ordering. 22 plies ain't going to happen, much less 30. The math just isn't there. I have seen _no_ program report depths > 12-14 in the middlegame, except for Junior which reports depth in 1/2 ply increments. If they can't hit 18-19 with everything included, they aren't going to hit >20 stripped down... > > >>I don't think you're going to get quite that good for most positions. First it >>assumes perfect move ordering. There might be tricks to get close to that. But >>also it assumes null move pruning works for almost all failing low moves, and i >>don't think that is true. A tempo is often worth a lot. >> >>Working out a model for effect of transposition tables on branching factor makes >>my head hurt. For now i'll just note that in practice it doesn't seem to help >>much in the middlegame. So i think apparent branching factors in the range 2 to >>4 will be the rule for the moment, for normal mid-game positions. >> >>If you could get down close to 2 that would make depths of 15 to 20 ply feasible >>at normal tournament controls. I guess most of us aren't there yet.
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