Author: Ratko V Tomic
Date: 09:48:54 10/17/99
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The effective branching factor would be a _constatnt_ branching factor which would produce the same number of nodes at the bottom of the tree for the same depth as the actual tree had (in the actual tree the branching is not constant; it may vary from node to node). So by the definiition you have relation: N = B ^ D where B is the effective branching factor, D is depth and N is the number of evaluated nodes (the leaf nodes since internal nodes are not evaluated). From here you can calculatete B as: B = exp(ln(N)/D) which is what I used to calculate B for the examples. Using ratios of processing times for Time(D+1)/Time(D) is only an approximation which ignores the times spent outside of the evaluation function. Namely, in that case the number of nodes evaluated at any level would be: N=T*NPS where NPS is nodes _evaluated_ per second (not same as nps in your column) and T is processing time in seconds. Since the branching factor (as defined earlier) is the ratio of N's for D+1 and D, you do get B=T(D+1)/T(D). But since relation N=T*NPS isn't accurate, since some time is spent outside of the evaluation function, i.e. the actual relation is T=N/NPS+X, where X is this extra time outside of evaluation, the B obtained via time ratios is only an approximation when X is ignored. Applying this to your table you will have: Depth Tot.kN Delta.kN BF Time[s] kN/s -------------------------------------------- 8 1044 .... .... 9.5 110 9 2121 1123 2.18 18.5 115 10 5782 3661 2.27 47.75 121 11 15431 9649 2.30 124 124 12 62174 46743 2.45 495 125 -------------------------------------------- So your Crafty (ver 16.19) does have much smaller effective branching factor than the one which came with Fritz (ver 16.6). The B might be also dependent on settings (I used defaults). Your version seems to be rigged for a more selective search (it goes deeper but possibly is less accurate).
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