Author: Ralf Elvsén
Date: 09:32:11 06/29/01
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On June 29, 2001 at 11:55:08, TEERAPONG TOVIRAT wrote: > >Hi Ralf, Hi > >>For even search depths: the ratio is (3w + 1)/(w + 3) >>For odd search depths: the ratio is w*(w + 3)/(3w + 1) > > >Do these 2 formula vary with depth? I mean is it true for depth=2,3 >and depth = 9 ,10? Here are the exact numbers (from an exact count, no approximations): 1 36 2 2,891891892 3 13,31481481 4 2,799861015 5 12,89826303 6 2,795078971 7 12,8813837 8 2,794879467 9 12,88075654 10 2,794872061 As you can see, the formulas I gave get "pretty true" quickly. I have exakt versions as well, but I will only take the trouble to type them if you really want to see them. They are not as nice as the approximations I gave. > > >>There is a pretty extreme odd-even effect. For e.g. w = 36 >>we have 2.8 (even) and 12.9 (odd). >> > >I'm quite surprised to know there is a big difference between odd >and even ply. How do you explain this phenomenon? >IMHO, it's the effect of Searchroot(). We don't have cutoff in Searchroot(). >So,the ratio of Move()/Gen() is 36 at the first ply. >Otherwise,I don't see any difference between ply . >It's the same recursive function . > >Teerapong Well, first you have the well known odd-even effect in the number of leaf nodes. When going from even depth to odd depth the number of leaf nodes increases by a factor of w/2, while when going from odd to even, this factor is only 2. So, when going from even to odd you get many more leaf nodes which gives many more makemoves. On the other hand, the nodes that were leaf nodes in the previous (even) depth, now will increase the movegen-count, but they were not so many. Perhaps I should make this clear: makemoves = total number of nodes - 1 (the rootnode). movegens = total number of nodes - leaf nodes. If you look at the odd-even effect for leaf nodes first, it will make sense. Ralf
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