Author: TEERAPONG TOVIRAT
Date: 11:20:58 06/29/01
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On June 29, 2001 at 12:32:11, Ralf Elvsén wrote: >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 After more than an hour of thought and calculation,I think you calculate the formulas by... ply 1 nodes= w ply 2 nodes= 2w ply 3 nodes= square of w ply 4 and so on... then ratio= move()/gen() by the definition. The experiment result comfirm your calculation,I agree with you. I admit this is new to me. I wonder is there any secret about alpha-beta that I still don't know? But, more suprised for me... Let's modify your formula,in our case w is much more than 1 and 3. So,the first one becomes 3 and the second becomes w/3. Then,the geometric mean of this 2 figures is square root of w . Thanks for all data and explanation. Teerapong
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