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Subject: Re: The number of nodes of critical trees?

Author: Pham Minh Tri

Date: 19:54:39 10/31/00

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On October 31, 2000 at 22:01:05, Robert Hyatt wrote:

>On October 31, 2000 at 19:47:52, Pham Minh Tri wrote:
>
>>Hi,
>>
>>In the book "Scalable Search in Computer Chess", Dr. Ernst A. Heinz
>>said, "The best chess programs generate search trees with only 20%-30% more
>>nodes on average than the critical alpha-beta trees" (pp 22). His declare
>>makes me be curious how good my program is. Therefore, I tried to calculate the
>>number of nodes in critical trees. I found the simple formula in the
>>book "AI" of Patrick Henry Winston as the following:
>>
>>        s = 2 * b ** (d/2) - 1 for d even.
>>
>>With the branching factor b = 30, the depth d = 10, I have the number of
>>node s > 48 million. And if I include the quiescent search nodes, it must be
>>over 60 million. This number makes me surprise, because it is twice as many
>>as the one of my program (around 25m in the beginning without opening book)
>>and tens times as many as the ones of some commercial programs (like Fritz
>>around 1 m). I was wondering:
>>- Am I doing something wrong: wrong formula, wrong constants, wrong calculation,
>>wrong understand about critical trees?
>>- I guess that Dr. Ernst A. Heinz does not concern some techniques like
>>hash table, null move, rasoring and so on, which make the real trees could be
>>much smaller than critical trees.
>>
>>And could someone show me your number of search nodes at full depth of 10? I
>>want to compare my program with yours, but not commercial programs like Fritz,
>>they are too fast and make me feel sad about my work :).
>>
>>Pham
>
>
>Wrong calculation.  D is constant.  This means that _every_ path is searched to
>depth D only.  No extensions.  No pruning (null-move or etc).  And no q-search
>at all.
>
>no way to calculate such a thing for a modern program.

Yes, I agree that formula is for optimal trees, not for normal trees in model
chess programs. But I was wondering how to say "20%-30% more nodes on average
than the critical alpha-beta trees"? Is this comparison still meaningful?

>You _can_ search an optimal tree with some work... to count the nodes.  IE
>search it once and remember _every_ best move at every ply.  Then search the
>tree again, using perfect ordering.  That will give you a value to shoot
>for, node-wise.



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