Computer Chess Club Archives


Search

Terms

Messages

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

Author: Ricardo Gibert

Date: 01:59:26 11/01/00

Go up one level in this thread


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

If you really interested in the theoretical side of computer chess programming,
you may want to check out chapter 9 "An Analysis of Alpha-Beta Pruning" from D.
Knuth's book called "Selected Papers on Analysis of Algorithms".

You may find it a bit too dry for your tastes, but important insights can be
derived with patience. I spotted this book at a Borders book store.



This page took 0 seconds to execute

Last modified: Thu, 15 Apr 21 08:11:13 -0700

Current Computer Chess Club Forums at Talkchess. This site by Sean Mintz.