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Subject: Re: Exponential explosion of alpha-beta trees

Author: Omid David

Date: 09:06:58 07/06/02

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On July 05, 2002 at 19:10:57, Dann Corbit wrote:

>On July 05, 2002 at 19:08:30, Dann Corbit wrote:
>
>>On July 05, 2002 at 17:36:11, Omid David wrote:
>>[snip]
>>>If as you pointed out the programs reach the depth of 50 plies, I believe most
>>>of the games will end in a draw.
>>
>>Sounds like a hunch to me.  I wonder if any experiments have been run to see if
>>we get the same drop off in computers that we do in GM's.  I suspect that with
>>the GM's they are deliberately drawing once they get some small advantage.
>>
>>>But I don't see alpha-beta based programs reach even the depth of 20 plies in
>>>next 50 years!!! No matter how fast the hardware will be, it won't match the
>>>exponential explosion of alpha-beta trees.
>>
>>Most modern programs get anywhere from 10 to 15 plies on a reasonable search
>>(say G/90 on fast hardware).  Let's take the pessimistic estimate of 10 plies.
>>That means we need ten more plies.
>>
>>CPU speed doubles every 12 months (used to be once every 18 months so it is
>>accelerating).  But we will use the pessimistic figure of 18 months.
>
>{oops, I used 12 months -- but it won't change things much}
>
>20 * 1.5 years would be 30 years.  But there are also some chess programs with
>branching factors smaller than 4.  Anyway, you get the picture, I am sure.
>
>>Suppose a branch factor of 4 (many computer programs do better than that).
>>
>>Two doublings buys us a ply.
>>
>>We need 20 doublings to get ten more plies.
>>
>>So in 20 years, the average computer program will search 20 plies (even from the
>>most difficult positions).
>>
>>I suspect it will be a lot sooner.

You are right, I calculated b_factor as 6...
But even a search of 20 plies can't help any program play the Classical King's
Indian which I still use to beat many top engines :-)




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