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Subject: Re: Exponential explosion of alpha-beta trees

Author: Uri Blass

Date: 10:17:13 07/06/02

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On July 06, 2002 at 12:06:58, Omid David wrote:

>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 :-)

I think that it may be dependent on the program and if we talk about the future
searching deeper is only going to be one of the advantages of the top programs.

I am also not sure if 20 plies cannot help the engines that you play against
them.

You cannot be sure without letting them search 20 plies.
It may be interesting if you can find positions when all the top programs
blunder if you give them to search for 20 plies.

In my correspondence games in the Israeli championship I usually chose a move
that one of my program suggested but I admit that I did not play the classical
king's indian.

There were only few cases when I did not do it.

Here is one of them

[D]bq4r1/4bp1k/4p3/1P2n1p1/2P1P2p/P3BP1P/1N1R1QP1/7K w - - 0 35

I played Ba7 inspite of the fact that all the programs that I tried told me to
play a4(the game was finished in a draw).

I analyzed a4 f5 exf5? g4 and my consequence was that black is probably winning.
I remember that all the programs that I tried suggested a4 but maybe I did not
give them enough time or my hardware was not good enough.

It may be interesting to see the opinion of top programs of today if they get
some days to analyze.

I suspect that some of them may find Ba7 but they may need a long time for it.

Uri



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