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Subject: Re: branching factor question

Author: José de Jesús García Ruvalcaba

Date: 07:01:39 03/07/00

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On March 07, 2000 at 07:48:21, Jan Pernicka wrote:

>On March 06, 2000 at 06:25:00, blass uri wrote:
>
>>On March 06, 2000 at 06:00:20, Jan Pernicka wrote:
>>
>>>On March 03, 2000 at 15:53:31, blass uri wrote:
>>>
>>>>Suppose you have a program with evaluation of 0.00 for every position so the
>>>>order of moves is always perfect.
>>>>Suppose this program does no prunning and no extensions.
>>>>
>>>>What is the branching factor of this program and how many nodes does it need to
>>>>search to get 17 plies in the positions that deeper blue is supposed to get 17
>>>>plies with no prunning and a lot of extensions?
>>>>
>>>>It seems to me that it is impossible with no hash tables to get 17 plies in 3
>>>>minutes even if you can search 200,000,000 nodes/second,have a perfect order of
>>>>moves and do no extensions.
>>>>
>>>>Hash tables can help to reduce the branching factor but how much do they help?
>>>>
>>>
>>>  Hi,
>>>let's suppose that at every position you have w moves to choose and you
>>>don't use any hashtables. Then (it's well known) - when using alpha-beta
>>>prunning - your branching factor is something like  sqrt(w) - i.e square
>>>root, when searching to the depth d (still the same, no extensions...),
>>>you have to examine about d^(w/2) (leaf) positions  (x^y means "x powered to
>>>y"), so you can estimate how long does it take (for your program) to search
>>>17 plies ahead...  Simply said - you can search two times deeper...
>>
>>I think that the formula is sqrt(w)^d=w^(d/2)
>>
>>If w=36 in the middle game then the formula is 6^d without hastables and f(w)^d
>>with the hashtables when the question is if f(w) is really close to 6.
>>
>>If f(w) is really close to 6 then the claim that deeper blue could search 17
>>plies in the middle game with no pruning is wrong.
>>
>>Uri
>
>  I don't know whether 17 plies is the depth of exhaustive search or selective
>one (in the case of deeper blue).
>I also apologise for changing(swapping) the variables in my formula. Your
>correction is correct, Uri (:-). My expression means that you would be able to
>search VERY deep...
>  So one question arises: What's the average gain (with respect to time) when
>you start to use hash tables - when  f(d) is the (average) count of nodes
>explored with simply alfa-beta (even with perfect ordering of moves) into
>depth d -
>what's relation between g(d), which is the same as f(d) except the fact
>that you use hash tables now. Well,  if it's true, that g(d)=c.f(d), where
>c is constant which DONT depend on d (e.g: c=0.1), then my calculations
>are correct (after correcting my formula (:-)). More interesting it
>would be if g(d)/f(d) is not constant and is smaller and smaller when
>d is bigger and bigger (I don't know that term in English for such a
>function).

	"Decreasing function".
José.

>But I don't know it could be answered because:
>   1) to find it out from artificial trees is out of reality (chess
>          is our reality)
>   2) how to correctly define "average" count
>   3) measurements could be made only to restricted depth (how is it
>       for lim (g(d)/f(d)) (where d->infinity)
>
>                             Jan Pernicka



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