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Subject: Re: PVS and MTD(f) branching factor

Author: Uri Blass

Date: 05:45:52 06/18/03

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On June 18, 2003 at 06:15:41, Thomas Mayer wrote:

>Hi Uri,
>
>>You need to assume also not using hash tables for pruning.
>>There is an assumption that alpha beta includes no pruning by null move or by
>>hash tables.
>
>my godness, Uri - we are talking about pure alpha beta the hole threat... pure
>alphabeta definitely excludes any type of pruning...

Ok
In this case it is only a question of definition.

I think that everybody says that program use alpha beta so I thought that
talking about alpha beta does not mean automatically no pruning.

>
>>I do not see a reason to make this assumption when most of the programs use
>>pruning and(or) hash tables.
>
>it's simple - that was the question of the initiator of this thread. :)
>
>> The right sentence is:
>> "With perfect move ordering, alpha-beta (with no pruning including not using
>> the hash tables for pruning) has a branching factor of the square
>> root of the min-max branching factor."
>
>wrong, correctly it must be written the following:
>
>> "alpha-beta has a branching factor of the square
>> root of the min-max branching factor."
>
>that's it. Move ordering has no influence at all on the theoretical branching
>factor...For perfect ordering alpha beta would need N(D)=SQRT(Nm(D)) where N(D)
>is nodes in alpha beta of a certain D=Depth and Nm(D) is Nodes with minimax for
>a certain D=Depth... when move ordering is not perfect the practice has shown
>that N(D)=5*SQRT(Nm(D)) is a good approch near to reality to calculate the nodes


practise of who?
I never used pure alpha beta(no extensions and no qsearch and no pruning).

>- the branching factor would not be affected... On first sight this looks
>strange - when you think a little bit deeper about that it is logical - better
>move ordering will bring you a constant speed up which does simply not affect
>the branching factor...

No It is not logical.
Better order of moves gives exponential speed up.

Uri




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