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Subject: Re: Branching factor, make me confuse more that ever.

Author: Robert Hyatt

Date: 07:51:07 04/02/00

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On April 01, 2000 at 22:49:09, leonid wrote:

>On April 01, 2000 at 20:24:02, Robert Hyatt wrote:
>>On April 01, 2000 at 13:38:00, leonid wrote:
>>>Maybe you could take me out of my endless confusion about "branching factor".
>>>Confusion come from the way that you can compare two different games. Would like
>>>your help in finding useful numbers about this factor.
>>>Reason for concern about "branching factor" is that it make me loose 10 times
>>>speed when logic search 10 ply deep starting from ply 3.  Calculation was done,
>>>as precise as I could, comparing brute force search without any extensions for
>>>two games.
>>>Branching factor for me (I know it is not the usual one but very practical one)
>>>is division of number of nodes seeing in ply against total number of nodes for
>>>given ply. If number of nodes seeing was 5 and number of nodes for this ply 32
>>>-"branching factor" is around 16%.
>>>Confusion is that when I found my branching factor for the entire game it was
>>>around 7%. When I see the branching factor for the ply over two lowest it is as
>>>high as 21%. In good games I could see branching factor only starting from ply 6
>>>and it is around 15%. I have no idea what is the branching factor in other games
>>>calculated for entire game.
>>>Please indicate me branching factor for entire game and for the ply over 6 if
>>>you can. It could help me. Please say me this factor only for the brute force
>>>search. In quick logic my branching factor is different and much smaller.
>>>Thanks for your help,
>>the 'branching factor' number is generally used wrongly. It is roughly 38 in
>>the game of chess, averaged over the complete game.  "effective branching
>>factor" is the number you are really looking for.  Best way to calculate that
>>is to do a search, then compute the following:
>>for each iteration, compute exactly how much time it took. IE suppose you
>>get the following times:
>Do the "iteration" signify simply number of ply? And do you say "get the
>following times" in the sense of time to solve the position for given ply in
>(maybe) seconds ?
>>iteration   time
>>     1        0
>>     2        3
>>     3        9
>>     4       24
>>you compute three values:
>>t1=3-0 = 3;
>>t2=9-3 = 6;
>>you can compute two estimates of your effective branching factor:
>>those are the interesting numbers. IE if you know the time to do a depth=n
>>search, what do you multiply that by to compute how long it will take to do
>>depth N+1?
>I have the impression that your way to calculate is different from mine. If the
>word "iteration" I undertood really as it must be.
>My biggest problem, in all my calculation, was the fact that I can see the time
>that it took in other games starting from ply 6, on mine AMD 400Mhz. This way I
>have no access to find the speed for the lowest two plies. And it is those
>lowest two plies that do the most of the work. They can dramatically change the
>speed of the entire game. I know, for instance, that you also have written your
>lowest ply in different way and probably many other did.
>With my respect!

what you want is the total time to complete iteration N divided by the total
time to complete iteration N-1.  Or the total nodes for each, which ought to
be roughly equivalent.

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