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

Author: Robert Hyatt

Date: 05:56:00 04/04/00

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On April 04, 2000 at 04:21:07, Tom Kerrigan wrote:

>On April 03, 2000 at 22:32:30, Robert Hyatt wrote:
>
>>On April 03, 2000 at 17:56:20, Tom Kerrigan wrote:
>>
>>>On April 03, 2000 at 15:33:48, Robert Hyatt wrote:
>>>
>>>>On April 03, 2000 at 00:06:03, Tom Kerrigan wrote:
>>>>
>>>>>On April 01, 2000 at 13:38:00, leonid wrote:
>>>>>
>>>>>>Hello!
>>>>>>
>>>>>>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.
>>>>>
>>>>>You are taking a totally different approach to computer chess than everybody
>>>>>else in the world.
>>>>>
>>>>>You are driving a boat when everybody else is driving a car.
>>>>>
>>>>>This is fine, but the problem is that you are insisting on comparing your boat
>>>>>to everybody's car. You're trying to equate sail size to wheel diameter. It's
>>>>>possible, but it couldn't be more useless.
>>>>>
>>>>>Your program does not do quiescence searches, it does not do extensions, it
>>>>>probably doesn't do iterative deepening, etc. Comparing your program to other
>>>>>programs which DO have these features is not productive.
>>>>>
>>>>>Until you decide to add these features, you should simply concentrate on
>>>>>improving your program and not worry about what other people are doing.
>>>>>
>>>>>If you have to know, here's how you can compute your branching factor: count how
>>>>>many moves you search at each node. Divide by the number of nodes.
>>>>>
>>>>>-Tom
>>>>
>>>>
>>>>That's not 'branching factor'.  that is "effective branching factor".  Because
>>>>at many nodes you search 1 branch, but there are obviously many more moves there
>>>>that _could_ be searched...
>>>>
>>>>this has been a source of confusion almost forever...
>>>
>>>So it's totally correct for me to say that Crafty's branching factor is 38.
>>>
>>>-Tom
>>
>>
>>NO
>>
>>Crafty doesn't have a "branching factor" of 38.  The game of chess has a
>>branching factor of roughly 38.  Crafty has an "effective branching factor"
>>of 2.5-3.0, roughly.
>>
>>As I said, branching factor is the average number of legal moves at any node
>>in the tree, which is why checkers is often given as 38, while go is on the
>>order of 120 or so.  Alpha/beta can 'effectively' lower these numbers, but
>>the proper term is then "effective branching factor".
>
>It seems to me that this issue can be cleared up by drawing some trees.
>
>If you draw a chess tree, it is pretty clear that the branching factor (branches
>from each node) is ~38.
>
>If you draw Crafty's search tree, it is pretty clear that the branching factor
>is ~3.

No.. and that is what is causing the confusion.  The branching factor is _not_
influenced by the program.  The branching factor stays at 38, no matter whether
you search one move per ply or 38... because 'branching factor' is the term
used to define the typical number of moves to search at any node in the tree
by a minimax search.

Crafty would therefore have a branching factor of 38.  But we also use the
term "effective branching factor" which is the number you are after, as it
gives the number of moves per node actually searched.  And this can be anywhere
from 1 to 38... or with alpha/beta from roughly 1 to 2*sqrt(38) depending on
lots of things.

The literature has always said "38" for chess, period, for 'branching factor'.
It has been "bent" into smaller numbers using 'effective branching factor' but
often the 'effective' is omitted leading to confusion.




>
>So I would say that the game of chess has a branching factor of 38, whereas
>Crafty has a branching factor of 3.
>
>I don't see why you're so keen about this "effective" prefix. As long as you
>know which tree you're talking about, it seems unnecessary.

How do I know which tree is being discussed?  One term is a constant.  The
other is a variable depending on alpha/beta efficiency, forward pruning stuff,
etc...




>
>If you read my original post again, it is clear that I'm talking about Lenoid's
>branching factor, and not the branching factor for the game of chess.
>
>-Tom

I realize that...  I was simply pointing out the precise term that is correct,
such as 'femur' as opposed to "some bone".  Because you could be talking about
one bone and I am talking about another.



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