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Subject: Re: Definition of branching factor?

Author: Tony Werten

Date: 16:35:47 02/02/01

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On February 01, 2001 at 20:28:28, Larry Griffiths wrote:

>On February 01, 2001 at 08:40:23, Severi Salminen wrote:
>
>>>I would also like to know these things.  It looks like my branching factor is
>>>varying from 3 to 6 on average.  Are these results for chess?  Is it from the
>>>initial board position?
>>
>>Yes, we are still talking about chess :) And we are talking about position after
>>1.e4 e5 2.d4 d5 .The EBF depends a little on how you calculate it.  My 3.6 is
>>from:
>>
>>EMF=pow(leaf_nodes/legal_rootmoves, 1/(depth-1));
>>
>>If I use time for calculation my EBF from ply 8 to 9 is about 2.9.  And you
>>probably get similar results if you use the node count from successive plies.
>>Could you post your numbers on this position also? I'll post mine tomorrow when
>>I get to the right computer. Also indicate how you calculate EBF. (Effective
>>Branching Factor)
>>
>>Severi
>
>Using this position...
>
>[D]rnbqkbnr/ppp2ppp/8/3pp3/3PP3/8/PPP2PPP/RNBQKBNR w KQkq d6 0 3
>
>My program does not have code to setup the d6 en-passant square
>so the totals below do not account for this...
>
>I made 2 runs.  Both runs use negamax with alpha/beta cutoffs
>and 1 killer with interative deeping.  The first run scores only material.
>The second run always returns a score of zero.  The BF column is a
>branching factor that I calculate by dividing ply/moves by ply-1/moves.
>BF does not use decimal points.
>
>Leaf Effective Branching Factor is
>   Leafnodes/Rootnodes^1/(Depth-1)
>
>TLeaf Effective Branching Factor is
>   Totalnodes/Rootnodes^1/(Depth-1)
>
>I do not get smooth regular branching factors.

Quite normal when you evaluate with material only or eval=0

>They tend to be much
>higher on even plys.

Comes with (plain) alfa-beta. You try to get around it with nullmove, extensions
and an elaborated evaluation function.

Some work left for you,

Tony

>
>Elapsed Time= 85.56 seconds
>
>Ply ---CAPTURES-- -----MOVES----- -----TOTAL----- BF
>  1            16             288             304  2
>  2           307             566             873 12
>  3         1,015          10,224          11,239  2
>  4        10,061          18,174          28,235 10
>  5        29,735         271,993         301,728  2
>  6       248,747         489,118         737,865  9
>  7       787,016       6,063,615       6,850,631  1
>  8     4,462,525       8,069,477      12,532,002  6
>  9     9,669,768      68,076,351      77,746,119  0
>    _____________ _______________ _______________
>       15,209,190      82,999,806      98,208,996
>
>       Captures/Moves Per Second=       1,147,797
>
>  Leaf Effective Branching Factor=            4.74
> TLeaf Effective Branching Factor=            6.24
>
>-----------------------------------------------------------------------
>
>Elapsed Time= 43.16 seconds
>
>Ply ---CAPTURES-- -----MOVES----- -----TOTAL----- BF
>  1            16             288             304  2
>  2           304             304             608 16
>  3           707           9,408          10,115  1
>  4         8,574           8,436          17,010 14
>  5        18,460         220,600         239,060  1
>  6       176,288         195,692         371,980 11
>  7       416,115       4,005,585       4,421,700  1
>  8     2,745,104       2,814,264       5,559,368  7
>  9     4,345,790      35,926,605      40,272,395  0
>    _____________ _______________ _______________
>        7,711,358      43,181,182      50,892,540
>
>       Captures/Moves Per Second=       1,179,269
>
>  Leaf Effective Branching Factor=            4.37
> TLeaf Effective Branching Factor=            5.75
>
> Larry.



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