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Subject: Re: Definition of branching factor?

Author: Larry Griffiths

Date: 17:28:28 02/01/01

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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. They tend to be much
higher on even plys.

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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