Author: Tord Romstad
Date: 02:44:49 10/03/03
Go up one level in this thread
On October 02, 2003 at 21:14:31, Dann Corbit wrote:
>On October 02, 2003 at 21:01:23, macaroni wrote:
>
>>does this look like a reasonable branching factor? for this evaluation I had
>>killers, history, and captures all turned on as move ordering. I do have null
>>moving with R of 2.
>>
>>Analyzing the position after 1. a3
>>1 7 0 22 Nf6
>>2 2 0 110 Nf6 d4
>110/22 = 5
>>3 7 0 269 Nf6 d4 Nc6
>269/110 = 2.45
>>4 2 0 1616 Nf6 d4 Nc6 Nf3
>1616/269 = 6
>>5 7 6 5012 Nf6 d4 Nc6 Nc3 e5
>5012/1616 = 3.1
>>6 2 39 38381 Nf6 d4 Nc6 Nf3 d5 Nc3
>38381/5012 = 7.7
>>7 4 269 246052 Nf6 d4 Nc6 Nc3 d5 Nf3 Qd6
>246052/38381 = 6.4
>>8 4 555 531125 Nf6 Nf3 Nc6 Nc3 d5 d4 Qd6 e3
>531125/246052 = 2.15
>>9 5 1813 1674270 Nf6 Nc3 Nc6 d4 d5 Bf4 Nh5 Be5 Nf6
>1674270/531125 = 3.15
>
>Alpha Beta will bring the average from 30-40 in branching factor down to 6.
But this is assuming that recursive null move pruning is not used, I
think. With nullmove R=2 (which macaroni uses), the branching factor
should be considerably less than 6, I think.
>Your later plies (where it really matters) show a very good branching factor.
Yes, it looks OK.
By the way, I have often wondered how people measure the branching factor
of an engine. I often read statements like "my branching factor is
less than 3", but I have no idea what they mean. Obviously, measuring
the branching factor in just one position will be very inaccurate. Many
positions are needed. But what kinds of positions do you use? Positions
from all parts of the game, or only middle game positions? Positions where
the best move changes frequently, or only positions with a stable PV? Do
you consider only the branching factor in the later plies, or also the
first few plies?
Here are my results for macaroni's position. Like in most positions
close to the initial position, my results are a bit strange, probably
because I have a strong odd-even oscillation in scores. My branching
factor is usually much bigger when the score drops than when it increases
(probably as a result of using MTD(f)). There is also a clear tendency
that my branching factor increases considerably when the hash table starts
to get full, which worries me a bit.
1 0.73 0.00 23 b8c6
2 0.00 0.00 261 b8c6 b1c3
261/23 = 11.35
3 0.72 0.00 604 b8c6 b1c3 g8f6
605/261 = 2.32
4 0.00 0.02 2993 b8c6 b1c3 g8f6 g1f3
2993/604 = 4.96
5 0.66 0.04 5241 b8c6 b1c3 g8f6 g1f3 d7d5
5241/2993 = 1.75
6 0.00 0.16 22790 b8c6 b1c3 g8f6 g1f3 d7d5 d2d4
22790/5241 = 4.35
7 0.58 0.28 42950 b8c6 b1c3 g8f6 g1f3 d7d5 d2d4 c8f5
49250/22790 = 1.88
8 0.02 1.01 172922 b8c6 b1c3 g8f6 g1f3 d7d5 d2d4 c8f5 c1f4
172922/42950 = 4.03
9 0.33 2.06 406572 b8c6 b1c3 g8f6 d2d4 d7d5 g1f3 c8f5 c1f4
e7e6
406567/172922 = 2.35
10 0.11 12.50 2487822 b8c6 b1c3 d7d5 d2d4 c8f5 g1f3 e7e6 c1f4
f8d6 f4g5
2487822/406567 = 6.11
11 0.33 34.80 6605868 e7e5 b1c3 b8c6 e2e4 g8f6 g1f3 d7d5 e4d5
f6d5 d2d4 c8g4 c3d5 d8d5
6605868/2487822 = 2.66
12 0.08 179.83 34397108 e7e5 d2d4 e5d4 g1f3 d7d5 f3d4 c7c5 d4b5
a7a6 b5c3 g8f6 c1f4
34397108/6605868 = 5.21
13 0.22 580.63 107726305 e7e5 e2e4 b8c6 g1f3 g8f6 b1c3 d7d5 e4d5
f6d5 f1b5 c8g4 d2d4
107726305/34397108 = 3.13
>Have you read Ernst Heins' book?
Does it contain much information apart from what is found in his
online papers?
Tord
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