Computer Chess Club Archives


Search

Terms

Messages

Subject: The law of diminishing returns

Author: Ed Schröder

Date: 11:56:11 07/12/02


Hi CCC,

In Rebel I maintain a statistic file, on every iteration a counter is
incremented with 1 (see column 2) representing the iteration depths Rebel has
searched. When a new best move is found a second counter is incremented with 1
(see column 3) representing how many times a new best move has been found on the
given iteration depth, between brackets the percentage is calculated.

As you can see the very first plies Rebel often changes to new best moves,
however when the depth increases and increases the chance Rebel will change its
mind drops and drops. From 16 plies on the chance a new better move is found is
below 2%.

I wonder what this all means, it is still said (and believed by many) that a
doubling in computer speed gives 30-50-70 elo. That could be very well true for
lower depths but the below statistic seem to imply something totally different,
a sharp diminishing return on deeper depths.

Interesting also is colum 4 (Big Score Changes), whenever a big score difference
is measured (0.50 up or down) the percentage is calculated. This item seems to
be less sensitive than the change in best move. However the maintained "Big
Score Changes" statistic is not fully reliable as it also counts situations like
being a rook or queen up (or down) in positions and naturally you get (too) many
big score fluctuations. I have changed that and have limit the system to scores
in the range of -2.50 / +2.50 but for the moment have too few games played to
show the new statistic.

Anyway the number of positions calculated seem to be more than sufficient (over
100,000) to be reliable. The origin came from extensive testing the latest Rebel
via self-play at various time controls.


                 SEARCH OVERVIEW
                 ===============

Depth    Moves          Moves         Big Score
       Searched        Changed         Changes

 1     113768         0 =  0.0%        0 =  0.0%
 2     113768     44241 = 38.9%    25329 = 22.3%
 3     113768     34262 = 30.1%    10707 =  9.4%
 4     113194     32619 = 28.8%     6939 =  6.1%
 5     113191     30697 = 27.1%     6353 =  5.6%
 6     108633     28516 = 26.2%     4954 =  4.6%
 7     108180     25437 = 23.5%     3952 =  3.7%
 8     102782     22417 = 21.8%     3265 =  3.2%
 9      82629     15400 = 18.6%     2541 =  3.1%
10      59032      9144 = 15.5%     1866 =  3.2%
11      39340      5183 = 13.2%     1384 =  3.5%
12      23496      2350 = 10.0%      982 =  4.2%
13      12692       957 =  7.5%      522 =  4.1%
14       6911       396 =  5.7%      369 =  5.3%
15       4032       193 =  4.8%      179 =  4.4%
16       2471        72 =  2.9%      127 =  5.1%
17       1608        26 =  1.6%       58 =  3.6%
18       1138        17 =  1.5%       42 =  3.7%
19        921         6 =  0.7%       26 =  2.8%
20        795         7 =  0.9%       22 =  2.8%
21        711         1 =  0.1%       18 =  2.5%
22        636         2 =  0.3%       10 =  1.6%
23        574         5 =  0.9%       10 =  1.7%
24        507         1 =  0.2%       12 =  2.4%
25        451         3 =  0.7%        7 =  1.6%
26        394         1 =  0.3%       10 =  2.5%
27        343         2 =  0.6%        3 =  0.9%
28        296         2 =  0.7%        7 =  2.4%
29        269         0 =  0.0%        7 =  2.6%
30        240         0 =  0.0%        6 =  2.5%
31        217         0 =  0.0%        6 =  2.8%
32        208         0 =  0.0%        7 =  3.4%
33        187         0 =  0.0%        3 =  1.6%
34        169         0 =  0.0%        1 =  0.6%
35        159         0 =  0.0%        1 =  0.6%
36        144         0 =  0.0%        0 =  0.0%
37        138         0 =  0.0%        0 =  0.0%
38        134         0 =  0.0%        0 =  0.0%
39        125         0 =  0.0%        0 =  0.0%
40        117         0 =  0.0%        0 =  0.0%
41        105         0 =  0.0%        0 =  0.0%
42         97         0 =  0.0%        0 =  0.0%
43         83         0 =  0.0%        0 =  0.0%
44         73         0 =  0.0%        0 =  0.0%
45         67         0 =  0.0%        0 =  0.0%
46         62         0 =  0.0%        0 =  0.0%
47         55         0 =  0.0%        0 =  0.0%
48         51         0 =  0.0%        0 =  0.0%
49         49         0 =  0.0%        0 =  0.0%
50         47         0 =  0.0%        0 =  0.0%
51         46         0 =  0.0%        0 =  0.0%
52         46         0 =  0.0%        0 =  0.0%
53         44         0 =  0.0%        0 =  0.0%
54         43         0 =  0.0%        0 =  0.0%
55         43         0 =  0.0%        0 =  0.0%
56         42         0 =  0.0%        0 =  0.0%
57         41         0 =  0.0%        0 =  0.0%
58         40         0 =  0.0%        0 =  0.0%
59         40         0 =  0.0%        0 =  0.0%
60         38         0 =  0.0%        0 =  0.0%



This page took 0.03 seconds to execute

Last modified: Thu, 15 Apr 21 08:11:13 -0700

Current Computer Chess Club Forums at Talkchess. This site by Sean Mintz.