Author: José Carlos
Date: 16:16:31 07/12/02
Go up one level in this thread
On July 12, 2002 at 14:56:11, Ed Schröder wrote:
>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.
Hi Ed, if I get this right, the second column (moves searched) is the number
of positions in which the program has reached the depth given by column 1. If it
was really "moves", there would be about 3x in depth 2 than in depth 1.
Then the idea is that many more changes happen in low depths because the
program is there many more times, so I (ignoring "Big Changes") calculated a
couple of other numbers:
The ratio moves changes / moves searched and the relative % of changes from
ply to ply:
SEARCH OVERVIEW
===============
(A) (B) (C) (D) (E)
Depth Moves Moves Moves Changed / rel % of changes from
Searched Changed Moves Searched ply n-1 to n
1 113768 0 = 0.0% 0
2 113768 44241 = 38.9% 0.388870333
3 113768 34262 = 30.1% 0.30115674 77.44%
4 113194 32619 = 28.8% 0.288168984 95.69%
5 113191 30697 = 27.1% 0.271196473 94.11%
6 108633 28516 = 26.2% 0.262498504 96.79%
7 108180 25437 = 23.5% 0.235135885 89.58%
8 102782 22417 = 21.8% 0.218102391 92.76%
9 82629 15400 = 18.6% 0.186375244 85.45%
10 59032 9144 = 15.5% 0.154899038 83.11%
11 39340 5183 = 13.2% 0.131748856 85.05%
12 23496 2350 = 10.0% 0.100017024 75.91%
13 12692 957 = 7.5% 0.075401828 75.39%
14 6911 396 = 5.7% 0.057299957 75.99%
15 4032 193 = 4.8% 0.047867063 83.54%
16 2471 72 = 2.9% 0.029138001 60.87%
17 1608 26 = 1.6% 0.016169154 55.49%
18 1138 17 = 1.5% 0.014938489 92.39%
19 921 6 = 0.7% 0.006514658 43.61%
20 795 7 = 0.9% 0.008805031 135.16%
21 711 1 = 0.1% 0.00140647 15.97%
22 636 2 = 0.3% 0.003144654 223.58%
23 574 5 = 0.9% 0.008710801 277.00%
24 507 1 = 0.2% 0.001972387 22.64%
25 451 3 = 0.7% 0.006651885 337.25%
26 394 1 = 0.3% 0.002538071 38.16%
27 343 2 = 0.6% 0.005830904 229.74%
28 296 2 = 0.7% 0.006756757 115.88%
29 269 0 = 0.0% 0 0.00%
Column (D) means the probability at a certain position at a certain depth to
get a change, according to your data, for a random position (I assume you chose
random positions, because this data comes from real games). This is interesting
because it might be possible to try to use time having this into account to
decide whether to continue searching or to save time for later moves.
Column (E) means what's the relative probability from ply n-1 to n. For
example, the probability of changing the move at depth 10 is 83.11% of the one
at depth 9, this is, 16.89% less. It is also a "big number" (for human eyes)
that help following how probability decreases. Anything under 100 is decreasing.
It's interesting to see the fluctuations at big depths, most probably because of
the small sample.
Thanks anyway for the interesting experiment.
José C.
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