How many Elo points change for a doubling of uP time?

[hgm]

I always thought that the problem of the draw margin should go away when you play games from initial positions that are on the brink of being wins or losses. There even a marginally better performance (on an absolute scale) should immediately result in a score. It would be interesting to see if this approach would be in quantitative agreement with the W/L ratio.

[Laskos]

Note that this can be an articaft from the increase in the draw rate at high playing level, which makes the conventional Elo definition a poor measure for the quality of play.

Yes, it is an artifact. If you do not include draws in the calculation, the decrease in rating points per doubling is much less as the quality of play increases.

I have been collecting data using nodes in place of a time control. The following data is the measured difference in strength between Gaviota playing at x nodes per move and 2x nodes per move:

With draws

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Nodes (in thousands)	rating difference
128	124.4
112	122.5
96	123.1
80	133.1
64	126.2
56	131.5
48	138.6
40	138.5
32	146.4
28	140.1
24	147.3
20	146.1
16	151.5
14	157.6
12	154.9
10	159.1
9	161.1
8	164.6
7	169.4
6	170.3
5	177
4.5	179.9
4	178.4
3	186.6
2	194.4

Without draws

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Nodes (in thousands)	rating difference
128	245.3
112	234.8
96	234
80	252.1
64	234.4
56	243.9
48	251.2
40	247.7
32	254.4
28	241.4
24	253.9
20	249.1
16	252.5
14	264.2
12	254.5
10	256.8
9	255
8	263.1
7	262.1
6	257.3
5	263
4.5	265.5
4	259.5
3	266.5
2	265.4

Chess is a drawish game, so when you exceed a certain quality of play you might be able to draw no matter how much better your opponent is.

I think that this is supported by the data from the rating lists. The difference in strength of two engines has a much smaller effect on the draw rate than the average strength.

This W/L argument was discussed here, 1 year ago.
http://www.talkchess.com/forum/viewtopi ... 3&start=12

[JayRod]

Yes, based on the information in this thread (and the threads referenced therein) I've concluded the following, which I'm still trying to get more information on, so the numbers below are not final and very crude.

If a modern chess engine running on weak hardware (in my case I am using a Pocket Fritz running on an iPAQ, which at 12 KNps is like a Pentium II running at 266 MHz (see http://www.sedatcanbaz.com/chess/?page_id=19) ) then at lower seconds per move [less than ten seconds per move for this hardware, which examines at 12 kNodes/sec] the nodes examined are around less than 128KNodes total, see http://www.talkchess.com/forum/viewtopi ... 04&t=53287 which means the 'doubling is about roughly 124 to 194 Elo points per doubling (or halving) of time. However, once you get significantly above this total number of nodes examined, you get a sort of saturation that brings the Elo points per doubling (or halving) of time to about 70 or so Elo points or 100 points or 125 points (the exact number depends on the program). The Elo drop per halving also depends on the strength of the program, in that if the programmer has programmed shortcuts so the program is strong even with a few seconds per move (see here: http://talkchess.com/forum/viewtopic.ph ... 94&t=46370 where you can see even at a few seconds per move, Komodo is strong enough so a doubling or halving of time only gives 81 Elo points from 2 seconds to 4 seconds, and only at 0.5 s/move to 1 s/move do you get 107 Elo points difference.

The above was for Komodo, but for Gaviota I found for time doubling (or halving), the saturation occurs as high as 120+ Elo points rather than 81.

I plotted the Gaviota lines and found a nonlinear relationship of Elo drop for 28k nodes or less, with Elo drop occurring much greater as fewer nodes were searched, and then saturation if more kNodes (total) were searched, with saturation around 125 Elo points per doubling of nodes (or time, since if saturation then time and nodes merge).

From the above I concluded that some of the commercial programs ' programs, you get saturation quicker, and also the programs seem to have a smaller Elo gain (81 pts vs 125 pts) per node doubling per move or per time doubling. Why is this? I speculate some programs are written for "blitz" and maybe examine the optimal/most probable lines in their move evaluation list more quickly than others. I wish I had a list of programs and their Elo gain per nodes examined per move and time per move, so I can test my hypothesis for more than just the Komodo and Gaviota programs.

In any event, an algorithm to compute Elo drop for halving of time (or, going the other way, doubling of time) is, for halving the time:

1) find out the 'saturation' Elo, typically at 180 seconds per move, as published in most Lists (or sometimes it is 60 seconds per move average)

2) use either 75 points per halving or 100 points per halving (good compromise) or 125 points per halving (upper bound), depending on the program, for the first few halvings, increasing the Elo lost per halving by about 8% per halving (this number seems to be a good average, roughly) until ...

3) ...you get to about 60k Nodes, which for a Fritz 2.0 on a iPAQ happens at about 5 seconds per move. Below this time, that is, for even faster than 5 seconds per move, you have to drop the Elo much more than 8%, and you use a table since the relationship is non-linear.

That's the best I can do at the moment based on very rough and incomplete information.

JayRod

[Adam Hair]

This W/L argument was discussed here, 1 year ago.
http://www.talkchess.com/forum/viewtopi ... 3&start=12

Yes, your thread influenced me. I needed to generate a large amount of games, and I realized that for my purposes using nodes instead of a time control would be more reliable.

By the way, W/L is much flatter with Gaviota, but it is also close to 4 like you found with Houdini. Also, W/L increases for White as nodes increase.