Drawing Frequency

[Howard E]

Does drawing frequency change as programs get stronger among "equal" opponents?
Say we define equal opponents as differring by 50 rating points.
What do stats tell us about the drawing frequency of 2400 engines competing among themselves vs. 3200 engines doing the same?

This might be something Bob has at his fingertips given the matches of various Craftys over time.
Also, since there are so many accomplished engine testers, they may know the answer to this already
from years of observation.

[Edmund]

The draw ratio depends on the strength difference between the competitors, the average strength level and the drawishness of the openingbook-line.

regarding the average strength and the strength difference, you might want to consult the statistics provided by Kirill Kryukov about his testgames: http://kirill-kryukov.com/chess/kcec/draw_rate.html

an indicator for the correlation with the average strength of the engines can also be deducted by looking at the statistics from the various testers for different time controls. Higher time-control means higher level of strength.

Eg some old stats I once collected from the CEGT:
(timecontrol) - (draw ratio)
40/4 - 30.9%
40/20 - 35.6%
40/120 - 41.3%
40/120 (4cpu) - 45.2%

or the CCRL:
40/4 - 31.0%
40/40 - 37.2%

regards,
Edmund

[Gerold]

Does drawing frequency change as programs get stronger among "equal" opponents?
Say we define equal opponents as differring by 50 rating points.
What do stats tell us about the drawing frequency of 2400 engines competing among themselves vs. 3200 engines doing the same?

This might be something Bob has at his fingertips given the matches of various Craftys over time.
Also, since there are so many accomplished engine testers, they may know the answer to this already
from years of observation.

Match CCC. Houdini Vs.Rybka 4. 25 draw/37games played.
Long TC.

Best,
Gerold.

[simonhue]

Here is analysis of draw rates in tournament games:
http://chess-db.com/public/research/draw_rate.html

[Adam Hair]

Here is a graph I constructed recently using the CCRL 40/4 database. I used Bayeselo's computed drawElo instead of draw rates, but it has a similar relationship to average Elo as the draw rate does.

I collected all games where the opponents were within 50 Elo of each other. I then separated the game into 100 Elo bins by collecting all games were the opponents were rated 3100 to 3199, then 3000 to 3099, and so on. I took the midpoint of each interval to be the "average Elo". I threw out the highest level games and the games below 2200 Elo (many engines below this level have trouble checkmating, which artificially raises the draw rate). This is the resulting graph:





The curve in the graph is a logistic curve of the form a/(1+exp(-(x-b)/c).