Author: Stephen A. Boak
Date: 22:52:01 04/27/01
Go up one level in this thread
On April 28, 2001 at 01:23:42, Uri Blass wrote: >On April 28, 2001 at 01:11:16, Stephen A. Boak wrote: > >>On April 28, 2001 at 00:58:13, Stephen A. Boak wrote: >> >>Uri, >> >>Here are the figures you wanted. Quite interesting! >> >>Relative Ratings from Fixed Delta Ply Settings: >> >> PLY >> T14 DF DELTA BOTH Games Ave/Ply >>>79.4 -79.4 0 0.0 600 - >>>231.5 53.7 1 142.6 500 143 >>>375.8 190.0 2 282.9 400 141 >>>557.3 372.6 3 464.9 300 155 >>>557.7 614.1 4 585.9 200 146 >>>603.9 798.3 5 701.1 100 140 >> >>The relative rating average, per delta ply, is extremely linear--approx 145 pts >>ave. >> >>Aren't you the mathematician? > >Yes but there is no simple fomula to calculate rating correctly and I did not >know which program to use to calculate it. > >Your data suggest that there is no evidence for diminshing return in the nunn2 >match at small depthes. > >I believe that there is a diminishing return but we need to wait to games at >bigger depthes to prove it. > >Uri I used to believe in diminishing returns (based on some thinking & intuitive notions). With this remarkably linear data (limited though it is), I am not so sure. If chess is as complex as we think it is, every extra ply may provide equal dividends--up until a program can see far enough ahead that the game is 'solved' (win, loss or draw). Since the game is far too exponential for any current computer to 'solve' it, in the general opening or middle game situation, each extra ply that plumbs the depths of that complexity may provide approximately the same return. This may indicate, for example, that there are relatively as many win, loss & draw nodes, generally speaking, at each fixed ply depth, no matter how many plies are calculated--even if those results are not precisely calculatable by the program! Therefore the program that calculates x plies more than its opponent will have approx the same increased chances to steer toward the winning lines. [I hope you can understand the concept I am trying to communicate.] NOTE 1--The number of games you played at large ply deltas is less than the number of games played at smaller ply deltas. NOTE 2--the Elo rating scale is based on the following important fact: the win expectancy (expected win percentage) is the same for any fixed rating delta, regardless where those ratings are on the overall rating continuum. For example, a player rated 2000 has a winning expectancy of 64% vs. a 1900 player. A player rated 2600 also has a winning expectancy of 64% vs. a 2500 player. In both situations, the higher rated player has a rating advantage of exactly 100 points. --Steve
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