Author: Ralf Elvsén
Date: 04:43:55 07/16/00
Go up one level in this thread
On July 16, 2000 at 06:32:00, Graham Laight wrote: >On July 16, 2000 at 03:34:45, Ed Schröder wrote: > >>Right. >> >>A few months ago Christophe posted some interesting stuff here regarding >>this topic and nobody really was in agreement with him (me included) until >>I did an experiment which worked as an eye opener for me. The story is not >>funny and goes like this... >> >>In Rebel Century's Personalities you have the option [Strength of Play=100] >>The value may vary from 1 to 100 and 100 is (of course) the default value. >> >>Lowering this value will cause Rebel to lower its NPS. This opens the >>possibility to create (100% equal!) engines with as only difference >>they run SLOWER. >> >>I was interested to know HOW MANY games it was needed to show that a 10% >>faster version could beat a 10% slower version and with which numbers. So >>I created two personalities: >> >>FAST.ENG (default settings) [Strength of Play=100] >>SLOW.ENG (default settings) [Strength of Play=80] >> >>and started to play 600 eng-eng games with Rebel's build-in autoplayer >>with pre-defined fixed opening lines both engines had to play with white >>and black. >> >>The personality with as only change [Strength of Play=80] caused Rebel to >>slow down with exactly 10% on the machine the marathon match took place. >>Note that this value (80) may differ on other PC's in case you want to do >>similar experiments. >> >>Here are the results of the 600 games played between the FAST and SLOW >>personalities. The first 300 games were played on a time control of "5 >>seconds average". The second 300 games were played on a time control of >>"10 seconds average". >> >>FAST - SLOW 162.5 - 137.5 [ 0:05 ] >>FAST - SLOW 147.0 - 153.0 [ 0:10 ] >> >>The first match of 300 games at 5-secs looks convincing. A 54.1% score >>because of the 10% more speed seems a value one might expect. >> >>But what the crazy result of match-2? Apparently after 300 games it is >>still not enough to proof that the 10% faster version is superior (of >>course it is) but the match score indicates both versions are equal >>which is not true. >> >>So how many games are needed to proof that version X is better than Y? >> >>I am sure I am trying to reinvent the wheel. The casino guys who make >>themselves a good living (with red and black) have figured it all out >>centuries ago. Perhaps there is a FAQ somewhere on Internet that >>explains how many times you have to turn the wheel to get an exact >>50.0% division between red and black. 1000? 2000? >> >>To answer this question I wrote a little program that randomly emulates >>chess matches. It shows that 100 games is nothing, too often scores like >>60-40 appear on the screen. 500 games (and higher) seems to do well as >>most of the time match scores fall within the 49.0 - 51.0 area. >> >>The bad news (in any case for me) is that it hardly makes any sense to >>test candidate program improvements using (even) long matches. Back to >>common sense: 10% = 10% = better. Oh well... >> >>Ed > >I remember from doing a statistics ancillary in my computing degree that there >is a distribution (not "normal" distribution) for calculating binary event >result probabilities - but I can't remember what it is called. Are you thinking of the binomial distribution? In chess, however we have three outcomes: win, loss, draw - is this called trinomial distribution? :) > >However, I have myself written programs to simulate these outcomes, and my >observation is that if you do 10x as many simulations, your accuracy level >increases by one decimal place. The uncertainty typically goes as 1/sqrt(n) so 10x more games decreases the uncertainty with a factor of 3. > >-g
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