Author: Bas Hamstra
Date: 05:37:20 07/16/00
Go up one level in this thread
On July 16, 2000 at 03:34:45, Ed Schröder wrote: >>posted by Dann Corbit on July 15, 2000 at 20:21:54: > >>Simplifying. I have a penny. >>I toss it twice. >>Heads, heads. >>I toss it twice >>Heads, heads. >>I toss it twice >>Tails, heads. >>I toss it twice >>Heads, tails. > >>I count them up. > >>Heads are stronger than tails. > >>My conclusion is faulty. Why? Because I did not gather enough data. > >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? You can *never* be sure. But you can say something like this: 99.7 % of the time the outcome will lay between 50-3*sigma and 50+3*sigma. Sigma can be calculated as SQR(n*p*q) where n is the number of games, and p=0.50 and q=0.50 (q = 1-p). Example: if you run 100 games (or throw that much coins, or turn the weel), the result will be 99.7% of the time between 50-SQR(100 * 0.50 * 0.50) and 50+SQR(100 * 0.50 * 0.50) that is between 45% and 55%.
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