Author: Christophe Theron
Date: 16:04:47 03/20/00
Go up one level in this thread
On March 20, 2000 at 17:28:37, blass uri wrote:
>On March 20, 2000 at 13:56:59, Christophe Theron wrote:
>
>>On March 20, 2000 at 06:46:37, Bertil Eklund wrote:
>>
>>>On March 19, 2000 at 22:26:49, Christophe Theron wrote:
>>>
>>>>On March 19, 2000 at 15:41:30, Bertil Eklund wrote:
>>>>
>>>>>
>>>>>Hi!
>>>>>
>>>>>A very impressive result from Shredder4.
>>>>>
>>>>>IMO Shredder plays positionally very good and excellent in the endgames.
>>>>>Nimzo is a bit stronger tactically.
>>>>>
>>>>>Shredder4 used all 4 Turbo-CDs.
>>>>>
>>>>>Bertil
>>>>
>>>>
>>>>Bertil,
>>>>
>>>>I am not sure this message is going to be well accepted. So let me first state
>>>>that I have the greatest respect for your work and the SSDF.
>>>>
>>>>Let me also state that I have a lot of respect for Nimzo, Shredder, and their
>>>>respective authors.
>>>Yes it's all great programs.
>>>
>>>
>>>>However, I can only strongly disagree with your sentence "a very impressive
>>>>result from Shredder4".
>>>
>>>57,5% against a program known as one of the best on tournament time-control
>>>impressed at least me. I only talk about this 40 game match. Maybe it loses to
>>>Tiger in the next match but it's another match.
>>
>>
>>Maybe Tiger loses, actually I do not know.
>>
>>But 57.5% must be taken with a statistical grain of salt. From the statistical
>>data I have, and I'm open to discussion about this, on a 40 games match you can
>>expect the error margin to be +/- 8.0% if you want 80% confidence.
>
>1)If you assume probability of 50% for win and of 50% for loss between equal
>players and assume that colours of the players are not relevant the standard
>error is
>sqrt(0.5*0.5*40)=sqrt(10)>3.1 points and in this case 3 is almost the standard
>error
>
>3.2/40=8% so in this case the error margin is really +/- 8.0%
I was assuming 1/3 wins, 1/3 draws, 1/3 losses.
>2)If you assume probability of 20% for win and of 20% of loss and 60% for a draw
>between equal players(colours are not relevant) the standard error is:
>sqrt(0.4*0.5*0.5*40)=sqrt(4)=2
>
>when 0.4*0.4*0.5 is the variation in on game
>0.4*0.5*0.5*40 is the variation in 40 games
>and I do square root of it to calculate the standard error.
>
>In this case the standard error is only 5%.
>I think this assumption assumes more draws then there are between computers.
>
>3)If you assume 40% for white 30% for a draw 30% for black between equal players
>then the variance in one game is
>0.4*0.45*0.45+0.3*0.05*0.05+0.3*0.55*0.55=0.4*0.2025+0.3*0.0025+0.3*0.3025=
>0.1725
>
>In this case the variance in 40 games is 0.1725*40=7.1 and the standard
>deviation is sqrt(7.1)<2.7
>
>2.7/40=6.75% and the standard deviation is +-6.7%
Isn't it closer to 6.8?
>The last case seems to be something close to the realistic case in games between
>equal programs(I believe that there are more draws between equal programs and
>this reduce the standard deviation but I am not sure)
I have no evidence that the rate of draws is higher between equal programs.
Maybe it's possible to make a study from the database of SSDF games?
>The probability for a draw is also dependent on the style of the programs.
Style is not part of my maths. I'm just a bean counter. :)
Christophe
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