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Subject: Re: Proving something is better

Author: Uri Blass

Date: 13:51:59 12/21/02

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On December 21, 2002 at 16:39:01, Peter Fendrich wrote:

>On December 20, 2002 at 20:01:17, Uri Blass wrote:
>>On December 20, 2002 at 19:56:58, Peter Fendrich wrote:
>>>On December 20, 2002 at 19:30:38, Uri Blass wrote:
>>>>On December 20, 2002 at 19:07:04, Peter Fendrich wrote:
>>>>>On December 20, 2002 at 12:16:25, Uri Blass wrote:
>>>>>>On December 20, 2002 at 11:03:14, Peter Fendrich wrote:
>>>>>>>On December 20, 2002 at 04:10:35, Rémi Coulom wrote:
>>>>>>>>On December 19, 2002 at 19:28:01, Peter Fendrich wrote:
>>>>>>>>>I did, some 15-20 years ago, in the Swedish "PLY" a couple of articles that
>>>>>>>>>later became the basics for the SSDF testing.
>>>>>>>>>A year or so ago you posted a question about how to interpret results with very
>>>>>>>>>few games. In a another thread I posted a new theory for this as an answer
>>>>>>>>>"Match results - a complete(!) theory (long)".
>>>>>>>>>I also made a program to use for this that can be found at Dann's ftp site.
>>>>>>>>Hi Peter,
>>>>>>>>If you had not noticed it, you can take a look at a similar program I have
>>>>>>>>Basically, I started with the same theory as you did, but I went a bit farther
>>>>>>>>in the calculations. In particular, I proved that the result does not depend on
>>>>>>>>the number of draws, which is intuitively obvious once you really think about
>>>>>>>>it. I also found a more efficient way to estimate the result. I checked the
>>>>>>>>results of my program against yours and found that they agree.
>>>>>>>For me it's not so obvious that you can through the draws out.
>>>>>>>I just took a short look at your paper and maybe I misunderstood some of it.
>>>>>>>Take this example: A wins to B by 10-0
>>>>>>>Compared with: A wins to B by 10-0 and with additional 90 draws.
>>>>>>>Not counting the draws will get erronous results.
>>>>>>>The results between our programs shouldn't agree, I think, because I heavily
>>>>>>>relies on the trinomial distribution (win/draw/lose). One can use the binomial
>>>>>>>function (win/lose) and add 0.5 to both n1 and n0 for draws. That will probably
>>>>>>>give a fairly good approximate value but the only correct distribution is the
>>>>>>If the target is only to find which programs is better we can throw draws.
>>>>>>You can imagine the following game chessa:
>>>>>>One game of chessa includes at least one game of chess.
>>>>>>chessa is finished only when a chess game is finished in a win.
>>>>>>if a chess game that is played as part of chessa is finished in a draw then
>>>>>>chessa continues and the sides play chess with opposite colors.
>>>>>>By these rules in both cases the winner won 10 games of chessa with no draws
>>>>>>(draw in chessa cannot happen).
>>>>>In that case you don't need anything more than the result.
>>>>>What I'm doing is producing a statment like:
>>>>>A is better than B with the probability of x%.
>>>>>The 10-0 result will raise x very high but the 55-45 result will lower the
>>>>>probability even if A is still regarded as the best.
>>>>if the 55-45 is result of 90 draws then 55-45 give the same probability that the
>>>>winner is better as 10-0.
>>>>The draws are only relevant for estimate of the difference in rating but not for
>>>>deciding about the better player.
>>>That is essentially the same thing. Different estimates of rating gives
>>>different probabilities of A beating B. The both are closely related.
>>>If the ratings are changed the probabilties should be changed.
>Do you really mean that increased rating diff doesn't mean increased probability
>that A beats B and vice versa?

difference in rating does not give probabilities for a draw.
>>It is not the same suppose player A beat B 1000-0 with 999999000 draws
>>you are going to have no doubt that A is better but if the result is
>>500000500-499999500 with no draw then it is clearly possible that the results
>>are random.
>First: Then you are saying that draws has something to with it.
>Second: That is not the full answer (A is better than B). A is probably better
>than B, we know that. The question is how confident we are saying that.
>That confidence is changing if the ratings are. I would say that it's more
>likely that a 2800 rated player will beat you than a 1800 rated player.
>Wouldn't you?


>Third: "no doubt" doesn't mean anything meassurable. There is always a doubt,
>even if it's small.

I meant to say that practically the doubt is very small when you seee 1000-0
with 999999000 draws so practically you can be sure.

>>If you throw a fair coin 1000000000 times then in most of the cases the
>>difference between the number of heads and the number of tails is going to be
>>more than 1000.



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