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Subject: Re: Proving something is better

Author: Peter Fendrich

Date: 13:39:01 12/21/02

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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?

>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.

>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.


>if you

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