As a mathematician I can't approve your proof
You're right. If you do something on purpose then it is not buggy
But then It is buggy to call something ELO rating if it is not. Arpad Elo would be mad.
Also, in few games I saw that sum of all ELO changes is not = 0 (necessary condition for Arpad)http://www.boiteajeux.net/jeux/dix/partie.php?id=28522
1. lega1985 [ELO +41] (1466 --> 1507)
1. leGica [ELO +17] (1638 --> 1655)
3. zlatovrana [ELO -22] (1620 --> 1598)
4. Franfrin [ELO -41] (1500 --> 1459)
(There wasn't replacements in game)
Maybe something went wrong in order of calculation...
So I am able to do a pretty complex calculator but do not know how to type "ELO" into a search engine
I've noticed that a lot of people ask the same question but there is no response.
Only answer that has already been posted before.Really nice, and please
I am asking you to give me a link to the post where it is explained
or you explain me
or verify that the formula is secret