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Blue Tigeroo you are correct.
http://www.3dkingdoms.com/chess/elo.htm
Practically of course there are a few problems,
a) elo is only good if opponents are selected at random
b) elo is not a good predictor for large rating differences (the tail shape studies show that normal distribution is not the correct shape) (i.e. I have no chance of beating Carlsen, no matter what my elo 'chance' might say)
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| "elo is only good if opponents are selected at random" |
Isn't ELO generally a good indication of playing strength that becomes more accurate with every game that is played?
Isn't the problem really the number of games played because the distribution auto-corrects over time?
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an elo rating is only valid for a population if it is based on random matches between players in that population. e.g. if you just played against a mate on QA, one of you would get a really high elo, and one a really low one, even though you might both be GMs.
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Ok so then more specifically, the problem is number of games played in equal proportion to number of unique opponents; I just don't see where the random comes in... 
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It has to be a large sample with mostly random player selection so as to
limit patterns that would compromise a normal rating distribution.
If smaller groups are arranging games within a bigger group,
they can't even compare ratings within that larger group.
Although I agree with what whyBish stated, I think he
could beat a Carlsen once in a thousand games. The elo
distribution develops from the other characteristics of chess,
such as a lucky position that allows a much lower rated
player to occasionally win. If it really was just
about skill, you could never beat someone 400 points
ahead of you. Their knowledge is a couple of levels higher at least!
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