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I believe your reasoning is flawed there. The concept of "two groups" doesn't actually exist because through the process of "natural selection" the players that win leave the "other group". 
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Although I agree with what whyBish stated, I think he
could beat a Carlsen once in a thousand games. |
Cheers, beat him with boredom maybe 
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It wouldn't be the first time my reasoning was flawed (see my games for reference). 
Have you've ever seen how large telescopes are polished?
The polishers move randomly to get the perfect curvature. If any pattern is programmed
into the polishers, the curve is compromised. It's not intuitive but it works!
Getting back to chess, if you have a group of thousands it is not possible for all players
to play a set number of games with everyone else. You have two choices, random player selection
or smaller groups playing set numbers of games. The first choice, just like the polishing gives
you a better distribution curve while the latter could result in very uneven ratings overall.
Sure there is a natural selection (interesting term!), but even here on Queen Alice, many players
may play mostly amongst themselves in private tourneys and challenge games. Perhaps other 'groups' play mostly
in Open tourneys where there is no selection out of the group.
whyBish, a win is a win! 
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Well I mean if a player's score is 100, 200 or more points above the group, I would consider it very surprising he would want to play in that group and that the other players would want to play him.
Also, I would expect that he would be getting challenges from other players in his score range and that he would also be arranging matches with those in his range, so that if he was overrated his score would auto-correct.
Essentially I guess we are just talking about semantics here because the concept of "random" is really already built into any community. I would prefer the terminology "large sampling" rather than "random sampling".
I got a challenge from Bergman when my rating was around 1550 and I just simply turned it down.
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Bluetigeroo, I should like to have a look with yuor randonmly polished telescope. Especially if you live where ther is relatively little light pollution
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