The Elo rating system is commonly used to rank chess players, giving some insight into the probably of one player defeating another, but how would it react in a situation where there are three players whose games consistently end in the following way:

Jenny defeats Phil
Phil defeats Andy
Andy defeats Jenny

If each player begins with an Elo score of 1200 (as is usual), what happens? How is the score affected if they play other "ranked" matches with people outside that circle?

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    $\begingroup$ they'd all stay at 1200 is my understanding, if Phil went off and beat stronger players, he would then start to pass his higher grade into the closed system. See 'grade inflation' for a discussion of how modern grades might now be higher than the past. I presume they'd all go into an initial calculation at 1200. If Phil starts beating 1800s, then in theory Jenny must be a stronger player, and in turn Andy beats Jenny so must be stronger. Sorry I don't know full details $\endgroup$ – Cato Sep 14 '16 at 14:48
  • $\begingroup$ I'm not saying this system inflates any grades, it was just an aside of how I recently read that the initial grades passed into the system are kind of uncontrollable, and despite all fair efforts they bubble up to the top, meaning that the current batch of high grades may or may not be fair compared to past masters. $\endgroup$ – Cato Sep 14 '16 at 14:50
  • $\begingroup$ they'd get the grade 'credit' for a win and the corresponding debit for a loss - on British Chess Federation it was said to be plus/minus 50 - so in that you'd constantly gain and lose 50 points from inputs going into a running average, and therefore stay the same $\endgroup$ – Cato Sep 14 '16 at 14:52

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