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Well, opinions are divided. The more additional coefficients, the less objective the rating becomes (the idea of an alternative rating is to calculate pure skill). On the other hand, tournament victories should be rewarded. What should we do?
1) Games with coefficients should be included in the old rating; they won't be in the alternative one.
2) Conduct a vote.
3) ...
I am ready to accept any of the options; it all depends on the community.