Hello, it seems something wonky is confusing amr with 2 rings and multiple strategies when it realises its an upgrade but wont pick it.
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Yeah… I still need to put in yet more code to deal with the fact that people can have two of them… and code to handle not putting the same stone in two different rings, etc.
First, appreciate the work.
Followed by the inevitable headache. 
It may be an edge case but the program seems unable to deal with having three rings with different gem setups, even when I lock the slots.
Not sure this is correct but I am curious if we can just go ahead and trust the BIB output but ignore the ring as it has no stats anyway. Then we could just do individual sims to figure out the best ring to use?
In most cases your ring will be your best choice, so yeah until I get this multiple-ring issue fixed you could use the Upgrade Finder to see ranked stone combinations, and run the best one.