The ring of wealth affects a very specific list of drops that are considered rare. Those drops are all shared among every monster that is affected by the ring of wealth. That means gems, half keys, and dragon spears/left halves.

I always like it when Jagex shows us how some of the behind the scenes actions work.

 

So, I assume F2P also has a rare drop table? Only gems and the 'no drop'? Interestingly I did a drop log for roaches(~1k) and the 'no drop' was equal to the total gem drop well 41-42.

I wonder if that ratio would be the same for the other monsters...

Well there is my next adventure!