I'm sorry, but you are the one that is wrong here. ^^ Yes, it does increase your chances of getting a rare drop. While you are completely correct on the fact that it does not affect he first wheel (and thereby does not increase the chance of getting to that second 'rare' wheel) it does increase the chance of getting on a 'rare' spot on that second wheel. The second wheel contains both rare and crap drops, a ring of wealth increases the amount of 'rare' spots on the second wheel and thereby increases your chances of getting a rare. The increase is not a very high percentage, I'll have to admit that, and because of that it is pretty hard to notice. Also it still comes down to a load of chance of course, you could wear the ring for ages and not get a good drop and then forget to wear it once and get those legs you where looking for. :P All in all, unless Jagex wants to fool us badly and thinks it funny in some way that we all hope the ring works while it doesn't, we can assume the ring works. Though I can imagine Jagex finding it quite fun to see all those debates about it. :P