The question here isn't whether the odds of consecutive rolls are independent--nobody here has even raised that as something to consider except you.
It's whether 14 failures in a row is just "bad luck" at the posted success probabilities, or a sign that the posted success probabilities are incorrect in some way.
It's funny that we both seem to actually agree with the OP, but we have devolved into internal debate anyway. I definitely can shoulder a large part of that blame, as I was the one who derailed the conversation re:probability vs. odds.
As I already admitted, I got stuck on the semantics of the word and not the intent of usage. The word "probability" was being bandied about without clarity of definition. I wasn't disagreeing with the notion that the odds seem to be skewed in the LivePlex/Aeria's favor. I was, however, pointing out that since it's statistically probable to have multiple failures in a row, it doesn't necessarily reflect that the posted percentage chances of success are incorrect.
I, too, would like confirmation that the percentages posted in NinjaKitten's Gameplay Guide
in are correct. I'd also like to know where those numbers came from and how the provided percentages in general are being calculated. Because it's really hard to judge the given percentages as accurate or inaccurate or even properly weigh the odds without a better look under the hood.
I also agree that a possible solution to resolve the frustration for enhancements would be to provide an increased chance of success after each failed enhancement attempt. I don't believe that providing such a bonus would even undercut Aeria's profits, considering failures at higher levels can result in the loss of an enhancement and that even with Narak shards, success with a high-level enhancement seems drastically (even unfairly) unlikely.