So I have downed Ultima HM 58 times now (ridiculous, I know; it's personal now). No caster ring. My group makeup has varied from having multiple casters (i.e. 2x BLM, 1x SMN), to me being the only caster (BLM). I'm wondering if there's something I'm doing to nerf my chances of this dropping?

By my math, which I'm sure is wrong, there are 10 items that drop in this trial, so a 10% probability. Of course my odds don't increase/decrease depending on the previous drop(s), so it's always 10% (unless group makeup alters this percentage). I don't think I'm falling victim to the gambler's fallacy. In this case, 100*(0.9^58) (probability of NOT dropping caster ring ^ 58 kills) puts me at a 0.22% chance that this wouldn't have dropped by now.

So my question is, is there anything I can do to increase the likelihood of it dropping? By the time I get the ring, I'm sure I'll have my 2nd i90 ring and it won't even matter. Like I said earlier...it's personal!