In response to the OP: "I believe that the numbers are accurate. I don't have any hard evidence"

From what I've seen the melding chances are not correct. It took me over 1200 materia to get my gamblers crown and a double meld with tier 1 materia is supposed to be around 42 percent chance. It wasn't even close to 42 percent, some times i would fail 35+ double melds in a row. I did keep track for a while and it seemed the average was about 15-20 percent chance. More closer to 15 percent imo but no where even close to 42 percent. It wasn't uncommon to fail 15 double melds in a row, finally get a double meld, then fail another 20 in a row.

The materia melding system is garbage. If you are unlucky you get screwed over while a small amount of people seem to consistently have good luck and reap the rewards from it. Would like to see a more balanced, less RNG system put in place.

P.S. This is a repost from another materia thread but i felt it applied to here too.