Real Math and Sq Enix Math - the twain shall never meet

[Kyros]

Random by definition means "no pattern". Having the 5x fails in a roll spaced out as a characteristic would be a pattern.

Exactly. Gosh. If you are finding patterns in your Random seed, then it really isn't random. They don't have to be spaced out, they can be wherever they damn want, as long as they fall within what's expected. That's why normality curves exists. If you are constantly having outliers outside your standard deviation, then your seed isn't working properly. it's as simple as that.

Here, a simple Wolfram example. Chance of 5 failures in a row is 1 in 3125. OP here had it happen in >500 touches. Likewise, chance of 3 fails in a row is 0.8%, or 1 in 125, and OP had it happen 19 times. I can't say much about the 5 failures since that requires a much bigger sample size, but the 3 fails in a row is such a huge outlier that really makes me question the seed working as intended.

On second thought, it seems he used no SHII, and I have no idea which touch skill he was using, so disregard that math.