Testing of Phantom Roll

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There is some debate about whether the augmented Commodore Tricorne +2 has a higher rate of "bonus roll" than the regular hat. Wearing the regular CT+2, a COR will get the phantom roll bonus (usually applicable to having the key job in the party) about 33% of the time.
I tested the augmented CT+2 as follows. I made note of my attack (usually around 500) and then, wearing the aug CT+2 and with no other players in my party, rolled a Chaos Roll. By checking my attack after the roll, I could determine whether I had received a bonus roll or not.
To illustrate: say my attack was 500 pre-roll and I rolled a IV. My attack would either be 625 (i.e. + 25%) if I got a regular roll, or 675 (+35%) if I got a bonus roll.
I rolled 200 times, and got 104 bonus rolls for an effective proc rate of 52%.
For the stats geeks out there, if you apply a standard binomial distribution to these results assuming a true rate of proc of 33%, the chance of an outcome > 103 is less than one in a million. In English, this means that, based on these test results, it is highly unlikely that the augmented hat has the same 33% proc rate as the regular one. --Kmera (talk) 22:04, May 18, 2013 (UTC)