Cogs42 wrote:
Feel free to point out the glaring flaws in my early Saturday morning pre-coffee fuzzy logic. But I think that's right?
Dammit, I knew I should have had the coffee first. It's even trickier than that. I didn't ensure that each of the die rolls were mutually exclusive.
The chance of a fumble with 5 dice, TN8, is the chance of rolling two 1's plus no 8+, plus the chance of rolling three 1's plus no 8+, plus the chance of rolling four 1's plus no 8+, plus the chance of rolling five 1's. Each of these needs to be calculated out. For example, the chance of rolling exactly two 1's and 2-7 on the three other dice is 1x1x6x6x6x(5down2)/100000 = 2.16%. Calculating these out, I get 2.16+0.36+0.03+0.001 =
2.551%,
not 3.43% as I claimed earlier.
I'm reasonably confident with this, because if you calculate the compliment (ie. the chance of rolling no 1's or one 1 and no successes), it all adds up to 16.8%. And the chance of at least one success is 83.2%.
The chance of rolling at least two 1's on five dice is
8.146% (calculated using the same approach), not 10%.
The chance of rolling two 1's and three successes at TN6, that is, two 1's and three 6-10's, is still 1*1*5*5*5*(5down2)/100000 =
1.25%. I got that one right.
So the chance of fumbling with 5 dice, TN6, minus two successes, is 8.146 - 1.25 =
6.9%. Still a lot larger than 2.55%.