okay, you got me, I don't know much about probability theories, I'm in a minority of humanitarians on this site.
Nevertheless I didn't count this as "he can't be the scum three times in a row so he's town". It was just my (false) observation. I don't really trust him.
39% for a letter to appear once
24,5% to appear 2 times
8% to appear 3 times
1,5% to appear 4 times
0,15% to appear 5 times
0,0064% to appear 6 times
Also, where on earth did these numbers come from?? :-P
What is wrong with the numbers? I spent the entire morning to count those!
Different letters had different probabilities, for one thing! What you want to do to work numbers like these out is to use the Binomial distribution with
n=6 rolls and set
k to be the number of times you want that letter to appear. Then set
p to be the probability of that letter appearing, which is 0.5 for T, 0.05 for C and D, and 0.1 for M, V, B and E.
Because of the weirdness with the "E" letters, there are a few game states that you can arrive at from multiple different letter roles, so what you probably care about more is the probability of having a doctor (or whichever role you're worried about) in the game.. there are just over 1900 different game states (I fudged my count a bit so that masons with and without using up the UB are counted separately), so that's a more complicated distribution to calculate, and you probably don't want to be doing it by hand :-)