Bowling Average

[irchans]

Puzzle:

If, each frame, you get a strike with probability x, and get a spare with probability s, and get an open frame with probability (1-x-s), what is your average score and standard deviation? (Let's assume that you get 9 pins if you don't get a strike on the first ball.)

(I have figured out the correct average, but I think my standard deviation is wrong. I will post the average formulas in a few days if no one else does.)

Cheers,
Irchans