Math puzzles!

P® = C(n,r)*(p^r)*[q^(n-r)]
p = 0.167
q = 0.833
n = 3
r = # times a given face of a die comes up

P(r=0) = 0.579
P(r=1) = 0.348
P(r=2) = 0.0697
P(r=3) = 0.00466

assuming win = p(r>1):

p = 0.348 + 0.0697 + 0.00466
= 0.42

avg. gross gain given win (where bet = x) [μ(gain|p(r>1)]: (2x+3x+4x)/3 = 3x

μ = 3x(0.421) - -x(0.579)
= 0.684; you'll walk away with 0.684 times what you bet on average