has 18 black and red numbers with 0 and 00.
Betting on Red or Black:
The probability of winning (Pwin or 1) = 18/38 = .473
The probability of losing (Plose or 1) = 20/38 = .526
The mean = .473(1) + .526(1) = .053
A
normal curve, which always peaks at the
mean ,
is guaranteed

by
a random population size (n or bets) greater than
30.

For 1 bet:
The variance = [1(.0530]^{2} x .473 + [(1)(.053)]^{2} x .526 = .997
The standard deviation (or s.d.) = .997 = .998 (1 bet)
Changing the mean shifts the curve. 

Changing the standard deviation
,
reshapes the curve.

For 100 bets:
s.d. (100 bets) = .998/100 = .0998 (100 bets)
3 standard deviations on both sides of the curve at, always = 99.7% of bets.
Gain(max) = +3 = (.053)+3 x .0998 = $24.64 (in 100 $1 bets) = $124.64 = 62%(max) win
Loss(max) = +3 = (.053)+(3 x .0998) = $35.24 (in 100 $1 bets) = $64.76 = 67%(max) loss
The Casino View: 100,000 bets
s.d. (100K bets) = .998/100,000 = .0032(100K bets)
The tiny (.0032) reshapes the curve to a spike with >99.85% NO winners!
The spike CANNOT be scaled. It would be 177 ft. high! 
Nobody Beats the House (<0.15%).