Roulette

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 mu= .473(1) + .526(-1) = -.053

The bell shaped curve.

A normal curve, which always peaks at the mean mu, is guaranteed
by a random population size (n or bets) greater than 30.

 

For 1 bet:

The variance sigma squared = [1-(-.0530]2 x .473 + [(-1)-(-.053)]2 x .526 = .997

The standard deviation sigma (or s.d.) = .997 = .998 (1 bet)

 

The meaning of life.

Changing the mean mushifts the curve.

Deviation Reshapes
Changing the standard deviation sigma, reshapes the curve.

 

For 100 bets: sigma for n bets

s.d. (100 bets) sigma for n bets = .998/100 = .0998 (100 bets)

The 3 sigma Rule.

3 standard deviations sigma for n bets on both sides of the curve atmu, always = 99.7% of bets.

Gain(max) = mu+3 = (-.053)+3 x .0998 = $24.64 (in 100 $1 bets) = $124.64 = 62%(max) win

Loss(max) = mu+3 = (-.053)+(-3 x .0998) = -$35.24 (in 100 $1 bets) = $64.76 = 67%(max) loss

 

The Casino View: 100,000 bets sigma for n bets

s.d. (100K bets) sigma for n bets = .998/100,000 = .0032(100K bets)

The losing spike.

The tiny sigma for n bets (.0032) reshapes the curve to a spike with >99.85% NO winners!

 

The spike CANNOT be scaled.

It would be 177 ft. high!

17 stories high

Nobody Beats the House (<0.15%).

Complete Menu Page.
Keep under a 100 bets.
The Best wide view.
The Best wide view.
Heaven.
Heaven.
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