[AaronBrown]

You will actually lose twice that much in roulette with two zeros. You pay $5 and win $10 18 times out of 38, for a return of $4.74, a $0.26 loss per bet.

The standard deviation of a fair coin flip for $5 is $5. The house edge in roulette does not change things much, the standard deviation is $4.99.

To translate that into swings, multiply the expected loss by the number of spins and the standard deviation by the square root of the number of spins. For example, after 100 spins you expect to lose 100 x 0.2632 = $26.32. Your standard deviation is 10 x 4.993 = $49.93.

About 1 time in 44 you will down more than two standard deviations, that is down more than $126.18. 1 time in 44 you will be up more than two standard deviations, up more than $73.55. About 1 time in 3 you will be down more than expectation but less than one standard deviation below it, that is between down $26.32 and $76.25. Another 1 time in 3 you will be above expectation but within one standard deviation of it, that is between down $26.32 and up $23.61. The rest of the time you will be between one and two standard deviations from your expectation. 29.9% of the time you will make money.
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