Here's a spreadsheet I made for z-score calculation for the following games:

No zero roulette

Single zero roulette

Double zero roulette

Baccarat

@Victor: I couldn't attach the spreadsheet here, it says:

Hi Marven, your spreadsheet is nice but it equals the z-score to the SD.

For instance: 1000 trials, strait bet, 48 hits, result= +4,09

Is the same result for the z-score and SD.

The formula I use for the binomial SD is: Square root of the sample times the prob to win plus the prob to lose.

This formula gives us the value of 1 sd.

square root of 1000x(1/37)x(36/37)=5,12

The mean is 27