This earlier question asked how to get a 5.76 standard deviation for a single number bet on Roulette. The answer gave the formula, but unfortunately, the formula doesn't easily generalize to more than two payout outcomes.
For example, Baccarat (Banker) has three outcomes. Here they are:
- 0.4587 probability with a profit of 0.95
- 0.0951 probability with a profit of 0
- 0.4463 probability with a profit of -1
The standard deviation is apparently 0.93. How do you get from the previous numbers to 0.93? In other words, what's the magic formula? I want the formula as general as possible so it can be extended to even 10 or more outcomes.