What is a formula to calculate skewness of bets?

Hello,

OK, I've stucked with matematics and can't do it alone.
I've read about skewness of roulette bets, for example it says if you bet 1$ on each of 30 numbers, then this bet combination has a skewness of -1,32.
Another example is, if you put 30$ on one single number then this bet has a skewness of +5,92.
Source of info

I know what skewness mean, so what I need is a formula and litle matematical information of skewness in roulette that will allow me to calculate the skew of any bet (American/European/French).

Thank you in advance.

Wikipedia has what you seek.
Skewness
Skewness changes as the number of trials increase.
This should be obvious. And with Roulette, the Skew does approach 0 as N gets larger.
Skew is what the data looks like on a graph.
Data Patterns in Statistics

My formula may be different from Wiki, it was from my class notes, and some Skew and Kurtosis formulas are different depending on what question one is trying to answer.

I show for a single number p=1/37, one trial = 5.8333
100 trials = 0.5833
1000 trials = 0.1845
So Skew by the 1000th trial has just about disappeared.

The 30 numbers p=30/37 -1.5872
100 trials = -0.1587
1000 trials = -0.0502

After work I may check into both formulas I have and see if I can find any difference and why.

Hope this helps.

Hi,
I would reply sooner but had to wait posting limitation to disapear :)

Wikipedia don't have to much but I found this excelent site that explains all about skewness and kurtosis.
So thank you by not giving me a complete solution (otherwise I wouldn't learn to much...)

Anyway I still have one more qustion,
I solved all of the formulas from that link abowe and I'm geting right results (same as yours), BUT, I was forced to use a mean equal to zerro (u = 0) to solve 2nd, 3th and 4th moment of distribution (part of the SKEW and KURT formula).
What confuses me here, is that in roulette mean isn't zerro but -0,027 (for european whell).

Now if I calculate moments of distribution where mean isn't equal to zerro the results are not same as yours(they become somewhat lower! because mean (first moment) is bellow 0).
for example formula of 3th moment is: Capital SIGMA(X - mean)^3
Do you have any idea why mean must be zerro and not -0,027 to get right result?

Also how did you derive at conclusion that skewness is geting lower as trials become grater??
I've used 37 as number of trials in my calculation, and even if I set Trials over 1000 the result will be the same according to the formulas from the link and assuming normal distribution of outcomes.

I hope this question does not become boring lol.

Have a nice day!