How to measure good or bad luck in roulette I want to analyze and represent the performance of a bet (X numbers out of 37 total roulette numbers) for a series of spins (N spins).
For example, let's say that I choose 5 numbers (my bet) and these 5 numbers win in 10 out of 100 spins.
How can I measure (and show) how lucky or unlucky I was? What if I use a scale from 1 to 10.. 1 for worst results against my favour, 5 neutral and 10 for most favourable results.
I thought about comparing the actual win % to the expected average win %, but i don't really know how to do it.
As for visualizing the results, I would like to represent variance/deviation/luck with a bar like that
 A: Let $p$ be the true probability of your bet winning in a single spin (what you call the "average win" probability).
The number of wins $X$ in $n$ spins follows a $\text{Binom}(n, p)$ distribution. When $n$ is large, this roughly follows the normal distribution $N(np, \sqrt{np(1-p)})$. The "luckiness" or "surprisingness" of the actual number of wins you get in the $n$ spins can be expressed in the form of how far you are from the mean $np$.

*

*One way to do this is to report the $Z$-score $\frac{X-np}{\sqrt{np(1-p)}}$. This will be a real number (that usually is between $-2$ and $2$) that counts how many standard deviations you are away from the mean. A score near zero means you are quite close to the mean (which is typical), a large score means you won much more often than expected, and a very negative score means you won much less than you expected. (You can translate this to your scale from $1$ to $10$ if you wish, although I do not really see a reason to do so.)

*Another way to do this is to report the tail probability, i.e. "what is the probability of being farther from the mean than I already am?" For example, if $p=1/2$ and $n=100$, and you got $60$ wins, you might say "that's higher than $50$. What is the probability of getting $\ge 60$ wins in $100$ spins?" Here, $P(X \ge 60) \approx 2.5\%$, so you would consider yourself quite lucky. If you are under the mean, you can compute the probability of the left tail to see how unlucky you were. (Note that computing the probability $P(X=60)$ is not very informative. Even the most likely event $X=np$ has a small probability.)


Edit: Note that in my last bullet point (and comment below), I used $n=100$ and $p=1/2$ as an example. As BruceET points out, your situation has $p=5/37$ and $n=100$.
A: Gambling has the scoring built-in. Just track how much money you lose (or win)!
