My friend loves roulette. She has a simple strategy: if a number hasn't come up in a while, then that number is more likely to come up, and therefore you should start betting on that number.
I tried to tell her that each spin is an independent event and that any given number has the same probability on each spin. Then, after thinking about it more, I came up with the following idea:
If we choose a number, say, $0$, on the (American) roulette wheel the probability that any other number would come up would be $37/38$. So, if we continue to spin the wheel $x$ amount of times the probability that a number that is not $0$ would appear would be $(37/38)^x$.
Therefore, as $x$ increases the probability that a number that is not $0$ gets smaller and the probability that $0$ comes up gets higher.
Is this correct?