Suppose you are playing multiple independent rounds of roulette where you bet $x$ dollars on black then with probability $18/38$ you will double that bet (net gain of $x$ dollars) and with probability $20/38$ you will lose that money.
If you decide to bet 50 dollars on each round, let J be the amount of money you have after playing 20 rounds of roulette. Find $E(J)$ and $SD(J)$.
The answers are $E(J)=947.37$ and $SD(J)=223.3$
I am not sure how to approach this problem; initially I tried to think of it as an indicator problem where each indicator $=1$ when the $i$th round lands black on the roulette, but did not arrive at the correct solution. Any help is appreciated!