The questions reads:
There are $37$ numbers, from $0$ to $36$. Each number has an equal chance of turning up. Zero is green in color and odd numbers are in black and even numbers are in red. If you place $\$1$ on red (black) you get $2$ dollars if you are right and $\$0$ if you are wrong. For each bet there are $19$ losing numbers and $18$ winning numbers.
Suppose you place $\$1$ bets $18$ times on red. What is your expected gain or loss after $18$ tries?
Expected value of one game = $2(18/37) + -$1(19/37)
Expected value of 18 games = ($2(18/37) + -$1(19/37))^18
Is this right?
Suppose I use a dollar for each color bet? How many games can I play if I have an initial capital of $18?
Not sure how to start on this...