I want to calculate the expected pay-out of european roulette spins.

Particularly, I want to know what is the expected pay-out at the 200th spins.

I assume the following:

a. the customer's initial amount is $100;

b. the customer places a flat bet of $10 each spin [total bet];

c. the customer has the following strategy (and play this each spins)

$1 on number 5

$2 on even

$3 on odd

$2 on 1-6

$2 on 13-24

d. the customer can inject further money in case he/she goes bankrupt before getting to the 200th spin.

I used excel poptools to run Monte Carlo simulations (5000 simulations) and obtain that the average amount of money that the customer has at the 200th spins is $44.

This is in line with the theoretical expected value

(that is, customer's initial amount + 200 * (expected total paid per spin - total bet) = 46).

Now, I have two questions:

1. what is the theoretical expected pay-out if the customer cannot inject further money, that is the customer cannot continue playing if he/she goes bankrupt? How can I calculate this?

2. Would it make sense to run simulations and calculate the average pay-out at the 200th when the money at the 200th might be zero for lots of simulations?

Any suggestion is welcomed. Thank you,

Fede