A gambler decides to play roulette. His initial investment is $200. He bets $100 each time and will quit when one of the following events happens:

i.He loses his money, within less than 8 bets.
or
ii. He's got $500, within less than 8 bets.
or
iii. He has played 8 times ending up with any amount.

a. What is the number of ways the betting can ocur?
b. What is the most likely length of his play (number of bets) within the above constraints?
c. Provide the probabilities of each of the three events (i, ii, iii).

Remark: Assume betting on even chances i.e. w/l=1

d. (bonus question) Would your answers change if the w/l odds were 18/19?