1 Calculate the probability of winning a round of craps.

2 Calculate the expected gain of the gambler A if he has $1.000 for gambling.

3 Calculate the expected gain of the gambler A if he has $1.000.000 for gambling.

4 Calculate the expected gain of the gambler B if he has $100 for gambling.

5 Calculate the expected gain of the gambler B if he has $10.000 for gambling.

6 Write a programme by using Python 3.

Two gamblers start playing craps with two different strategies:

Gambler A starts with betting $1 and doubles the bet after every loss, so that the first win would recover all previous losses plus win a profit equal to the original stake. He stops if he doubles his gambling money or he does not have enough money for the next bet.

Gambler B bets an amount with the probability density function f(x) = (2*x) / (r^2), 0 where r is the current round number. He stops if he wins $500 or does not have enough money for the next bet.

Craps rules are as the following: Each round, two dice are rolled: If their sum is 7 or 11, gambler wins. If the sum is 2, 3, or 12, gambler lose. Otherwise, the dice are rolled until either the initial sum is repeated, in which case the gambler wins or a sum of 7, in which case the gambler loses.