A game is played between a gambler and a ’banker’. A fair coin is tossed repeatedly in a sequence of identical experiments. The probability of heads is, 0 ≤ p ≤ 1, and if this occurs, the gambler wins 1 unit. The probability of tails is q = 1 − p; if this arises, the gambler loses 1 unit. The gambler starts the game with k pounds.

Part A:

Note:

The game ends when either:

(a) the gambler is bankrupt (has £0) and is ruined.

(b) the gambler reaches a total of N pounds, has won the game, and retires.

Write a MATLAB that calculates and plot the following parameters:

Number of times Gambler Wins.

Number of iteration when a total of N pounds has been collected by gambler.

A table with each iteration result and accumulative balance of gambler and banker simultaneously.

Part B:

If a toss of coin is unfair in a sequence of identical experiment having 70% of heads occurrences, then determine:

No of Wins of banker against gambler.

Calculate the overall winner of Gambling after 100 events.