R problems

Suppose you have $100 to play a casino game. Each trial of the game is independent. You are smart and figured out how to shift the odds of the game in your favor. On each trial, the probability you win is 0.55, and the probability you lose is 0.45. When you win, your payoff is double the bet amount. When you lose, you lose the risked amount. You plan to play the game 1,000 times. In this question you will investigate what is the optimal proportion of your money you should risk for each trial of the game. Assume that the proportion is the same for all 1,000 times you play.

a.What is your average bankroll after 1,000 game-plays if you risk 80% on each trial?

b.What is your average bankroll after 1,000 game-plays if you risk 20% on each trial?

c.Can you find the proportion to risk on each trial that would maximize your bankroll after 1,000 game-play?

Look up the Kelly Criterion if you are interested in this question.