Consider a casino game that an individual (Joe) wants to play. It costs him N dollars...

Consider a casino game that an individual (Joe) wants to play. It costs him N dollars each time to play. He loves this game and wants to continue playing until he is either broke or he breaks the bank (wins all the money). The probability of winning is p; the probability of losing is q. These are fixed probability values every time the game is played.

Joe brought $M to the casino. Every time one plays you either lose the entrance fee ($N) or you win and are paid back D dollars.

(a) How much money does Joe expect to have after playing n times? Derive a formula for how much money he has.

(b) Suppose Joe starts with $100, p=0.3, q=0.7, N=$5, and D=$20. Is it likely that Joe will break the bank?

(c) If the answer to (b) is no, how many times is it likely that Joe can play this game before he is broke?

Expert Solution

milcah answered 2 hours ago

Suppose a casino offers a game that costs $20 to play. The game works as follows:...

Suppose a casino offers a game that costs $20 to play. The game works as follows: the dealer will give you a hand (randomly chosen from a regular 52 card deck) of four cards, and you will then win 10X dollars, where X is the number of aces in your hand. What are the expected winnings for this game? The expected profit? Is this a fair game?

A card game at a casino costs $10 to play. One card is selected at random...

A card game at a casino costs $10 to play. One card is selected at random from a standard deck. If a heart is selected the player wins $19. If a spade is selected, the player wins $14. If a club or diamond is selected, the player wins nothing. What is the expected value of this game to the player? Round your answer to the nearest cent. Do not include the $ sign in your answer. A homeowner purchases an...

Joe wants to get a buy a condo, and the following information is available to him:...

Joe wants to get a buy a condo, and the following information is available to him: Purchase price: 600,000 CAD 20% Down payment: 120,000 CAD Interest rate: 3.5% compounded semi-annually (25-year mortgage, i.e. 300 months) a) What is the monthly mortgage payment Joe needs to make? b) How much total interest would Joe have paid over the life of the mortgage (25 years, 300 months), assuming the same interest rate over the life of mortgage. c) If Joe sells the...

1)A casino wants to introduce a new game. In this game a player rolls two 4-sided...

1)A casino wants to introduce a new game. In this game a player rolls two 4-sided dice and their winnings are determined by the following rules: Otherwise, the player wins nothing. If 3 ≤ sum ≤ 5 the player wins $25. If sum ≥ 6 the player wins $100. a)Determine the probability distribution for this gamble. Probability Distribution X P (X) b)How much should the casino charge for this game if they want to make a profit in the long...

What is the difference between advantage play and cheating on a casino game? Please provide detailed...

What is the difference between advantage play and cheating on a casino game? Please provide detailed examples. Please provide relevant data and examples.

A game of chance offers the following odds and payoffs. Each play of the game costs...

A game of chance offers the following odds and payoffs. Each play of the game costs $100, so the net profit per play is the payoff less $100. Probability Payoff Net Profit 0.10 $700 $600 0.50 100 0 0.40 0 –100 a-1. What is the expected cash payoff? (Round your answer to the nearest whole dollar amount.) a-2. What is the expected rate of return? (Enter your answer as a percent rounded to the nearest whole number.) b-1. What is...

Consider the Stage Game below, and consider the repeated game where players play twice (T =...

Consider the Stage Game below, and consider the repeated game where players play twice (T = 2). Payoﬀs for each agent are simply period one plus period two payoﬀs. L C R T 6,6 0,7 1,2 M 7,0 1,1 2,0 B 2,1 0,1 3,3 (a) Do any strategies dominate any other? (b) What are the two NE of the Stage Game? What is the diﬀerence between the two? (c) Call the TL strategy proﬁle (1 plays T, 2 plays L)...

Joe is going to a buffet that allows him to eat as many chicken wings as he wants at a fixed price.

Joe is going to a buffet that allows him to eat as many chicken wings as he wants at a fixed price. How would you predict the number of chicken wings that Joe will eat using utility theory?

Let’s play a game! It costs you only $10 to play! Roll two dice. If you...

Let’s play a game! It costs you only $10 to play! Roll two dice. If you roll snake eyes (two 1’s), then I’ll give you $500. If you roll anything else, then I’ll give you nothing. Using expected value, decide if you should play this game!

Two players play a game where they start with a row of n piles of varied...

Two players play a game where they start with a row of n piles of varied amounts of money. The players take turns and in each turn a player can pocket either the money in the first pile or the last pile in the row of piles that remains. Design an efficient algorithm (using dynamic programming), which on any given sequence of amounts, determines the maximum amount of money that player 1 can win. If n is even, prove that...

Question