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Question 8 10 pts In a casino game based on the standard gambler's ruin problem, the...
B2. Describe the basic ideas behind the gambler's ruin model. For an unfair game where the...
B2. Describe the basic ideas behind the gambler's ruin model. For an unfair game where the gambler has probability p of winning and q (1-p) of losing, show that the probability that the gambler attains a fortune of N starting from an initial sum of j is given by 1-(a/p) obtain a similar expression for φ, the probability that, starting from €, the gambler is ruined before reaching EN and show that dj+ ,-1 for all j 0,1, ,N. Explain...
(6(4 pts) A player (Joe) goes to a casino and plays a fair game. The player...
(6(4 pts) A player (Joe) goes to a casino and plays a fair game. The player may wager any amount of money. There is a 0.5 probability of winning. If the player wins, then the player get twice the amount of the bet in winnings. If the player loses, the player gets nothing. Think of betting on a coin toss. If you win you double your money, if you lose you lose your money. This is a "fair" game because...
1. Consider the following "Gambler's Ruin" problem. A gambler starts with a certain number of dol...
1. Consider the following "Gambler's Ruin" problem. A gambler starts with a certain number of dollar bills between 1 and 5. During each turn of the game, there is a .55 chance that the gambler wil win a dollar, and a .45 chance that the gamble will lose a dollar. The game ends when the gambler has either S0 or S6. Let Xn represent the amount of money that the gambler has after turn n. (a) Give the one-step transition...
4. [6 marks] Consider a play of the casino game 'Quick Draw'. In this game, the...
4. [6 marks] Consider a play of the casino game 'Quick Draw'. In this game, the player pays $10 to play. He/she picks onē card from the standard deck of 52 cards (i.e. four A's, four K's, etc.). If the player selects an "A", he/she wins $50 (i.e. the profit is $40); if the player selects a "K", he/she wins $30 (i.e. the profit is $20). Otherwise, the player wins nothing and also loses the bet of $10. Let the...
Gambler’s Ruin. A gambler, player A, plays a sequence of games against an opponent, player B....
Gambler’s Ruin. A gambler, player A, plays a sequence of games against an opponent, player B. In each game, the probability of player A winning is p. If player A wins, he wins $1 which is paid by player B. If he loses a hand with probability q = 1-p, he must pay $1 to player B. The game ends either player B wins all the money from player A, and he is “ruined,” or when player A wins all...
Daniel Reisman of Niverville, NY submitted the followine question to Marilyn vos Savant's December 27, 1998,...
Daniel Reisman of Niverville, NY submitted the followine question to Marilyn vos Savant's December 27, 1998, Parade Magazine column, "Ask Marilyn." At a monthly 'casino night,' there is a game called Chuck-a-Luck. Three dice are rolled in a wire cage. You place a bet on any number from 1 to 6. If any one of the three dice comes up with your number, you win the amount of your bet. (You also get your onen stake back). If more than...
12. A popular casino game is three-card poker. One aspect of the game is the "pair-plus"...
12. A popular casino game is three-card poker. One aspect of the game is the "pair-plus" bet in which a player is paid a dollar amount for any hand of a pair or better, regardless of the the dealer has. The table shows the profit and probability for various hands of a player playing the $6 pair-plus bet. Profit (S) Probability Straight flush 200 12/5525 Three of a kind (425 36/1105 274/5525 150 30 20 6 72/425 Flush Other 822/1105...
Question 3 (15 pts). A gambler plays a game in which a fair 6-sided die will be rolled. He is all...
Question 3 (15 pts). A gambler plays a game in which a fair 6-sided die will be rolled. He is allowed to bet on two sets of outcomes: A (1,2,3) and B (2,4,5,6). If he bets on A then he wins $1 if one of the numbers in A is rolled and otherwise he loses $1 -let X be the amount won by betting on A (so P(X-1)-P(X1)If he bets on B then he wins $0.50 if a number in...
You are helping a corporation create a new system for keeping track of casinos and customers....
You are helping a corporation create a new system for keeping track of casinos and customers. The system will be able to record and modify customer and casino information. It will also be able to simulate games in the casino. You may complete this project individually or in a group of no more than 2 other people. Requirements do not change if you choose to complete the project individually or as part of a group. Customer-specific requirements You can create...
Problem 5: Gambler's Ruin Our old friend John Doe who tried his luck at blackjack back in Homework 2 now decides to win a small fortune using slot machines mstead. Having ganed some wisdom from h...
Problem 5: Gambler's Ruin Our old friend John Doe who tried his luck at blackjack back in Homework 2 now decides to win a small fortune using slot machines mstead. Having ganed some wisdom from his previous outings, he starts off small with just one dollar. He plays the slot machines in the following way He always inserts one dollar into the slot machines After playing it, the machine returns two dollars with probability p and returns nothing with probability...
B2. Describe the basic ideas behind the gambler's ruin model. For an unfair game where the gambler has probability p of winning and q (1-p) of losing, show that the probability that the gambler attains a fortune of N starting from an initial sum of j is given by 1-(a/p) obtain a similar expression for φ, the probability that, starting from €, the gambler is ruined before reaching EN and show that dj+ ,-1 for all j 0,1, ,N. Explain...
(6(4 pts) A player (Joe) goes to a casino and plays a fair game. The player may wager any amount of money. There is a 0.5 probability of winning. If the player wins, then the player get twice the amount of the bet in winnings. If the player loses, the player gets nothing. Think of betting on a coin toss. If you win you double your money, if you lose you lose your money. This is a "fair" game because...
1. Consider the following "Gambler's Ruin" problem. A gambler starts with a certain number of dollar bills between 1 and 5. During each turn of the game, there is a .55 chance that the gambler wil win a dollar, and a .45 chance that the gamble will lose a dollar. The game ends when the gambler has either S0 or S6. Let Xn represent the amount of money that the gambler has after turn n. (a) Give the one-step transition...
4. [6 marks] Consider a play of the casino game 'Quick Draw'. In this game, the player pays $10 to play. He/she picks onē card from the standard deck of 52 cards (i.e. four A's, four K's, etc.). If the player selects an "A", he/she wins $50 (i.e. the profit is $40); if the player selects a "K", he/she wins $30 (i.e. the profit is $20). Otherwise, the player wins nothing and also loses the bet of $10. Let the...
12. A popular casino game is three-card poker. One aspect of the game is the "pair-plus" bet in which a player is paid a dollar amount for any hand of a pair or better, regardless of the the dealer has. The table shows the profit and probability for various hands of a player playing the $6 pair-plus bet. Profit (S) Probability Straight flush 200 12/5525 Three of a kind (425 36/1105 274/5525 150 30 20 6 72/425 Flush Other 822/1105...
Question 3 (15 pts). A gambler plays a game in which a fair 6-sided die will be rolled. He is allowed to bet on two sets of outcomes: A (1,2,3) and B (2,4,5,6). If he bets on A then he wins $1 if one of the numbers in A is rolled and otherwise he loses $1 -let X be the amount won by betting on A (so P(X-1)-P(X1)If he bets on B then he wins $0.50 if a number in...
Problem 5: Gambler's Ruin Our old friend John Doe who tried his luck at blackjack back in Homework 2 now decides to win a small fortune using slot machines mstead. Having ganed some wisdom from his previous outings, he starts off small with just one dollar. He plays the slot machines in the following way He always inserts one dollar into the slot machines After playing it, the machine returns two dollars with probability p and returns nothing with probability...
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