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Probability
In a game of Chuck-a-Luck, a player can bet $1 on any one of the numbers 1, 2, 3, 4, 5, and 6. Three dice are rolled. If the player's number appears k times, where k > 1, the player gets $k back, plus the original stake of $1. Otherwise, the player loses the $1 stake. Some people find this game very appealing. They argue that they have a 1/6 chance of getting their number on each die, so at least a 1/6+1/6+1/6 = 50% chance of doubling their money. That's enough to break even, they figure, so the possible extra payoff in case their number comes up more than once puts the game in their favor. a) What do you think of this reasoning? b) Over the long run, how many cents per game should a player expect to win or lose playing Chuck-a-Luck?

In a game of Chuck-a-Luck, a player can bet $1 on any one of the numbers 1, 2, 3, 4, 5, and 6. Three dice are rolled. If the player's number appears k times, where k > 1, the player gets $k back, plus the original stake of $1. Otherwise, the player loses the $1 stake. Some people find this game very appealing. They argue that they have a 1/6 chance of getting their number on each die, so at least a 1/6+1/6+1/6 = 50% chance of doubling their money. That's enough to break even, they figure, so the possible extra payoff in case their number comes up more than once puts the game in their favor. a) What do you think of this reasoning? b) Over the long run, how many cents per game should a player expect to win or lose playing Chuck-a-Luck?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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In a game of Chuck-a-Luck, a player can bet $1 on any one of the numbers 1, 2, 3, 4, 5, and 6. Three dice are rolled. If the player's number appears k times, where k > 1, the player gets $k back, plus the original stake of $1. Otherwise, the player loses the $1 stake. Some people find this game very appealing. They argue that they have a 1/6 chance of getting their number on each die, so at least a 1/6+1/6+1/6 = 50% chance of doubling their money. That's enough to break even, they figure, so the possible extra payoff in case their number comes up more than once puts the game in their favor. a) What do you think of this reasoning? b) Over the long run, how many cents per game should a player expect to win or lose playing Chuck-a-Luck?
Transcribed Image Text:In a game of Chuck-a-Luck, a player can bet $1 on any one of the numbers 1, 2, 3, 4, 5, and 6. Three dice are rolled. If the player's number appears k times, where k > 1, the player gets $k back, plus the original stake of $1. Otherwise, the player loses the $1 stake. Some people find this game very appealing. They argue that they have a 1/6 chance of getting their number on each die, so at least a 1/6+1/6+1/6 = 50% chance of doubling their money. That's enough to break even, they figure, so the possible extra payoff in case their number comes up more than once puts the game in their favor. a) What do you think of this reasoning? b) Over the long run, how many cents per game should a player expect to win or lose playing Chuck-a-Luck?
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