Chapter 5, Problem 4CP

Sagittarius Casino

The Sagittarius Casino’s strategy for establishing a competitive advantage over its competitors is to periodically create unique and interesting new games for its customers to play. Sagittarius management feels it is time for the casino to once again introduce a new game to excite its customer base, and Sagittarius's Director of Research and Development. Lou Zerbit, believes he and his staff have developed a new game that will accomplish this goal. The game, which they have named POSO! (An acronym for Payouts on Selected Outcomes), is to be played in the following manner. A player will select two different values from 1, 2. 3, 4, 5, and 6, two dice are then rolled. If the first number the player selected comes up on at least one of the two dice, the player wins $5.00: if the second number the player selected comes up on both of the dice, the player wins $10.00. If neither of these events occurs, the player wins nothing.

For example, suppose a player fills out the following card for one game of POSO!

When the two dice are rolled, if at least one die comes up 4 the player will win $5.00, if both dice come up 2 the player will win $10.00, and if any other outcome occurs the player wins nothing.

Managerial Report

Sagittarius management now has three questions about POSO! These questions should be addressed in your report

1. 1. Although they certainly do not want to pay out more than they take in, casinos like to offer games in which players win frequently: casino managers believe this keeps players excited about playing the game. What is the probability a player will win if she or he plays a single game of POSO!
2. 2. What is the expected amount a player will win when playing one game of POSO!
3. 3. Sagittarius managers want to take in more than they pay out on average for a game of POSO! Furthermore, casinos such as Sagittarius are often looking for games that provide their gamers with an opportunity to play for a small bet. And Sagittarius management would like to charge players $2.00 to play one game of POSO! What will be the expected profit earned by Sagittarius Casino on a single play if a player has to pay $2.00 for a single play of POSO!. Will Sagittarius Casino expect to earn or lose money on POSO! If a player pays $2.00 for a single play? What is the minimum amount Sagittarius Casino can charge a player for a single play of POSO! And still expect to earn money?