Every Week a Charter Plane Brings a Group of High-Stakes

question 48

Short Answer

Every week a charter plane brings a group of high-stakes gamblers into Las Begas.Half the group stays and begins gambling at Hot Slots near the Strip, and the other half is housed and begins gambling at Better Bandits, some distance away.(Both hotel/casinos are owned by the same corporation.)Once an hour, dedicated shuttle buses will transport to the other
casino any of the group members who wish to try their luck at the other casino.The transition probabilities are as follows:
$\begin{array}{c}\text { Next Hour }\\\begin{array}{lcc} &\text { Hot Slots }&\text { Better Bandits }\\\text{This Hot Slots} & .8&.2 & \\\text{Hour Better Bandits} & .3 & .7\end{array}\end{array}$

A.After three hours, what proportion of these gamblers are in the Hot Slots Casino?
B.What is the long run average percentage of these gamblers who
will be at Hot Slots Casino?

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Definitions:

Utility-Maximizing

Utility-maximizing is a principle in economics where individuals or entities choose the options that provide the highest satisfaction or utility from the available choices, given their preferences and constraints.

Substitute Goods

Products or services that can be used in place of each other. When the price of one falls, the demand for the other product falls; conversely, when the price of one product rises, the demand for the other product rises.

Consumer Behavior

The analysis of how consumers' preferences and economic decisions affect the demand for goods and services.

Marginal Utility

The change in total utility a person derives from consuming an additional unit of a good or service.