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Chapter 11: Problem 24

If the expected value of a game is negative, what does this mean? Also describe the meaning of a positive and a zero expected value.

Short Answer

Expert verified
The expected value of a game denotes the average winnings a player can expect in the long run. Negative expected value indicates a player will tend to lose money over time, a positive expected value means they can expect to win more than they bet, and a zero expected value suggests neither a net loss nor gain in the long run.

Step by step solution

01

Explain Expected Value

The expected value of a random variable gives us a long-run average value of repetitions of the experiment it represents. It's essentially the arithmetic mean of a large number of repetitions of the experiment.
02

Meaning of a Negative Expected Value

In the gaming context, when a game has a negative expected value, it indicates that a player will lose money in the long run. It refers to less than the amount paid initially, meaning the average winnings are less than the cost of playing.
03

Meaning of a Positive Expected Value

If a game has a positive expected value, it means that a player stands to win more than they bet or spent to play the game over the long run. It implies the average winnings are more than the cost of playing.
04

Meaning of a Zero Expected Value

A zero expected value for a game means that the player will not lose or gain any money in the long run. For each play, the average winnings exactly balance the cost of playing. The net gain or loss is zero over time.

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