Expected value Flashcard

Front

What is expected value in probability?

Back

Expected value is the average outcome of a random event, calculated by multiplying each possible outcome by its probability and summing the results.

Front

How do you calculate expected value?

Back

Expected value (EV) = (Probability of Outcome 1 x Value of Outcome 1) + (Probability of Outcome 2 x Value of Outcome 2) + ...

Front

What does a positive expected value indicate?

Back

A positive expected value indicates that, on average, a player can expect to win money over time.

Front

What does a negative expected value indicate?

Back

A negative expected value indicates that, on average, a player can expect to lose money over time.

Front

In a game, if the probability of winning is 0.2 and the prize is $10, what is the expected value of winning?

Back

EV = (0.2 x $10) = $2.00.

Front

If a player pays $1 to play a game with a 50% chance to win $3, what is the expected value?

Back

EV = (0.5 x $3) - $1 = $0.50.

Front

What is the expected value of a fair game?

Back

The expected value of a fair game is $0, meaning neither the player nor the host has an advantage.

Front

How does the number of outcomes affect expected value?

Back

More outcomes can complicate the calculation of expected value, as each outcome must be weighted by its probability.

Front

What is the expected value of a game where you win $5 with a probability of 0.1 and lose $1 with a probability of 0.9?

Back

EV = (0.1 x $5) + (0.9 x -$1) = $0.50 - $0.90 = -$0.40.

Front

What is a 'fair game'?

Back

A fair game is one where the expected value is zero, meaning players neither gain nor lose money on average.