Q#37: Rolling to win!

Suppose you are playing a game with a fair die (e.g. no bias for any one side), and your expected payout based on the # you roll is in the table below:

Given it costs $2 to play, is it worth it to play this game?

TRY IT YOURSELF

ANSWER

This question tests your understanding of probability and statistics, specifically expected value.

Expected value/outcomes can be calculated as the average expected returns. In this case, rolling a fair die is a 1/6 chance of rolling each value. Therefore the expected winnings is:

1/6*($4)+1/6*($2) +1/6*($1) + 1/6*(0) + 1/6*(0) + 1/6*(0) = $1.17

However, remember that it costs $2 to play each time, so the expected returns is:

$1.17-$2 = -$0.83

Thus we should not play this game frequently as we are expected to lose 83 cents each time.