Question

a game consists of cutting a shuffled deck of cards. if you cut a face card (jack, queen, or king) you win 10 cents. if you cut an ace you win 25 cents. if you cut anything else you lose a nickel. what is the expected win/loss for this game?

Answer 1

The expected win/loss for this game is approximately a loss of 0.577 cents per play.

Step-by-step explanation:

To find the expected win/loss for this game, we need to calculate the expected value. The expected value is found by multiplying each outcome by its probability and summing them up. In this game, the probabilities of cutting a face card, an ace, or anything else are 12/52, 4/52, and 36/52 respectively.

Expected value = (10 cents)(12/52) + (25 cents)(4/52) + (-5 cents)(36/52) = -0.577 cents, rounded to the nearest cent. Therefore, the game has an expected loss of approximately 0.577 cents per play.

Based on the calculations, your long-term average loss on this game would be approximately 0.577 cents. You should not play this game to win money because the expected value indicates an expected average loss.