The Black MarketTeam F

Welcome to the Black Market. You have to pay $52 to play this game and then you will draw one, and only one card. Your reward depends on the type of card you draw. If it is a red card (hearts or diamonds), you unfortunately win nothing (hence “The Black Market”). If you draw a black card (clubs or spades) you are in better luck. Depending on the face value, 2-10, you win 10 times the money of that number, for example if you draw a 2 then you win $20, if you draw a 3 you win $30, etc. If you draw a face card (Jack, Queen, King) then you win $150 and if you draw an Ace of Clubs you win $200. Finally, if you draw an Ace of Spades you win $250. It’s easy!

Card Probability Winnings

Red Card (Anything) 1/2 $0

Black 2 1/26 $20

Black 3 1/26 $30

Black 4 1/26 $40

Black 5 1/26 $50

Black 6 1/26 $60

Black 7 1/26 $70

Black 8 1/26 $80

Black 9 1/26 $90

Black 10 1/26 $100

Black Face Card 3/26 $150

Ace of Clubs 1/52 $200

Ace of Spades 1/52 $250

Your Chances

Expected Value

Standard Deviation

Expected Value and Standard Deviation

Amounts of Money Earned when Cards Drawn

$150 $0 $30 $0 $150

$0 $0 $0 $80 $0

$0 $0 $0 $100 $90

$200 $0 $60 $0 $0

$60 $0 $50 $0 $0

$150 $50 $20 $50 $0

$0 $150 $90 $0 $40

$70 $60 $0 $90 $0

$0 $0 $80 $0 $50

$0 $0 $50 $70 $0

Results of the Game

$70 $80 $90 $100 $150 $200 $250

2 2 3 1 4 1 0

Results of GameAmount of Winnings (x)

$0 $20 $30 $40 $50 $60

Number of times

26 1 1 1 5 3

Expected Value:

Standard Deviation:

The expected value of the game simulation computed turned out to be lower than the expected value of the game computed theoretically, but the values were still close. This could be because there were many red cards that were drawn that result in no money and also there were few aces and face cards drawn which result in the most money. The expected values ended up being close because out of the 50 turns in the simulation, about half of the cards drawn were red and about half were black. Some improvements that could be made are maybe increasing the costs of the red cards to a very low amount and also making sure that the cards are completely shuffled before picking another card.

Comparing Results