2. 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!

3. 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

4. 
Expected Value

Standard Deviation

5. 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

6. Amount of
Winnings
(x)
$0
$20
$30
$40
$50
$60
Number of
times
$70
26
1
1
1
5
3
$80
$90
$100
$150
$200
$250
2
2
3
1
4
1
0
Expected Value:
Standard
Deviation:

7. 
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.