Expected Value Project

Team W

• The game is called, “7 and Up”

• Group Members: Jordan Cutler

Game Description

1. The game is played by paying $25 then picking a card randomly from a deck without jacks, queens, kings, or aces.

2. The deck will have 36 cards in it, using only cards with numbers listed on them.

3. The player will pick a card from the deck of 36, if it is 7 or higher (7,8,9,10), they win $50.

4. The card will be replaced if the player chooses to play again.

Probability Distribution (Theoretically)

Card Number:

2 3 4 5 6 7 8 9 10

ProbabilityP(X):

4/36 4/36 4/36 4/36 4/36 4/36 4/36 4/36 4/36

Random Variable (X) = Card number

Expected Value (Theoretically)

• Cost to play: $25

• Expected payout: $22.22

• House advantage: $2.78

• Mean (x): 6

• Standard Deviation (x): 2.58

Expected Value (Experimental Data)

Results are as follows. The experiment was conducted 50 times.Card

Chosen2 3 4 5 6 7 8 9 10

Tally 7 4 6 12 3 3 4 4 7

Experimental Probability Distribution

Random Variable (X) = Card number

Card Number

2 3 4 5 6 7 8 9 10

ProbabilityP(X):

7/364/36or1/9

6/36or1/6

12/36or1/3

3/36or

1/12

3/36or

1/12

4/36or1/9

4/36or1/9

7/36

Expected Value (Experimental)

• Cost to play: $25

• Expected payout: $15.28

• House advantage: $9.72

• Mean (x): 7.97

• Standard Deviation (x): 4.07

Explanation and Evaluation

Theoretical• With a cost to play of $25 and

an expected payout of $22.22, the theoretical simulation gives the house an advantage of $2.78.

• Slightly over 10% earnings.

• Mean (x) : 6

• Standard Deviation (x) : 2.58

Experimental• With a cost to play of $25 and

an expected payout of $15.28, the experimental simulation gives the house an advantage of $9.72

• 38.9% or about 40% earnings.

• Mean (x) : 7.97

• Standard Deviation (x) : 4.07ImprovementsThe cost could be decreased to something more appealing, which in the long run may

increase profits by getting more people to play. The probability of winning could be changed by choosing a different number, such as 8 and higher or 4 and below. The winning payout can be changed which will decrease the expected payout, and give the house a higher advantage, but this may lower the amount of people interested in playing.