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Description of GameThe name of our game is “Stat Kats”. It costs $4.00 to

play. The objective of this game is to win as many Kit Kats as

possible. In order to win Kit Kats, the player must roll two dice.

The sum of the two numbers rolled on the dice will determine

how many Kit Kats the player will receive. Certain sums are

more valuable than others. For example, sums that have a

greater probability of being rolled are of less value (6, 7, 8).

Sums that have a lower probability of being rolled are of higher

value. For example 2 and 12. To see the number of Kit Kats you

can win by rolling the two dice, check the table on the next slide

by clicking on this arrow.

Probability of Sum Sum Number of Kit Kats Won

1/36 2 102/36 3 73/36 4 54/36 5 35/36 6 16/36 7 05/36 8 14/36 9 33/36 10 52/36 11 71/36 12 10

Theoretical Outcomes

Expected Value/Mean of Theoretical Outcomes- 3.11 Kit Kats Standard Deviation of Theoretical Outcomes- 3.06

Sum of Two Dice

Frequency

2 1

3 2

4 4

5 5

6 9

7 7

8 5

9 7

10 7

11 1

12 2

Stimulation Data

Expected Value of Winnings- 3.12Standard Deviation- 2.67

Trial # # Kit Kats

1 1

2 3

3 5

4 1

5 7

6 1

7 5

8 5

9 1

10 3

11 7

12 0

13 5

14 3

15 1

Trial # # Kit Kats

16 5

17 5

18 0

19 3

20 3

21 0

22 1

23 3

24 5

25 0

26 3

27 0

28 1

29 1

30 1

Trial # # Kit Kats

31 10

32 3

33 3

34 1

35 0

36 1

37 10

38 5

39 0

40 1

41 10

42 5

43 3

44 7

45 5

Trial # # Kit Kats

46 3

47 1

48 1

49 10

50 3

Result Analysis After playing Stat-Kat fifty times, we analyzed our theoretical and

experimental results by comparing the means and standard

deviations. Originally we had theorized an expected mean of

winnings to be 3.12 Kit-Kats, but the stimulated outcome was

surprisingly close, coming out to be 3.12 Kit-Kats. Our theoretical

standard deviation on the other hand, was not as close. The

theorized standard deviation was 3.06, but the experimental results

showed that the standard deviation was 2.67. Based on the

experimental expected winnings, there is a good house advantage

since we are charging $4 and the average winnings is only 3.12 Kit-

Kats. From the house’s perspective, we could improve the game by

charging more per game to have an even larger house advantage

more often, instead of only when the player rolls common numbers

like sevens. Another way we could improve the results of the game is

by having more trials, by increasing the number of trials the

theoretical and experimental numbers would be more precise.