1. Team I

2. The 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.

3. Probability of Sum
Sum
Number of Kit Kats
Won
1/36
2
10
2/36
3
7
3/36
4
5
4/36
5
3
5/36
6
1
6/36
7
0
5/36
8
1
4/36
9
3
3/36
10
5
2/36
11
7
1/36
12
10
Expected Value/Mean of Theoretical Outcomes- 3.11 Kit Kats
Standard Deviation of Theoretical Outcomes- 3.06

4. 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
Expected Value of Winnings- 3.12
Standard Deviation- 2.67

5. Trial #
# Kit
Kats
Trial #
# Kit
Kats
Trial #
# Kit
Kats
Trial #
# Kit
Kats
1
1
16
5
31
10
46
3
2
3
17
5
32
3
47
1
3
5
18
0
33
3
48
1
4
1
19
3
34
1
49
10
5
7
20
3
35
0
50
3
6
1
21
0
36
1
7
5
22
1
37
10
8
5
23
3
38
5
9
1
24
5
39
0
10
3
25
0
40
1
11
7
26
3
41
10
12
0
27
0
42
5
13
5
28
1
43
3
14
3
29
1
44
7
15
1
30
1
45
5

6. 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.