Unveiling Chance:

A Statistical Analysis of Dice Rolls

Writing for Engineering

Al Narcida

March 8^th, 2024

Abstract:

         In this lab report, a digital simulation of rolling 2 die is simulated 100 times and the results are recorded. In this experiment, the possible outcomes range from a sum of 2-12. The most frequent sums that occurred were from 5-9. However, the outcome of 7 was the most frequent out of the 5-9 range and there was an outlier of 11 having a large frequency as well.

Introduction:

            To increase your chances of winning money in casinos or board games, it’s important to understand how to roll a lucky seven. Whether you’re playing with dice in a casino or at home, knowing the odds helps you decide how much to bet. Probability is important because it helps us figure out which numbers are likely to show up when we roll dice. Since there are 12 possible outcomes when rolling a pair of dice, rolling a seven is the most likely since seven has the most possible combinations, as shown in figures 1 and 2.

Fig. 1  – Combinations for each sum

Fig. 2 – Combinations for each sum, Visualized (Probability: Dice, n.d.)

Materials:

• Dice Rolling Simulator: https://rolladie.net/#!numbers=2&high=6&length=1&sets=&addfilters=&last_roll_only=false&totals_only=true
• Data Sheet
• Pen

Method:

1. Open online dice rolling simulator.
2. Simulate rolling two, six-sided die.
3. Record the outcome of the trial.
4. Repeat steps two and three until you have reached 100 trials.

Results:

            After the 100 trials of rolling two, six-sided die, and recording the outcomes the results are shown in figure 3. Given the trials, the most frequent outcomes were from the range of 5-9. The least amount of outcomes were from 2-3 and, 10 and 12, although there was an outlier of 11.

Fig 3 – Frequency of Sums 

Analysis:

The frequency distribution of the sum of two dice rolls exhibits characteristics that deviate from the expected uniform distribution. The most frequent outcomes occur in the range of 5 to 9, with the highest frequency being 17 occurrences for a sum of 7, which similar to my hypotheses since the outcome of 7 has the most combinations. This clustering of frequencies around the middle range suggests that combinations leading to sums in this range are more probable than those leading to smaller or larger sums.

The least frequent outcomes occur in the range of 10 to 12. Notably, there is an outlier of 11, with 12 occurrences, while the expected frequency based on a uniform distribution would be higher. This outlier indicates a deviation from the expected pattern and warrants further investigation.

Conclusion:

            In conclusion, the experiment demonstrates that the frequency distribution of rolling two six-sided dice does not perfectly align with the theoretical uniform distribution. The most frequent outcomes occur in the range of 5 to 9 with the most frequent outcome being 7 like stated in my hypotheses, while the least frequent outcomes occur in the range of 10 to 12, with an outlier of 11 having a large frequency. Further experiments and analysis are necessary to determine the underlying factors contributing to these deviations and to refine our understanding of probability in dice rolling scenarios. Therefore, when there are high stakes, playing a game that involves rolling dice, you now know what to choose.

Work Cited:

• Probability: Dice. (n.d.). https://www.pdx.edu/learning-center/sites/learningcenter.web.wdt.pdx.edu/files/2020-07/Probability_Dice.pdf

Appendix:
Table of results:

Dice Rolls
Trial	Outcome of Roll
1	9
2	5
3	5
4	7
5	11
6	4
7	7
8	7
9	11
10	5
11	11
12	10
13	8
14	4
15	11
16	10
17	9
18	7
19	12
20	10
21	7
22	11
23	8
24	4
25	6
26	7
27	11
28	3
29	6
30	6
31	5
32	4
33	4
34	10
35	6
36	9
37	7
38	3
39	6
40	9
41	7
42	7
43	9
44	6
45	5
46	5
47	10
48	9
49	7
50	12
51	11
52	9
53	6
54	9
55	7
56	9
57	9
58	10
59	7
60	5
61	8
62	10
63	9
64	11
65	6
66	5
67	11
68	5
69	4
70	6
71	8
72	8
73	6
74	9
75	11
76	8
77	11
78	7
79	5
80	7
81	5
82	12
83	5
84	11
85	2
86	7
87	9
88	6
89	2
90	10
91	3
92	5
93	2
94	9
95	5
96	4
97	7
98	8
99	7
100	8