Rolling a pair of dice 100 times

What is the truth behind it?

Abstract:

In this report we are rolling a pair of dice 100 times. We want to see the probability of each number being rolled, ranging from 1-12. My hypothesis was that the numbers in the middle of 1 and 12 would be rolled the most. This hypothesis was proven right because the numbers 5, 6, and 7 were rolled the most with 5 being rolled 17 times making it the most amount rolled.

Writing for Engineering

          Ryan Zaman

  10/7/24

Introduction:

Rolling dice is a very interesting topic primarily because of the percentage of getting an outcome. If a person were to roll 2 dice at the same time, the highest number that could be rolled is 12 and the lowest is 2. A 1 can not be rolled because it is impossible for two dice to roll a 1. The goal of this dice roll experiment is to determine which combination of the two rolls will have the highest chance of being rolled when being rolled 100 times. My hypothesis is that the numbers that will be rolled the most are somewhere between 5-9. 

Materials:  

• 2 dice
• A computer (google docs)

Methods:

1. I get my pair of dice from my monopoly game set.
2. I boot up my pc and open google docs
3. I make a table set with 100 columns and 2 rows. I name the first row “times rolled” and the second row “Total of from the outcome”.
4. Roll the pair of dice 100 times to get results.
5. I add up all the times a number has been rolled and compare it to my hypothesis.

Results:

After tallying the results, the numbers that have been shown to be rolled the most are the middle numbers. From numbers 5-7 the numbers were shown the most, 5 being shown the most out of all of them with it being rolled 17 times.

Figure 1: Table graph

Number	Amount of times rolled
1	0
2	2
3	6
4	9
5	17
6	15
7	13
8	11
9	11
10	7
11	6
12	3

Figure 2

Analysis:

As my hypothesis stated, I believed that when rolling a pair of dice 100 times the most amount of numbers rolled would be the numbers in the middle of 1 and 12. After counting the data, the numbers that have been demonstrated to be rolled the most are the middle numbers. The numbers that were displayed the most were 5-7, with 5 being seen the most (17 rolls) of any number. This data proves my hypothesis to be right because 5 through 7 are in the center of 1 and 12.

In another dice roll study I stumbled upon, I have found the results to be rather similar to mine. For example, in the article, “Roll the Dice: A fun probability experiment for all ages” by Kyle Mclyntre, his students roll the dice multiple times to try and get results. For example, in the 100 roll test, 5 and 9 were the most prominent (Mclyntre 2022). Another test where the students rolled 1000 times, the most rolled number was 7 (Mclyntre 2022). This is similar to my hypothesis because I said that a number within the middle range would be rolled the most.

Conclusion:

In conclusion, according to my theory, the numbers in the center of 1 and 12 would be rolled the most often when two dice were thrown 100 times. The numbers that have been shown to be rolled the most frequently are the intermediate numbers after the data has been counted. The most often shown numbers were 5-7, with 5 being shown the most (17 rolls) out of all the numbers. This information validates my theory because 5 through 7 are located in the middle of 1 and 12.

Further Experiments: 

• Rolling a dice 1000 times
• Rolling a dice 50 times
• Rolling a single dice

What can be done with this info:

Someone who is into  gambling could possibly use this information to win money. As long as they choose a number within the middle range, the person has a higher chance of winning.

Works cited:

Mclyntre, K.M., 2022, “Roll the Dice: A fun probability experiment for all ages”, https://medium.com/@kylejmcintyre/roll-the-dice-a-fun-probability-experiment-for-all-ages-c949727ffd1b

Complete data set:

Times rolled	Total from the outcome
1	6
2	3
3	3
4	5
5	8
6	11
7	6
8	6
9	9
10	9
11	5
12	7
13	6
14	11
15	2
16	6
17	6
18	3
19	8

20	10
21	7
22	4
23	11
24	6
25	5
26	5
27	5
28	7
29	10
30	10
31	8
32	9
33	6
34	7
35	7
36	9
37	4
38	8
39	5

40	10
41	6
42	10
43	9
44	9
45	9
46	5
47	5
48	2
49	5
50	4
51	8
52	9
53	11
54	8
55	6
56	7
57	9
58	5
59	4

60	9
61	8
62	5
63	6
64	11
65	7
66	6
67	10
68	5
69	8
70	4
71	6
72	3
73	5
74	7
75	12
76	5
77	7
78	8
79	3

80	12
81	4
82	7
83	6
84	8
85	5
86	9
87	7
88	7
89	4
90	4
91	5
92	5
93	7
94	3
95	11
96	8
97	10
98	12
99	4

100

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