Dice in Action:

A lab report on Dice rolling probability

Shah Akther

10/7/2024

Abstract: This dice probability experiment looks into the odds of rolling two six-sided dice 100 times while closely paying attention to how frequently a number appears as the sum. To find out how many times a number appears between two and twelve, a controlled experiment was done. After experimenting, the sum of 7 showed up more often than any other, supporting my hypothesis. On the other hand, 12 was the most rare number. The result of this experiment was analyzed and contrasted with previous scholarly articles on similar experiments to have a better understanding of the principle of probability on dice rolling.

Introduction: In many games, the simple act of rolling a dice has captured me for years rolling a dice and crossing my fingers using all the strategies I know in the world to win a game that is solely based on luck. In other words, while playing a game we often struggle to decide whether we should take a risk to continue to play or drop out, knowing the probability of getting that number can help us immensely. This dice-rolling experiment is to see how often a number will occur while rolling the two dice 100 times. Where the sum of  7 should appear more often because more numbers add up to the sum of 7 than any other number on the other hand 2 and 12 should be the numbers that least appear as only two sides can add up to those numbers.

Materials:

• A pair of dice
• A pen or pencil
• A datasheet
• A calculator 

Methods: To experiment seamlessly you need to prepare a pair of dice and prepare a datasheet with two columns, use the first column to record the number of times you roll the dice and the second column for the sum of the two dice. And start recording data after each roll. When you reach 100 make a second table table with two columns to record which number appears how many times. For visual learners a graph is really helpful, in my case I used a spreadsheet.

Results:

chart

Sum of the pair of Dice	Number of outcomes
2	7
3	9
4	7
5	9
6	9
7	14
8	13
9	10
10	11
11	7
12	4

Fig. 1 – This chart displays the number of turnouts for each sum that was recorded by rolling the dice.

Bar graph 

Fig. 2 – This bar graph displays the number of turnouts for each sum that was recorded by rolling the dice.

Analysis: The data gathered from the experiment, which involved rolling the two six-sided dice 100 times, confirmed the theory of rolling the number 7 more frequently than any other number. One of the most frequent results is the sum of 7 which had the maximum number of possible outcomes with 14 combinations. The sum of 6 and 8 follows closely with the outcome of 9 and 13 meaning this result is concentrated in the middle. While I was expecting to find 2 and 6 to appear the least amount of times, 6 was the only number that didn’t appear as frequently. The sum of two appeared a total of 7 times while the sum of 12 appeared a total of 4 times. 

There was a similar study done to figure out the probability of a three-dice. Where they rolled three dice instead of two and compared the data to see the frequency. They also conducted the dice-rolling process 5000 times instead of 100 times to get more accurate results. In this experiment, they used technology to create their unique data. Originally I thought the results would be the same as rolling two dice but I was surprised to see how much the data differed from each other. According to Lukaac Stanislav’s article on Investigation of Probability Distributions Using Dice Rolling Simulation the outcomes of the sum of 7 was only 345 and the number that had the highest frequency was 10 with 692 outcomes. And the sum of 3 and 18 had a frequency of 11 and 23. 

Conclusion: The idea of rolling the two six-sided dice the sum of 7 would appear more frequently than any other other sum has been confirmed by the dice rolling probability experiment. In this case, the sum of 7 appeared 14 different times within 100 rolls because there are more possible combinations than any other numbers. In comparison to the highest frequency 12 appeared only 4 times within 100 rolls. A significant amount of changes was notable in probability distributions while comparing the results with three dice, indicating how the number of dice can affect the outcome. To further develop our understanding of dice rolling probability it is a good idea to use different amounts of dice and alter the number of rolls as well. The information gathered from this experiment can be used in the world out there giving us a better understanding of statistics and probability when we are in a decision-making situation or gaming.

References: 

Lukac, S., & Engel, R. (2010). Investigation of Probability Distributions Using Dice Rolling Simulation. Australian Mathematics Teacher, 66(2), 30–35.

Appendix:

1	3
2	9
3	10
4	11
5	6
6	3
7	2
8	7
9	10
10	3
11	4
12	8
13	10
14	6
15	5
16	9
17	7
18	7
19	2
20	5

21	10
22	6
23	10
24	5
25	11
26	8
27	10
28	7
29	10
30	8
31	11
32	12
33	4
34	6
35	5
36	5
37	2
38	8
39	3
40	11

41	6
42	6
43	2
44	6
45	8
46	2
47	11
48	5
49	3
50	7
51	9
52	7
53	10
54	2
55	12
56	10
57	7
58	9
59	4
60	10

61	7
62	7
63	8
64	8
65	7
66	9
67	7
68	9
69	3
70	4
71	9
72	6
73	5
74	7
75	11
76	8
77	9
78	12
79	8
80	10

81	2
82	8
83	4
84	9
85	5
86	5
87	3
88	7
89	4
90	8
91	3
92	7
93	6
94	4
95	8
96	9
97	3
98	8
99	11
100	12