Calling all gamblers : The study of probability through dice

Kamar Ledgister

Professor Adam Bubrow

Writing for Engineering

October 30, 2018

 

 

 

 

 

 

 

 

Abstract

In this study we examined the rolling of a pair of dice and we analyzed the dice probability outcome over the number of rolls. The results were collected from rolling a pair dice at least 100 times to determine occurrence odds of the dice. The data that accumulate determine dice probability odds and how frequently you predict an outcome.

Introduction

The dice probability experiment was studied by rolling a pair of dice, a small cube object with each side having a different number of spots on it, ranging from one to six. Dice is arguably one of oldest gambling games that is still in existence today, which involve chances, or, as referred here, probability. The main purpose of this experiment is to determine the probability of the dice when it is rolled and to determine how often each result occurs over the course of one hundred rolls. Reducing the number of times a pair of dice is rolled will result in the odds of rolling a seven are higher with fewer rolls attempts will increase chance of predicting a better outcome. This is because the more times the pair of dice is rolled the lower the probability will become of rolling any combination.

Materials

• Pair of dice
• Wooden surface

Methods

1. Put a pair of dice in your hand and gently shake your hand while moving in a forward motion.
2. Stretch your hand out in a vertical position and then release the dice on wooden surface.
3. Record the result from the pair of dice.
4. Repeat steps 1-3 100 times and record the results of each roll.
5. The researcher did not weigh the pair of dice.

Results

During the accumulation  of data  the study revealed that when the pair of dice were rolled they landed face up. The dice probability odds outcome become lower between 2,3, 4, 6, 11 and 12. While on the other hand dice probability outcome become higher  between 5,7,8, 9 and 10.

Table 1. The dice probability result data

Number of Counts	Probability of Dice
2	3
3	5
4	4
5	18
6	3
7	17
8	17
9	11
10	7
11	3
12	3

 

 

 

 

 

 

Figure 1. Data of the dice probability when plotted.

Analysis

In this experiment we studied the dice probability to determine occurrence. A two was rolled 3 times out of 100 attempts, a three was rolled 5 times out of 100 attempt, a four was rolled 4 times out of 100 attempts, a five was rolled 18 times out of 100 attempts, a six was rolled 3 times out of 100 attempts, a seven was rolled 17 times out of 100 attempts, a eight was rolled 17 times out of 100 attempts, a nine was rolled 11 times out of 100 attempts, a ten was rolled 7 times out of 100 attempts, a eleven was rolled 3 times out of 100 attempts and a twelve was rolled 3 times out of 100 attempts . These data illustrate that odds of rolling between 2-4 and 11-12 are lower than odds of rolling 5 or 7 through 10. Rolling a 6 is a lower probability.

Dice probability yields better chance of rolling a 5 or 7 through 10. According to similar dice probability studies conducted by C. Foster and D. Martin, when the data were compared with a previous experiment, there were similarities in both data sets. 2-4 and 10-12 had lower probability. While on the other hand from 5-9 dice probability odds are higher at that time period. Foster and Martin’s study supported the present experiment. There data in the article has similar result

There could have been some contributing factors of error by following: inefficiency space to rolled the pair of dice on the wooden surface and collision of dice in midair could have change the outcome of the dice.

Conclusion

In this experiment, we demonstrate that dice probability odd occur best during 5, 7-10. While on the other hand the dice probability odds are worst between 2-4, 6, 11 and 12. Reducing the number of times a pair of dice is rolled will result in the odds of rolling a seven are higher with fewer rolls attempts will increase chance of predicting a better outcome. This is because the more times the pair of dice is rolled the lower the probability will become of rolling any combination When the dice were rolled ten more times, a 5 and an 8 were rolled twice each and a 7 was rolled thrice. This showcase that if I was recommend individual to gamble the best outcome is to choose number between seven through ten.

Appendix 1. Dice Probability data result.

Roll	Black	Yellow	Total	Black Percentage	Yellow Percentage
1	3	2	5	60%	40%
2	1	4	5	20%	80%
3	2	2	4	50%	50%
4	5	2	7	71.4%	28.6%
5	3	3	6	50%	50%
6	1	4	5	20%	80%
7	4	4	8	50%	50%
8	2	6	8	25%	75%
9	4	4	8	50%	50%
10	6	5	11	54.5%	45.5%
11	5	3	8	62.5%	37.5%
12	1	6	7	14.3%	85.7%
13	5	6	11	45.5%	54.5%
14	1	3	4	25%	75%
15	6	6	12	50%	50%
16	2	3	5	40%	60%
17	2	3	5	40%	60%
18	1	1	2	50%	50%
19	2	5	7	28.6%	71.4%
20	6	4	10	60%	40%
21	4	3	7	57.1%	42.9%
22	2	6	8	25%	75%
23	2	1	3	66.7%	33.3%
24	5	4	9	55.6%	44.4%
25	4	1	5	80%	20%
26	6	3	9	66.7%	33.3%
27	1	2	3	33.3%	66.7%
28	3	6	9	33.3%	66.7%
29	4	4	8	50%	50%
30	1	6	7	14.3%	85.7
31	3	6	9	33.3%	66.7%
32	2	2	4	50%	50%
33	2	4	6	33.3%	66.7%
34	6	1	7	85.7%	14.3%
35	1	6	7	14.3%	85.7%
36	6	3	9	66.7%	33.3%
37	2	6	8	25%	75%
38	3	3	6	50%	50%
39	1	1	2	50%	50%
40	3	1	4	75%	25%
41	3	3	6	50%	50%
42	5	4	9	55.6%	45.4%
43	3	4	7	42.9%	57.1%
44	2	4	6	33.3%	66.7%
45	1	4	5	20%	80%
46	1	6	7	14.3%	85.7%
47	6	2	8	75%	25%
48	5	5	10	50%	50%
49	5	5	10	50%	50%
50	5	5	10	50%	50%
51	4	3	7	57.1%	42.9%
52	4	1	5	80%	20%
53	2	4	6	33.3%	66.7%
54	4	2	6	66.7%	33.3%
55	4	5	9	44.4%	55.6%
56	4	4	8	50%	50%
57	3	2	5	60%	40%
58	4	3	7	57.1%	42.9%
59	3	2	5	60%	40%
60	2	4	6	33.3%	66.7%
61	6	4	10	60%	40%
62	5	4	9	55.6%	44.4%
63	6	6	12	50%	50%
64	3	6	9	33.3%	66.7%
65	2	1	3	66.7	33.3
66	1	4	5	20%	80%
67	1	1	2	50%	50%
68	3	4	7	42.9%	57.1%
69	1	2	3	33.3%	66.7%
70	4	5	9	44.4%	55.6%
71	6	2	8	75%	25%
72	4	4	8	50%	50%
73	1	4	5	20%	80%
74	3	2	5	60%	40%
75	4	4	8	50%	50%
76	4	4	8	50%	50%
77	5	5	10	50%	50%
78	6	6	12	50%	50%
79	1	5	6	16.7%	83.3%
80	6	2	8	75%	25%
81	1	4	5	20%	80%
82	2	6	8	25%	75%
83	1	4	5	20%	80%
84	5	2	7	71.4%	28.6%
85	1	4	5	20%	80%
86	1	6	7	14.3%	85.7%
87	2	5	7	28.6%	71.4%
88	4	4	8	50%	50%
89	3	2	5	60%	40%
90	6	5	11	54.5%	45.5%
91	2	4	6	33.3%	66.7%
92	6	1	7	85.7	14.3%
93	2	6	8	25%	75%
94	1	6	7	14.3%	85.7%
95	6	4	10	60%	40%
96	3	6	9	33.3%	66.7%
97	1	5	6	20%	80%
98	1	2	3	33.3%	66.7%
99	1	4	5	20%	80%
100	5	1	6	83.3%	16.7%

 

 

 

References

Dice.(n.d). Merriam- Website Collegiate Dictionary online. Retrieved

from https://www.merriam-webster.com/dictionary/dice.

Foster, C., & Martin, D. (2016). Two-dice horse race. Teaching Statistics, 38(3), 98–101.

https://doi-org.ccny-proxy1.libr.ccny.cuny.edu/10.1111/test.12108