How to roll the best numbers with Dice

Experimenting with the probability of Dice 

Allen Fang

3/13/2034

Abstract:

In this experiment, we are finding the most probable sum to occur when rolling a pair of dice 100 times. The pair of dice can only roll the sum within the range of 2-12 and we are to find what is the most repeated sum that happens, resulting in also finding the number that will occur the most frequently when you want to play a game that requires you to roll a pair of dice. By the end of the experiment, I have fund that seven is the most likely outcome when rolling a pair of dice, but six and eight are also within a good range of being likely to occur while every other number outside that range has a low chance of happening. 

Introduction:

Probability is the math to finding the chance of something to happen. We see it throughout our lives, in games, the chance of us being late to class or even in gambling. Probability is finding the percentage or number in which something will or will not happen, and we can use that information however we want. 

In this experiment, we are rolling a pair of dice 100 times and finding the probability for the sum of the two dices. Doing so, we can answer the question: what’s the most probable sum of the two dices that can occur after 100 rolls? This experiment can be done by using a pair of dice, or using a website that generates the numbers of two rolled dice. By the end of the experiment, I think that seven will be the most likely number to be rolled because of my experience with playing games that requires a pair of dice.

Materials and Methods

• A computer

1. Using a computer, type rolladie.net into google and press enter. 
2. Then scroll down a little bit until you see it say, one dice six sides. 
3. Change the one into two because we will be using two of them for this experiment. 
4. Now below that, you should see it say, Roll one times. 
5. Now, change the one into 100.
6. Then once you have changed the numbers, click go, or you can press the start and stop button, allowing you to generate the numbers yourself. 
7. Once you’ve got your numbers, record it down on a table listing how many times the sums repeat from two through 12.

Results

With the data collected, you can know see the results of what the most common numbers is to occur when rolling a pair of dice.

Sums	Percentage of Sums frequency
2	2%
3	8%
4	5%
5	10%
6	12%
7	22%
8	17%
9	8%
10	8%
11	6%
12	2%

Figure 1 

Figure 2

You can see in both figure 1 and 2 that the chances of rolling a seven with a pair of dice is significantly higher than any other sum that you can roll. The lowest being both two and 12 being rolled twice for both numbers out of 100 times. 

Analysis

After 100 rolls, the sum of seven was rolled the greatest number of times as seen from figure 1 and 2. This means that when you roll a pair of dice, there is a high chance of you getting the sum of seven. This goes with my hypothesis, as I had guessed that seven would be the most likely sum to occur the most. I chose seven because of my experience with playing Catan, a strategy board game requiring a pair of dice to play, but also because there are multiple ways to roll the sum of seven with a pair of dice. The possible combination for the sum of seven are, (5,2),(6,1), and (4,3). This is the greatest number of combinations possible to get a sum of any number, seven having the greater number of combinations. 

In the article, “Weighted Dice: A physical Application for Probability studies” byProfessor Russel W. Kincaid, is a study on probability using normal and biased dice. Biased dice are dice where the outcomes are not equally likely. But when doing this experiment, Kincaid found that the expected outcomes of normal dice and biased dice are different except for the sums of six, seven and eight, where the chances are very similar. As shown in Figure 3, biased dices roll one through five more often than the sums nine through 12. But you can see in figure 3 that the seven has the highest expected outcome theoretically, which is of the normal dice. Since the biased and normal dice outcomes for seven are close to each other, it means that the most likely outcome of any six-sided pair of dice, seven occur most frequently.

Figure 3

Conclusion

After conducting the experiment, seven is most likely to occur when rolling a pair of dice. As stated by my hypothesis, I thought that seven would be the most repeated number, and I was right after conducting the experiment, but not only was seven the most likely, six and eight also had a high percentage of being likely to be repeated. This means that when you roll a pair of dice, you know that there will be a high chance of rolling a sum within the range of six through eight. To further experiment with this, you can use this and find the chances this has in gambling, such as in casinos, street craps, or other sorts of gambling that can be or uses a pair of dice. Therefore, when you’re playing a game that requires a pair of dice, like Catan, plan your strategy well around the numbers you know will occur the most. 

Works Cited

Kincaid, R. W. (2015). Weighted Dice: A Physical Application for Probability Studies.

https://kb.osu.edu/server/api/core/bitstreams/3419030b-e728-5959-86af-5091400a0c1d/content

Appendix

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