The Magical Seven: 

Probability of the Most Frequent Sum of Dice

Name: Tamim Uddin

Date: 10/28/2023

Instructor: Adam Bubrow

 Abstract 

Probability is crucial in our day-to-day lives. From sports to work, schools to communications, we experience the use of probability everywhere. Likewise, we’re analyzing the outcome probability of the most frequent dice in our experiments. Firstly, we rolled a pair of dice multiple times, 100 times, and then we recorded the data in a Google Spreadsheet. Lastly, we recorded the sum of the dice using codes in a Google Sheet. My initial hypothesis is that the highest possible sum of both dice is ‘twelve, because this is the maximum number it could possibly roll. In addition, I also hypothesized that the number seven would be the highest probable sum of dice. After all, through my experiment, I got the highest possible sum of seven’.

Introduction

Dice is usually a popular toy material that has been used as an indoor game, yet nowadays it’s being used in thousands of other ways, including experiments. In our experiment, we’re rolling two dice and recording their outcomes in Google Sheets. Then, we added and recorded their sum in our data table. Lastly, we looked for the most common sum number among the data. Then, we compared and analyzed our experiment with a peer-reviewed experiment in the CCNY library database, which also focused on dice probability.

Materials: 

1. A laptop with an internet connection.
2. Google dice roller.
3. Google sheet, or Microsoft Excel.
4. Microsoft word, or google docs.

Methods: 

1. In a google dice roller, we rolled a pair of die100 times.
2. In a google spreadsheet, I recorded the data.
3. Using, the code found the sum of both die: First, select the range of cells that you want to sum. Then, click the “Auto Sum” button in the toolbar.
4. Then,  I figured out the most frequent sum among dice, using the following code code.

Results

The frequency of dice rolling that has the most appearing sum of both die.

Dice Roll Table Table: Sum that Appears the Most

Dice number	Most appearing number
2	4
3	5
4	7
5	11
6	14
7	17
8	15

9	12
10	7
11	6
12	2

Figure 1: most appearing sum value

Graph of most Appearing Sum of Dice.

figure2: table graph of the dice probability.

Analysis

Through our deep analysis of the following experiment, it’s obvious that there’s a really big reference among the probability of the sum of both dies, and the above graph is a clear representation of that statement. My initial hypothesis was that the highest possible sum of both dice is ‘twelve’ because this is the maximum number of times it could possibly roll. In addition, I also hypothesized that the number seven would be the highest probable sum of dice. After all, through my experiment, in the above lab data, it’s shown that the highest frequent sum of this rolling probability is ‘seven’. The following hypothesis is also being supported by the Gaming Research and Review journal “The Probability Distribution of the Sum of Several Dice: Slot Applications” committed by Singh, Ashok K.; Dalpatadu, Rohan J.; Lucas, Anthony F. According to their research of the sum of three dice, “

Table 1: Probability distribution of the sum of dice

x	2	3	4	5	6	7	8	9	10	11	12
f(x)	1/36	2/36	3/36	4/36	5/36	6/36	5/36	4/36	3/36	2/36	1/36

.” Through this data table, we can clearly see that the seven is the highest probable sum of the following research which is 6/36. The above experiment has matched with my hypothesis as well. 

Conclusion

In conclusion, it’s clear that the probabilities of multiple sums of multiple dice were determined. Also, I was able to determine the highest probable sum of both dice. Hence, these possibilities may lead us to guess or determine the probability of many other things. However, it could be winning a chess game, winning a large amount of money in the stock market, and many more. Furthermore, the review journal “The Probability Distribution of the Sum of Several Dice: Slot Applications” also gives us some insights into how mathematical calculations might be used in terms of determining the probability of any outcomes. For this reason, it will be much easier, and the probable outcome will be much more precise and accurate, if we have the necessary mathematical formulas for calculations. Thus, this method might give us ideas for using it in broader fields, and with the help of scientists and mathematicians, we will be able to determine a much more accurate way of finding a more precise probability of many things. Therefore, it will be so soulful and play a great role in every other necessary field, such as sports, medicine, STEM, agriculture, and many other fields.

Reference: 

Singh, A. K., Dalpatadu, R. J., & Lucas, A. F. (2011). The Probability Distribution of the Sum of Several Dice: Slot Applications. UNLV Gaming Research & Review Journal, 15(2), 109–118.