ABSTRACT

This experiment delves into the probability of sums which is gotten by rolling two six-sided dice 200 times. Instead of physically rolling two dice 200 times, I programmed a code in order to do this for me. By importing a data package known as random, I used python’s extensive database in order to simulate these 200 rolls, then provide said rolls in a graph-like format. The sum of 7 appeared most frequently which was predicted in other studies as well. The results relatively matched the expectations.

INTRODUCTION

The purpose of this experiment is to observe the result of the sum that occurs when rolling a pair of dice in large quantities. According to Anas Ashraf’s published lab report on the predictability of randomness through a dice case study, there are some sums that are much more likely to appear than others. The number that was observed to appear the most out of the sums was the number 7, for it has the six possible combinations with the limited numbers given on two six-sided dice. The hypothesis for this experiment is that 7 will be the most frequent sum found out of the 200 dice rolled.

MATERIALS

A computer with python installed
A python script in order to emulate the dice rolls
Data analysis tools in order to record and analyze the outcomes of 200 rolls

PROCEDURE

Implement a random number generator using python in order to simulate rolling two six-sided dice. Do this by using the random.randint(1, 6) function which chooses a random integer between 1 and 6 and returns it to the module.
Each roll of two dice was simulated by generating two random numbers (one for each die) and adding them in order to record the sum.
Repeat this process 200 times using a loop, and record the results in a list.
After all 200 rolls, the frequency of each sum ranging from 2-12 was calculated and recorded in a table.

RESULTS

The following table shows the frequency of the sum of the simulated dice rolls listing from 2 to 12, starting at 2 because the lowest sum possible from both dice would be 1 + 1 and the ending at 12 because the highest sum possible from both dice would be 6 + 6.

Simulated Dice Roll Results (200 Rolls)

	Sum	Frequency
1	2	4
2	3	10
3	4	18
4	5	25
5	6	27
6	7	36
7	8	26
8	9	20
9	10	14
10	11	14
11	12	6

**Figure 1: Frequency Distribution of Dice Roll Sums**

ANALYSIS

The number of possibilities by rolling two six-sided dice can be found by calculating all the possible combinations of the two numbers randomly picked from 1-6. We found that the number 7 has the most combinations with the two numbers given from 1-6 which is 6 possible combinations. 1 + 6, 2 + 5, and 3 + 4 all equate to 7, giving us 6 different numbers in which the dice can add up to 7, this results in a 16.67% chance of the sum of the two randomly generated numbers being 7. In contrast to this the sums of 2 and 12 only have a single combination, making the chance of the two numbers equating to said sum to be only 2.78%. The sum of 7 being the most frequent of the 11 possible sums confirms our hypothesis that it is the number with the highest chance of occurrence.

When comparing my experiment with Anas Ashraf’s lab report, “The Predictability of Faux Randomness Through a Dice Case Study” it is pointed out that both experiments resulted in 7 being the most probable outcome when rolling two dice. Anas’ experiment simulated 23,171 trials while my experiment only simulated 200 trials, therefore Anas’ results would be more accurate, however since both experiments resulted in the same outcome being that 7 would have the highest frequency between the two numbers, it is safe to say that theory of probability distribution holds true for the case.

Conclusion

In conclusion, my experiment shows that when rolling two dice, the number 7 is most commonly found when finding the sum of the two random numbers, proving that my hypothesis is also true. Some other experiments that can prove useful in the context of probability of randomness is increasing the sample size and simulating thousands of rolls of dice instead of just hundreds, this would give more accurate data. Another possibility is to create an experiment when using multiple dice instead of only 2. Anas Ashraf’s lab report touches on this topic with the idea stated in the report as, “the sum of any n number of dice (where n is greater than one) has its frequency be that of the binomial distribution wherein the curve looks more ideal as n gets larger.”

With the information provided from this experiment there is a possibility of teaching probability in statistics and other random generation experiments. By using the evidence gained in this lab report, it is also possible to use the information in other avenues like machine-learning (AI), which could help in data analysis.

References

Ashraf, A. (n.d.). pD#l8&K*i+ie4: The Predictability of Faux Randomness Through a Dice Case Study. From the inductive to the rationally deductive. https://techsmith.commons.gc.cuny.edu/lab-report/

The Probability in Dice:Analysis of 200 Dice Rolls