Dice, usually thrown in a pair have a total of thirty six outcomes from (1, 1), (1, 2)… all the way to (6, 6). There are many possible outcomes, but some of them appear more frequent than others. An example would be seven, many numbers add up to seven like a five and two, four and three, six and one, but numbers like two only have one possible outcome and that is a one and a one. The probability of rolling the two die together was tested, and out of one hundred times rolled the percent that a two appeared was indeed lower as it came up only once of the one hundred throws. Whereas the number seven came up twenty-five times out of the hundred throws. These results prove that there are some numbers that have a higher percentage of showing up then others when rolling two dice.
As many people know a normal dice has six sides watch with numbers one through six. Some numbers appear more often than others when two dice are rolled together but alone there should be an even chance that all numbers show up. So why is it that some numbers appear more frequently than others? When rolling the two dice there are a total of thirty six possible combinations, I found this by multiplying the amount of faces on each dice. So in this case there are six faces multiplied by the other six faces of the other dice to get the thirty six combinations. We know that there is an unequal chance that when the dice are rolled, the outcomes are not equal for each of the numbers one though twelve. To find out how great the difference was between the numbers, I tested this by rolling a pair of dice for around a hundred times and recorded the results.
Materials and Methods
To do the experiment, not much was required. Only a pair of dice was needed and a piece of paper to record what came up on which dice and what was the combined total of the two dice. To further improve the accuracy of the test more rolls would be needed. To continue rolling the dice a couple more hundred times was tedious so, I wrote up a program that allowed the computer to roll the dice and record every outcome and every number that came up on each dice. The code can be found here at https://codeboard.io/projects/44714 and can be seen at the back of this report.
Using basic math I was able to find the probability that my results should match as seen in Figure 1. I found the only possible rolls that could equal a number and divided that number to find the probability to base my tests on.
The results after rolling a hundred times are shown in Figure 2.
Using the code I was able to roll the dice ten thousand times, the results are below
After rolling the dice a hundred times by hand the results I had were not that close to the probability that I had originally calculated between the two dice. Although some of the results were very close, like the percent of 12’s and 2’s, the other results like the amount of 8’s should have been lower than the amount of 7’s. By using my program I was able to make the computer roll the dice ten thousand times and the results were more favorable to the probability that should have appeared. The percent of all the outcomes were very close to the ones calculated in Figure 1. The only difference was that the percentage of 2’s that appeared in the ten thousand rolls was .68% off.
The results of both the computer rolled and hand rolled dice both shared a similar trend, which was that the amount of 6’s, 7’s and 8’s had a higher percentage of appearing than the 2’s and 12’s. This trend happens because there are a higher range of numbers that could add up to 6, 7, and 8, then the numbers that could add up to 12 and 2 as seen in Figure 1.
Rolling two dice I was able to find correlation between the frequencies in which a number appears compared to the other numbers that appeared. The numbers that were most likely to appear when rolling two dice would either be a 6, 7, or 8, because there are more numbers that add up to them than the others. Numbers that were the least frequent were the 2’s and 12’s because only rolling a ( 1,1) could get a 2 and only rolling (6.6) would get you a 12. Using the results from the experiments we can conclude that there are different percentages in which a number would appear; and there is not an even probability when rolling two dice.
Edkins, J. (n.d.). Throwing dice – theory. Retrieved March 19, 2017, from http://gwydir.demon.co.uk/jo/probability/calcdice.htm
Ramsey, T. (n.d.). Rolling Two Dice. Retrieved March 19, 2017, from http://www.math.hawaii.edu/~ramsey/Probability/TwoDice.html