Seven Gets the Job Done:
Evaluating the Most Frequent Outcome While Dice Rolling
Abstract:
A dice is a small cube with dots representing numbers on each side. It is used for gambling and to demonstrate probability. However, many individuals wonder which number to gamble on. This experiment examined the possible outcomes when rolling a pair of dice. The pair of dice has eleven possible outcomes which are two to twelve. The experiment includes two dice to roll 100 times and scrap paper to record the outcomes. The individual will roll the dice 100 times and record the outcome they received each time. Results showed that the outcome of seven occurred the most. It occured 24 times out of the 100. While the other outcomes ranged from four to eleven times each. This result is due to the sum of seven having the most possible combinations within the two dice. Seven has six possible combinations (1/6), (6/1), (2/5), (5/2), (3/4), and (4/3). Overall, the sum of seven occurs the most when rolling a pair of dice 100 times.
Introduction:
A die is a small cube with different numbers of spots on each side. The dots on each side range from one to six. Dice are considered the oldest gambling device, they have been around since 5000 BC. They are also used to teach probability. The outcomes for a pair of dice range from two to twelve. The outcomes are unequal due to there being more possibilities for one outcome than another. For example, the only possibility for the outcome of two is if both dice roll on one while there are four possibility for the outcome of ten. The outcome for two and twelve includes two possibilities. The outcome for three and eleven includes two possibilities. The outcome for four and ten includes three possibilities. The outcome for five and nine includes four possibilities. The outcome for six and eight includes five possibilities while the outcome of seven has six possibilities. This report discusses an experiment to study the most probable outcome in rolling a pair of dice. We will roll a pair of dice 100 times and determine the most frequent outcome. My hypothesis is that the outcome of seven will be the most frequent since the outcome has the most possibilities. The number seven can be created when rolling (1/6), (6/1), (2/5), (5/2), (3/4), and (4/3).
Materials:
- Two Dice
- One pen or pencil
- Scrap paper(s)
Method:
- Take the pair of dice in your hand
- Shake the dice for as long as you desire
- Throw the dice on the table or surface
- Read the numbers on each die and add them together for the outcome
- Record the outcome of the dice, including the number for each die (Example: 6 (1/5) ), on the scrap paper
- Repeat steps one through four 100 times
- Observe which number repeats the most
Results:
Seven was the most frequent outcome when rolling the pair of dice 100 times. See Figure 1 to see the frequency in the possible out comes. Based on the figure, the outcomes were rolled on a range of 4 to 24 times each. Two was rolled the lowest amount times, four times, and seven was rolled the most amount times, 24 times. The outcomes of ten and six were the second most frequent, both rolled 11 times.
Figure 1: The number of times each of the possible outcomes were rolled during the experiment.
Figure 2 is another way to demonstrate the values of the outcome. The pie graph represents the percentage of rolls for each outcome. The outcome of seven has the biggest part of the pie chart. Based on the pie chart, 24% of the times I rolled the pair of dice, I landed with a combination of seven. While only 4% of the time I rolled the pair of dice, I landed with a combination of two.
Figure 2: The percentage of times each of the possible outcomes were rolled during the experiment.
Analysis:
The number seven was rolled 24 out of the 100 times I rolled a pair of dice. Therefore, it was concluded that seven is the most frequent and most probable outcome. This was due to seven having the most combinations within the pair of dice. Table 1 in the appendix demonstrates all the possible combinations within the pair of dice and it is clear that the number seven has the most combinations. These results support my hypothesis that the outcome of seven would be rolled the most.
These findings were also concluded from a study by Colin Foster and David Martin from the University of Nottingham School of Education in Nottingham, England. They analyzed the “two-dice horse race” which was taught to students of the age 12 to 13. The “two-dice horse race” was “to throw two ordinary dice and add the scores to determine which horse (numbered 1 to 12) would move forward one space. The process was repeated until one of the horses had crossed the finishing line” (Foster & Martin, 2016). After completing the experiment they discovered that horse seven won the race. This was due to the number of combinations that would result in the sum of seven. Their findings matched the results of my experiment.
There is no deviation because the single measurement did not differ from a fixed value such as the mean. If you find the mean of all the possible outcomes you would discover the mean is seven. This is because 2+3+4+5+6+7+8+9+10+11+12= 77 and when you divide 77 by the 11 possible outcome you are given the value of 7. Therefore there is no deviation since the single measurement from my experience matches the fixed value both equaling 7.
Conclusion:
In conclusion, the experiment of rolling the pair of dice 100 times allows us to visually see the possibilities of each outcome and allows us to determine which outcome is the most probable. After completing the experiment, I was able to determine that my hypothesis match the findings of the results. I was able to conclude that seven occurred the most due to there being more combinations for the sum of seven. I was able to determine that the total seven is the most probable and the most frequent outcome.
References:
Foster, Colin, & Martin, David. (2016). Two-Dice Horse Race. Teaching Statistics: An International Journal for Teachers, 38(3), 98-101.
Appendix:
Table 1: Results of the 100 Rolls
| Roll Number | Outcome | Roll Number | Outcome | Roll Number | Outcome | Roll Number | Outcome |
| 1 | 7(4/3) | 26 | 10(6/4) | 51 | 7(4/3) | 76 | 10(5/5) |
| 2 | 5(1/4) | 27 | 9(5/4) | 52 | 9(5/4) | 77 | 5(4/1) |
| 3 | 8(4/4) | 28 | 8(5/3) | 53 | 6(4/2) | 78 | 6(2/4) |
| 4 | 4(3/1) | 29 | 11(6/5) | 54 | 4(3/1) | 79 | 6(1/5) |
| 5 | 7(5/2) | 30 | 7(2/5) | 55 | 7(2/5) | 80 | 10(6/4) |
| 6 | 10(4/6) | 31 | 4(1/3) | 56 | 9(3/6) | 81 | 4(3/1) |
| 7 | 7(3/4) | 32 | 7(1/6) | 57 | 12(6/6) | 82 | 2(1/1) |
| 8 | 6(4/2) | 33 | 10(5/5) | 58 | 11(5/6) | 83 | 5(1/4) |
| 9 | 5(1/4) | 34 | 12(6/6) | 59 | 3(1/2) | 84 | 3(2/1) |
| 10 | 7(1/6) | 35 | 8(6/2) | 60 | 7(6/1) | 85 | 8(3/5) |
| 11 | 4(2/2) | 36 | 5(2/3) | 61 | 7(1/6) | 86 | 10(4/6) |
| 12 | 6(2/4) | 37 | 7(3/4) | 62 | 5(3/2) | 87 | 7(3/4) |
| 13 | 5(2/3) | 38 | 3(1/2) | 63 | 5(1/4) | 88 | 8(5/3) |
| 14 | 6(5/1) | 39 | 12(6/6) | 64 | 2(1/1) | 89 | 3(2/1) |
| 15 | 10(4/6) | 40 | 8(4/4) | 65 | 2(1/1) | 90 | 9(4/5) |
| 16 | 8(3/5) | 41 | 10(5/5) | 66 | 6(4/2) | 91 | 12(6/6) |
| 17 | 7(3/4) | 42 | 8(2/6) | 67 | 4(3/1) | 92 | 7(6/1) |
| 18 | 9(4/5) | 43 | 6(1/5) | 68 | 12(6/6) | 93 | 10(4/6) |
| 19 | 6(2/4) | 44 | 2(1/1) | 69 | 7(5/2) | 94 | 7(1/6) |
| 20 | 4(1/3) | 45 | 7(6/1) | 70 | 11(6/5) | 95 | 10(6/4) |
| 21 | 7(3/4) | 46 | 3(1/2) | 71 | 7(1/6) | 96 | 7(6/1) |
| 22 | 6(4/2) | 47 | 5(1/4) | 72 | 9(5/4) | 97 | 5(2/3) |
| 23 | 9(5/4) | 48 | 9(3/6) | 73 | 10(6/4) | 98 | 7(1/6) |
| 24 | 11(6/5) | 49 | 7(2/5) | 74 | 9(6/3) | 99 | 7(1/6) |
| 25 | 6(3/3) | 50 | 11(6/5) | 75 | 7(2/5) | 100 | 12(6/6) |
Table 2: Frequency of Each Outcome
| outcome | number of times |
| 2 | 4 |
| 3 | 5 |
| 4 | 7 |
| 5 | 10 |
| 6 | 11 |
| 7 | 24 |
| 8 | 8 |
| 9 | 9 |
| 10 | 11 |
| 11 | 5 |
| 12 | 6 |
