What Should You bet On:
Simple Probability of Rolling Dice
This paper explains the simple probability of the addition of two dice. The expected result of this experiment would be that the number seven would be the most common product of the two dice. The results were not as expected as the number seven was actually second to the number six
Ethan Angress
3/21/19
Rolling dice is one of the most common forms of gambling and used heavily in board games. Dice were first portrayed in hieroglyphics of the Ancient Egyptians. They believed that the cast of dice was controlled by the gods and was used as signs from them. Dice were also believed to be used for game as a soon as their arrival. In today’s society, dice are mainly used in games, gambling, and teaching practices. It is imperative to understand the probability of the outcomes of rolling a dice when there is gambling or competition involved. Through simple probability calculations, if a dice is rolled 100 times, the number 7 should appear most frequently at 16.7%.
In order to test this probability, a dice should be rolled 100 times and recorded after each roll. Due to the absence of dice, a random dice number generator was used in order to obtain results for the trials. All that is needed for this experiment is a computer capable of accessing the internet. The site RANDOM.ORG was used to generate these numbers due to their unique system of generating the random numbers. This generator used atmospheric noise to generate random numbers, in which the site claims, “is better than the pseudo-random number algorithms typically used in computer programs.” RANDOM.ORG describes this process as , “There is now a distributed configuration in which a number of nodes in different geographic locations generate randomness, subject it to statistical tests and then stream the distilled random bits to a cloud hosting service from which the RANDOM.ORG services run.” This system is what created the numbers used in the experiment.
To conduct the experiment, first go to RANDOM.ORG and click on go to the two dice generator. Next click the roll button to start the generator. Record the numbers that appear on the dice and record it in a chart or table. Then repeat by clicking the roll button again for 100 trials.
After conducting the experiment, the product of 6 was the most frequently appearing number at 22 % followed by 7 at 20%. The data resembles a bell curve in which two and twelve are the low points with six and seven as the high points. The highest percentage that a product occurred was 22 times as 6 while the lowest was 3 occurring only 3 times.
This table shows the results of the experiment with the product of the two dice on the left and the occurrences on the left.
Bar graph of results of the experiment. Demonstrates the bell curve like shape that the data exhibits.
The relationship with the bell curve that the data exhibits shows that there is a clear correlation between the probability of a number occurring with it actually occurring. This makes sense since the farther that number gets from seven, the amount of possibilities to get that number decrease and thus the probability. The total percentages for the products are as follows: 2=4%, 3=3%, 3=4%, 5=6%, 6=22%, 7=20%, 8=9%, 9=11%, 10=10%, 11=7%, 12=4%. These values do not match the scientific percentages. The product 7, should have a percentage of 16.7 and as a number becomes further that 7 the percentages should be: 13.9, 11.1, 8.3, 5.6, 2.8.
The hypothesis that the product 7 should appear 16.7 percent of the time and be the most frequent was not supported. The number seven was actually the second most frequent behind the number six. The bell curve that the graph is supposed to create was present but no perfect as the value of three was below that of two’s occurrences.
Most other research with dice rolling is focused on the theoretical probabilities of rolling certain numbers. There are almost no experiments were people conduct an actual experiment with dice. This is most likely because probability is only the chance of something occurring and is not considered to mean law when applied to anything.
In conclusion, the hypothesis was not supported by the experimental data. The product of 7 was not the most frequently occurring number even though it had the highest probability of 16.6 %. The actual percentage that the product of 7 occurred was 20%. The reason that the hypothesis was not supported because a probability is in essence a guess. A probability will not be true most of them time. The purpose of probability is to show the chance that something has of appearing. This has little to do with the actual results that follow with experimentation. In order to improve this experiment, a real set of dice could be used because there is still question if a random number generator can ever be truly random. Also, the dice interacting with each other could cause different results than just simply clicking a button. This experiment tells us that someone should bet on the number seven in gambling and games, but should not be totally surprised when it does not occur has frequently as expected.
Works Cited
Bing, Microsoft, www.bing.com/images/search?view=detailV2&id=0566C80F0C7068245697EA8505CFE210FD759805&thid=OIP.CPY1j6bsV-yi2dcS8BMzyQHaFc&mediaurl=https://thumbs.dreamstime.com/z/purple-green-dice-8167661.jpg&exph=957&expw=1300&q=picture+od+two+dice&selectedindex=238&ajaxhist=0&vt=0&eim=1,2,6.
Dice History, www.dice-play.com/History.htm.
Haahr, Mads. “True Random Number Service.” RANDOM.ORG – The History of RANDOM.ORG, www.random.org/history/.
Haahr, Mads. “True Random Number Service.” RANDOM.ORG – Dice Roller, www.random.org/dice/.
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