Menu
- 4; 0; [email protected].
- As another example, consider a lottery. Although millions can be won for the price of a $1 ticket, the expected value of a lottery game shows how unfairly it is constructed. Suppose for $1 you choose six numbers from 1 to 48. The probability of choosing all six numbers correctly is 1/12,271,512.
Since there is no standardized definition, poker, for example, has been ruled a game of chance in Germany and, by at least one New York state Federal judge, a game of skill there. 6 Addiction edit.
A Brief History
On January 13, 2016, Powerball produced the largest lottery jackpot in history; the $1.586 billion jackpot was split by three tickets sold in Chino Hills, California, in Munford, Tennessee, and in Melbourne Beach, Florida. Nevertheless, the multi-billion dollar industry around gambling certainly is not a recent phenomenon. The origins of the word come from the Middle English word, gammlen, meaning “to play, jest, be merry,”, and if you look even further back, you will find it actually started in prehistoric times.
Digging Deeper
![Game Game](https://i.ytimg.com/vi/d2STHFVHGAg/maxresdefault.jpg)
Prehistory and the ancient dynasties
“The Egyptian game of Senet” by University of Brooklyn (CC BY-SA 3.0)
From the earliest cavemen calculating the odds of being able to kill their foes to punters placing bets using mobile apps, calculating probability is always at the back of our minds. Archaeological evidence suggests that as far back as the Paleolithic era, cavemen liked the occasional game of chance with the family after a hard day’s hunting.
An Egyptian game called Senet is featured on hieroglyphs and multiple tombs in Egypt and the accessories used even became a talisman for the journey of the dead. The game unsurprisingly depended heavily on luck, so people believed the winner was under the protection of the gods.
Revels with the Romans
“Dice players in Pompei” by Wolfgang Rieger (CC-PD-Mark)
BAFA was the game which swept the Roman Empire, played by everyone from the poorest slaves to Emperors. Caesar, Nero and Genghis Khan all rolled BAFA for coins, for property and even for clothes at Roman orgies. Furthermore, if proof were needed that we humans also have cheating in our collective DNA, weighted pairs of dice were found in the ruins at Pompeii, so perhaps what happened there was divine retribution!
The Greeks were also in on the act. Philosophers condemned gambling, resulting in severe restrictions to limit it. Having said that, Plato and Aristotle probably had the odd side-bet on the quiet…
Gruesome odds and hazardous gaming
“Players and courtesans under a tent” by Cornelis de Vos (CC-PD-Mark)
The first casino, The Ridotto in Venice, opened in 1638 to provide an environment where controlled gaming could take place. Even the refined Georgian period in England was notable for a game called, appropriately, “Hazard”. Entire fortunes could be lost in a night playing this fast-paced game, and losing thousands of guineas was not uncommon.
The lucky number that came good… eventually
If we think we have a chance, we love taking a punt, and it gives us the opportunity to spin a little mysticism or plain illogical thinking into the mix. Whether it is a scratchcard or a randomly generated number for the weekly bonanza draw, we are drawn to the possibility of winning a life-changing amount of cash. Sometimes, just sometimes, those dreams come true in a big way, like the lucky winner of the Powerball record jackpot on January 13th, 2016, where the payout was mind-blowingly enormous and, if fact, never matched since. It is the kind of payday dreamed of every week by the millions of people who chance their luck every day around the world.
If there had been a Paleolithic lottery back in the day, it would be interesting to see how the hunter-gatherers would play that one out – although every day was sure to be a form of lottery back then.
Question for students (and subscribers): What is the most you ever won in a lottery? Please let us know in the comments section below this article.
If you liked this article and would like to receive notification of new articles, please feel welcome to subscribe to History and Headlines by liking us on Facebookand becoming one of our patrons!
Your readership is much appreciated!
Historical Evidence
For more information, please see…
Crist, Walter, Anne-Elizabeth Dunn-Vaturi, et al. Ancient Egyptians at Play: Board Games Across Borders (Bloomsbury Egyptology). Bloomsbury Academic, 2016.
Zollinger, Manfred. Random Riches: Gambling Past & Present. Routledge, 2016.
The featured image in this article, a photograph by Tony Webster from Minneapolis, Minnesota, United States of a billboard for the Powerball and Mega Millions lottery game prizes in Missouri, is licensed under the Creative CommonsAttribution 2.0 Generic license. This image was originally posted to Flickr by Tony Webster at https://flickr.com/photos/87296837@N00/44555666811. It was reviewed on by FlickreviewR 2 and was confirmed to be licensed under the terms of the cc-by-2.0.
The news is full of accusations of the rigging of casino games and electronic games. When gamblers play slot machines over a long period of time, they expect to at least break even. When they do not, they may suspect the game is rigged. Some of us get lucky and win the jackpot during a short trip to Las Vegas, but this is not the normal experience of most players. Introductory statistics can show us what the outcomes of a fairly played game of chance should look like.
A Toss of a Coin
Random Chance Games
After repeated play, the outcomes of fair games should follow normal distributions. Although we do not know the outcome of a game of chance in advance, we expect it to produce random variables that follow a bell curve shape distribution. The toss of a coin is an example. Lucky nugget flash.
The laws of probability dictate that if a coin is repeatedly tossed, over time, it will come up heads 50% of the time and tails 50% of the time. Likewise, if you play a fair game 1,000 times that does not depend on skill, you would expect to win 50% of the time. A slot machine is an example of such a game. The roll of the dice is another.
The peak of the bell curve is 50%, and the symmetrical sides represent the normal distribution of the random data around th average. The average of the random coin tosses is the peak of the bell curve, or mean, 50%. In a normal distribution, 50% of the values are less than the mean and 50% of the values are greater than the mean.
The bell curve is commonly used to evaluate school grades, ages of students, intelligent quotients (IQs), and many other variables. The mean IQ of the population is 100, and it has a standard deviation of 15. In classes, we take the average of all scores and call it the mean class average.
A Fair Roll of Dice
The outcome of a roll of dice is a well-known example of the bell curve. If a dice is rolled 100 times, the percentage of times a 1 turns up will be around 15% to 18%. If the dice is rolled 1,000 times, the percentage of times a 1 is rolled will fall within the 15% to 18% range, and will eventually converge to 16.7% (1/6).
In a fair roll of two dice, there are 36 possible combinations. The probability of rolling a 2 (1 + 1) is 2.8% (1/36). The probability of rolling a 7 (with six possible combinations) is 16.7% (6/36).
This concept is also known as the law of averages. After many rolls, the average number of twos will be closer to the proportion of the outcome. The probabilities of the total set (all possible dice throws) must add up to one. Once we have determined the distribution of an event, we can figure out the probability that an event will happen in the future.
The Roulette Wheel and Standard Deviation
Let’s look at another example, the roulette wheel. George places his bet on the numbers 1 and 12. The probability of him winning is 12/38, and losing 26/38. Why? There are 38 slots on the roulette wheel. The chance that the ball will land on 1 is 2.63%. In gambling parlance, the odds are 37:1, or 1 chance in 38 that the ball will land on 1. The mean of the roulette game is 2.63%. All of George’s spin results are distributed randomly on either side of the mean.
The bell curve is calculated by the mean and standard deviation. As shown, the mean is the average of the data, represented by the middle of the bell curve. The standard deviation is a measure of how spread out the numbers are. It is represented by the height and width of the bell curve. If the standard deviation is large, the data points are more spread out and the curve is shorter and wider. When the SD is small, the bell curve will be tall and narrow.
The total area of the bell curve is equal to 1 (100%)
About 68% of the area under the curve falls within 1 standard deviation.
![Examples Examples](https://www.palottery.state.pa.us/uploadedimages/1mill_covered.png)
About 95% of the area under the curve falls within 2 standard deviations.
Games Of Chance Examples
About 99.7% of the area under the curve falls within 3 standard deviations.
Normal Distribution Calculator
Once we have confirmed that the roulette game follows a normal distribution, we can conclude that 95% of George’s spins will fall within two standard deviations on either side of the mean. Many statistical software packages are available to teach SPSS Essentials. SPSS allows you to plot and evaluate various outcomes. Through a chart called a Histogram, you can perform scenario analysis. Not all distributions are a bell curve, a normal distribution. The random data may be distributed to the right or skewed to the left. To experiment with different distributions data, use a normal distribution calculator.
In a normal distribution, the bell curve forms a symmetrical curve. Once we know the deviation of a distribution, we can forecast the probability that an outcome will fall within a range of the mean. Probability is shown in a range of 0 to 1. If an event has a probability of 0, it is not expected to occur. If an event has a probability of 1, it is likely to occur. Using the coin toss example, the probability that the coin toss will come up tails is 50%.
Simple Games Of Chance
If game manufacturers are rigging games, as several lawsuits contend, the outcomes will not be fair, or normally distributed. To prove the case, the lawyers will need to calculate the probability of the expected outcomes of the rigged machines to prove that the results deviated from expected behavior. Law is just one area in which normal distribution applies. Since 17th century French scientists discovered normal distribution while rolling dice, it has underpinned many disciplines. To master the practical application of statistics in your profession, enroll in The Workshop in Probability and Statistics or Quantifying the User Experience. Learning to use confidence intervals and hypothesis testing, and determine the size of errors and accuracy of estimates will help you establish the validity and reliability of the data you produce.