How a Mathematician Wizard Spotted a Major Casino Flaw
The top executives of the industry were worried. His company made machines for casinos that shuffled the cards to get the correct cards. Thousands of such machines were in use in casinos in Las Vegas and other cities around the world.
The company earned tens of millions of dollars every year from the rental of these machines and the company was listed on the New York Stock Exchange.
Company officials recently found out that their company’s machines have been hacked by a gang of fraudsters. The gang installed a hidden camera through a glass window to record the shuffling of cards.
The images recorded by the camera went to the gang member who was sitting in the car park outside the casino. He used to play these pictures in slow motion to show how and in what order the machine finally works. This information was later passed on to casino gamblers. By the time the group was discovered, the casino had lost tens of millions of dollars.
Company officials thought they would not allow these machines to be hacked again. He developed a new advanced model of shuffling machine which he kept in an opaque or glass box that did not see through.
Their engineers ensured that the machine would shuffle the cards at a time so quickly and randomly that it would take less time between turns and help beat cheating gamblers. will get
But company officials had to make sure their machine shuffled the cards correctly. For this he contacted Percy Deaconess.
Diaconus was a mathematician at Stanford University in the US who was formerly a magician. He was the world’s foremost expert in understanding the card shuffling process. In all the literature and information on the subject of card shuffling, his name came up again and again.
They couldn’t believe their luck when casino company officials approached them for internal testing of the card shuffling machine.
Along with Susan Holmes, her colleague at Stanford, Deacon flew to Las Vegas to inspect the new machines.
Both quickly discovered a fault in the machines. The shuffling process was as it should be, but it was not difficult to predict the order in which the numbers would appear in the resulting deck.
The cards that came out of these machines were either in ascending or descending order of numbers. To prove this point, Diana Koons and Susan Holmes came up with a way to predict card numbers. If the first card after the shuffling resulted in a five-of-hearts card, they predicted that a card that came out would be a six-of-hearts card.
He assumed that the numbers were increasing. But if it was reducing the numbers of the next card, it meant that the numbers were now starting to decrease and they predicted that the next card would be a three of hearts.
With this simple strategy, he was able to correctly guess the numbers of at least 9 to 10 cards in a deck, which would have doubled or tripled the advantage of any talented card counter. Card counting is a method by which a gambler can keep a record of which cards have been dealt, making it easier to predict wins or losses.
This method has been used for decades. This method is allowed in the game of bridge, but it is strictly prohibited in casino games like blackjack. It is illegal to use this technique in casinos.
After hearing the results of Deacon’s investigation, the company’s officers were furious and frightened. “We are not happy with your results,” he wrote to Deacon. The company quietly removed the new machine and installed a different one.
Deaconess spent her whole life trying to understand the order, the trinity, and the disorder of numbers. Then whether it is ‘message decoding’ or web search engine optimization, he used this information to understand the most important questions related to card shuffling.
His interest in cards was a mere coincidence. In 1958, when he was thirteen years old, at the Tannen Magic Emporium in Times Square, New York, he met Alex Emsley, a scientist and magician from Scotland, who taught him how to shuffle cards exactly, the ‘Perfect Shuffle’. ‘ was mastered.
Perfect Shuffle is also called ‘Farrow Shuffle’. In this, a deck of cards is divided into two parts. There are 26 cards in one side and 26 in the other side, and when the two sides of the card deck are joined, they snap together like a zipper. Very few people could do it in less than ten seconds. Deacons had this skill.
Magicians and gamblers have been using this method of shuffling cards for centuries. It looks like the cards are being shuffled randomly but they are not random at all. In fact, if this method of perfect shuffle is repeated eight times in a row, the cards return to their original order.
N. of Deaconess Card
Deacons would take a new deck of cards and write the word ‘random’ in black ink on one side to demonstrate the perfect shuffle. When they show the cleanliness of their hands, the words are reversed. Cards sometimes appear and then disappear when shuffled.
But when shuffled for the last and eighth time, the word ‘random’ appears again written on the face side of the card. The cards are in the same order as they were before.
At the Tanin Magic Emporium, Emsley explains to Deaconess the maths behind the trick. He said, “Imagine that you have a new deck of cards numbered from 1 to 52, with the top card being number one and the bottom card being number 52.”
When doing a perfect shuffle, the card numbers are moved around. For example, the card that was in the second position moved to the third position and the card that was in the third position moved to the fifth position. Similarly, the card that was number 27 will be number two, and so on.
After this meeting with Emsley, Deaconess ran away from home at the age of fourteen to learn magic under the tutelage of a master magician. The two spent ten years on the road learning every shuffling technique and finding every cheating gambler who came up with one new and successful card shuffling technique.
After talking with Emsley, Deacon became curious about what other connections there were between mathematics and magic. Deacons says he’s found that it takes seven shuffles to get the cards perfect.
This method is called ‘Ruffle Shuffle’. This is the method used by professional gamblers and casinos. In the Saas method, the deck of cards is divided into two equal parts and the cards are shuffled rather than stacked one on top of the other, in which one card is not necessarily placed on top of another. Maybe one card can be placed on top of one and sometimes two cards.
Under Raffle Shuffle only once or twice, some of the cards remain in their original order, but when you shuffle the cards for the seventh time, the cards are completely out of order, and no matter how many times you shuffle the cards after that, It doesn’t matter.
To understand this method, Deacons used a powerful mathematical tool called Marco Chains. “Marco chains are any repeated action whose outcome depends on its current state, not how that outcome was achieved,” says mathematician Sami Hais Asif at the University of Southern California. This means that Marco Chen has no memory of what happened before that moment.
This is a great model for card shuffling. The result of shuffling the cards for the seventh time is affected by the sixth shuffling, not the fifth or fourth shuffling.
Marko chains are used to understand the distribution of random numbers in statistics and computer sine. Google uses a simple method like Marko Chains to determine the order of popularity of different websites in the search engine.
This method evaluates the favorite websites of the billions of Internet users who click on them without thinking, and from this, Google infers which websites are the most popular. Google displays the most popular websites on the first page.
Working with mathematician Dave Beer of Columbia University in New York, Deacons showed that the seventh order of cards in a shuffle shuffle becomes exactly good muddled. This method or behavior is called the ‘cut-off phenomenon’ in mathematics and is used in problems involving mixing.
Imagine you are mixing cream into coffee. When you are mixing the cream, it first forms white streaks in the black coffee and eventually it blends completely into the coffee.
Remember how the cards are being shuffled. The cards are completely shuffled or remember something about their order, giving gamblers an edge over other gamblers.
In the 1990s, a group of Harvard and MIT University students succeeded when they played blackjack in various US casinos and used card counting and other card shuffling methods to To determine whether the deck of cards was properly shuffled or not.
In response, casino owners installed better card-shuffling machines and shuffled the decks well before gambling began. Apart from this, he started monitoring the players more. But even today it is rarely seen that a suit of cards is shuffled only seven times.
Casino executives paid little attention to Decanos and his research, but his influence on mathematicians, statisticians and computer scientists to understand the science behind ‘randomness’ or randomness of numbers remains. Want.
A conference was held at Stanford University in January 2020 to mark the 75th anniversary of Deaconess. His colleagues from all over the world lectured on a variety of mathematical topics, including how a serializer stops shaking after shaking a cardboard box and card shuffling.
