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Whenever a gang of gambling cheats sussed out how to beat the home, they inadvertently highlighted a loophole from the shuffled deck. It took a magician-turned-mathematician to reveal how.Metaverse Casinos: Gambling In Virtual Worlds
The industry executives were anxious. Their company manufactured precision card-shuffling machines for casinos. A large number of their mechanical shufflers were in operation in NEVADA and all over the world. The rental fees earned millions of dollars every year, and the company was listed on the New Stock Exchange.

However, the executives had recently found that among their machines had been hacked by way of a gang of hustlers. The gang used a hidden camcorder to record the workings of the card shuffler by way of a glass window. The images, transmitted to an accomplice outside in the casino parking lot, were played back slow motion to determine the sequence of cards in the deck, which was then communicated back to the gamblers inside. The casino lost millions of dollars before the gang were finally caught.

The executives were determined never to be hacked again. That they had developed a prototype of a sophisticated new shuffling machine, this time around in enclosed in an opaque box. Their engineers assured them that the machine would sufficiently randomise a deck of cards with one pass through the device, reducing the time between hands while also beating card-counters and crooked dealers. But they needed to be sure that their machine properly shuffled the deck. They needed Persi Diaconis.

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Diaconis, a magician-turned-mathematician at Stanford University, is regarded as the world's foremost expert on the mathematics of card shuffling. Through the entire surprisingly large scholarly literature on the topic, his name keeps showing up like the ace of spades in a magician's sleight-of-hand trick.

So, when the company executives contacted him and wanted to let him start to see the inner workings of these machine ? a literal "black box" ? he couldn't believe his luck.

Along with his collaborator Susan Holmes, a statistician at Stanford, Diaconis travelled to the business?s Las Vegas showroom to look at a prototype of these new machine. The pair soon discovered a flaw. Although the mechanical shuffling action appeared random, the mathematicians noticed that the resulting deck still had rising and falling sequences, which meant they could make predictions concerning the card order.

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To prove this to the business executives, Diaconis and Holmes devised a straightforward way of guessing which card will be turned over next. If the initial card flipped was the five of hearts, say, they guessed that the next card was the six of hearts, on the assumption that the sequence was rising. If another card was actually lower ? a four of hearts, for example ? this meant they were in a falling sequence, and their next guess was the three of hearts.

Cheaters were able to predict the order of cards in a shuffled deck by closely watching the card shuffle machine (Credit: Getty Images)
Cheaters could actually predict the order of cards in a shuffled deck by closely watching the card shuffle machine (Credit: Getty Images)

With this particular simple strategy, the mathematicians could actually correctly guess nine or 10 cards per deck ? one-fifth of the total ? enough to double or triple the advantage of a competent card-counter.

Card counting is a practice in which a player keeps track of which cards have already been dealt to be able to have a slight advantage predicting the probability that another card is a winner or loser. The practice 's been around for decades (and in a few games like Bridge is really a legitimate part of the gameplay), but is heavily cracked down on in casino games like Blackjack. The usage of technology to aid a card counter is outlawed.

The executives were horrified. "We are not happy with your conclusions," they wrote to Diaconis, "but we believe them and that is what we hired you for." The company quietly shelved the prototype and switched to another machine.

THE GALAXY IN A CARD DECK
A pack of handmade cards contains multitudes. A standard 52-card deck could be shuffled into an astronomical number of possible arrangements, or permutations. There are 52 possible values for the first card, 51 for the second, 50 for the third, and so on down through the deck, therefore the resulting number of permutations is 52x51x50?.x2x1. Mathematicians call this 52-factorial, or just 52!.

Despite the compact (if emphatic) notation, 52! is really a huge number ? 68 digits long. You can find as many possible arrangements of a deck of cards as there are atoms in our galaxy. Any one of those arrangements ? if randomly chosen ? is so statistically unlikely that it's almost certainly the 1st time it has ever occurred, anywhere.

Diaconis has spent an eternity studying problems that go on the borderlands between order and randomness. Whether it is decoding scrambled messages, reassembling strands of DNA, or optimising web se's, he has a knack for transforming these problems into a question about card shuffling.

His fascination with cards began with the opportunity encounter in 1958. At age 13, at Tannen's Magic Emporium in NY City's Times Square, Diaconis met Alex Elmsley, a soft-spoken Scottish computer scientist and magician who had mastered the "perfect shuffle". Sometimes called the "faro shuffle" or just "the technique", an ideal shuffle involves splitting a deck into two stacks of exactly 26 cards each and perfectly weaving them together just like a zipper, alternately interleaving one card from each hand. Very few people can do it correctly in less than 10 seconds. Diaconis is one.

The perfect shuffle has been used by gamblers and magicians for centuries because it provides illusion of randomly shuffling the cards. Nonetheless it is definately not random. In fact, if you perform the same sequence of perfect shuffles eight times in a row, the deck will magically restore its original order.

Diaconis likes to demonstrate an ideal shuffle by taking a new deck of cards and writing the word "RANDOM" in thick black marker on one side. As he performs his sleight of hand with the cards, the letters get mixed up, appearing now and then in ghostly form, like an imperfectly tuned image on an old TV set. Then, after he does the eighth and final shuffle, the term rematerialises on the side of the deck. The cards come in their exact original sequence, from the ace of spades to the ace of hearts.

Back in Tannen's Magic Emporium, Elmsley explained the subtle mathematics behind the trick. Suppose you number a fresh deck of cards in one to 52, where one may be the card near the top of the deck and 52 is the card at the bottom. As you perform an ideal shuffle, cards move to new positions in the deck. For instance, the card originally at position two will proceed to position three, as the card at position three will proceed to position five, and the card at position 27 should come back up to position two, etc.

As soon as you shuffle the deck seven times, the cards become truly mixed, at the very least so far as most statistical tests can prove
The perfect shuffle could be thought of as a complete series of cycles, like separate games of musical chairs. The quantity of shuffles necessary to return the cards to their correct order may be the least common multiple of the lengths of all the cycles: in cases like this eight shuffles (eight may be the smallest multiple of 1, two, and eight).

The year after his encounter with Elmsley at Tannen's Magic Emporium, Diaconis ran away from home, aged 14, to understand magic under the guidance of a famous sleight-of-hand magician. They spent a decade on the road, learning every possible design of shuffling and tracking down crooked dealers to learn their techniques.

But his conversation with Elmsley had sparked Diaconis' curiosity. What other connections lay between mathematics and magic?

Diaconis says he will have "seven shuffles suffice" carved on his tombstone. He could be referring to his most well-known realisation: that it requires seven "riffle shuffles" to sufficiently randomise a deck of cards. The riffle shuffle may be the familiar technique, used by casinos and serious card players, in which the deck is cut in two and then thumbed as well as a satisfying zip, often ending with a bridge finish that gathers the cards together right into a neat pile.

The riffle shuffle may be the unruly twin of an ideal shuffle. Instead of perfectly interleaving both halves of the decks, the halves are mixed together in disorderly clumps, planting a seed of randomness that progressively mixes the cards with each shuffle.

After a couple of riffle shuffles, some cards will remain in their original sequence. Even with 4 or 5 shuffles ? a lot more than most casinos typically use ? the deck will retain some trace of order. But once you shuffle the deck seven times, the cards become truly mixed, at least so far as most statistical tests can prove. Beyond that time, further mixing won't do much. "It's just as close to random as can be," Diaconis says.

The perfect shuffle, where each card is interwoven alternately, takes years to master (Credit: Getty Images)
The perfect shuffle, where each card is interwoven alternately, takes years to master (Credit: Getty Images)

To study riffle shuffles rigorously, Diaconis used a robust mathematical tool called a Markov chain.

"A Markov chain is any repeated action where the outcome depends only on the existing state and not on how that state was reached", explains Sami Hayes Assaf, a mathematician at the University of Southern California. Because of this Markov chains haven't any "memory" of what came before. This is usually a pretty good model for shuffling cards, says Assaf. The result of the seventh shuffle depends only on the order of the cards following the sixth shuffle, not on what the deck was shuffled the five times ahead of that.

Markov chains are widely used in statistics and computer science to handle sequences of random events, whether they are card shuffles or vibrating atoms or fluctuations in stock prices. In each case, the near future "state" ? the order of the deck, the power of an atom, the worthiness of a stock ? depends only on what's happening now, not what happened before.

Despite their simplicity, Markov chains may be used to make predictions concerning the likelihood of certain events after many iterations. Google's PageRank algorithm, which ranks websites within their search engine results, is founded on a Markov chain that models the behaviour of vast amounts of internet users randomly simply clicking web links.

Working with Dave Bayer, a mathematician at Columbia University in New York, Diaconis showed that the Markov chain describing riffle shuffles includes a sharp transition from ordered to random after seven shuffles. This behaviour, recognized to mathematicians as a cut-off phenomenon, is really a common feature of problems involving mixing. Think of stirring cream into coffee: as you stir, the cream forms thin white streaks in the black coffee before they suddenly, and irreversibly, become mixed.

Knowing which side of the cut-off a deck of cards is on ? whether it is properly shuffled or if it still preserves some memory of its original order ? gives gamblers a distinct advantage contrary to the house.

In the 1990s, several students at Harvard and MIT were able to beat the odds playing blackjack at casinos round the US through the use of card counting and other solutions to detect if the deck was properly shuffled. Casinos responded by introducing more sophisticated card-shuffling machines, and shuffling the deck before it really is fully played, in addition to stepped-up surveillance of players. But it is still rare to see a deck of cards shuffled by machine the requisite seven times at a casino.

Casino executives may not have paid much heed to Diaconis and his research, but he continues with an enormous influence on mathematicians, statisticians and computer scientists who study randomness. At a conference held at Stanford in January 2020 to honour Diaconis's 75th birthday, colleagues from around the globe gave talks on the mathematics of genetic classification, how cereal settles in a shaking box, and, needless to say, card shuffling.

Diaconis doesn't look after gambling much himself ? he says you can find better and much more interesting ways to earn a living. But he doesn't begrudge players who try to get an edge by using their brains.Online gambling is definately not being a novelty. Because the very inception of the internet, gamblers have considered virtual platforms because of their wagers while pinning their hopes of landing an absolute hand on online casinos.

And with real-life casinos shuttered across the world during the pandemic, bettors have increasingly embraced virtual gambling opportunities. But a definite LAS VEGAS has risen that beats all others - the metaverse. Although still a vastly unexplored concept, it can more simply certainly be a shared virtual world where real-life and digital experiences crossover, and users can take part in a vast amount of activities, from buying virtual goods to meeting new people and starting businesses.

Given the endless possibilities, or even better, its estimated yearly trillion dollar income generating potential, no wonder then that gambling has turned into a top activity in the metaverse. Players are blowing millions and raking in millions more in virtual world casinos. One such casino, ICE Poker, reported a revenue of $7.5 million in the initial 90 days of 2022. Even though it cannot be compared to the astronomical numbers pulled by the world?s gambling capital, Macau, it is yet a notable feat for an industry still taking its first steps in the metaverse.

What Is Decentralized Gambling
We can think of metaverse casinos, or crypto casinos, as extensions of regular online casinos or betting platforms, aside from the truth that all transactions are processed not in fiat but - yes, you?ve guessed it - in crypto currency. Decentralized gambling can lay claim to many benefits. In theory, by relying on blockchain technology, crypto gambling ensures a higher level of transparency, security and privacy.

Players may also welcome the theory that their bets are not being rigged and only the house while, however, the more creative casino cheats won?t find much luck in trying their tricks in the metaverse. Winnings and bets are recorded on the blockchain and frequently a crypto casino won?t charge fees when entering, say, a poker tournament or other gambling events.

And the taxes, you may ask? That?s still a gray area. The crypto industry is only now starting to turn into a subject of regulation, nonetheless it seems Uncle Sam won?t be coming for a cut of one's fortunes for the moment.


That isn't to state that gambling in virtual environments isn't without risks. There are lots of jurisdictions around the world where online gambling is illegal, including in virtual worlds, and we suggest you get familiar with your local laws.

Decentralized betting exchanges also depend on blockchain protocols to enable peer-to-peer matching of bets in a way that removes the necessity for a ?trusted middleman? - as may be the case with a traditional bookmaker or exchange. Because of this not only betting can be achieved at a fraction of the purchase price while eliminating counterparty risks, but also that players might feel a lot more welcomed.

All in all, it?s fair to state that the metaverse makes for a different and heightened gambling experience from that of physical casinos as well as online platforms.

Where Can You Gamble In The Metaverse
Amid the virtual glittering lights and neon glow of a parade of extravagant metaverse casinos, the buzziest digital City of Lights today is located in Decentraland - a decentralized virtual world built on the Ethereum blockchain. This metaverse is entirely owned by its users, without the intervention of a governing entity, and is managed through smart contracts.

Using an avatar, users can simply enter Decentraland and be transported to a digital twin of physical locations and experiences, be that visiting a skill gallery, attending a music concert or taking part in pop-up pursuits like a Scavenger Hunt. Users may also purchase virtual land in the platform, which gives them complete ownership and control of their metaverse properties and any applications they create within it.

Because of its decentralized technology, Decentraland can depend on a thriving open market where transactions are created through the in-platform cryptocurrency, MANA, that includes a market value of some $4.2 billion.

And while there are endless events occurring at any moment, turns out that folks enjoy visiting Decentraland?s Vegas City above all else. Actually, poker rooms in Decentraland frequently host about 50 % of individuals in its metaverse.

Taking clear inspiration from the famed Vegas Strip, Decentraland?s virtual casino district doesn?t differ much from the real-life thing. Entering one of its many casinos, users are greeted by crowds of gamblers sporting (sometimes quite questionable) streetwear fashion, from funky wigs to extravagant shoes and, of course, the mandatory sunglasses for the poker playing crowd.

Poker is the go-to gambling choice, but this digital sin city is hardly short on other offerings. Players can hit the tables virtually and play blackjack, backgammon, roulette or try their luck at the slot machine. The sound of the money register cha-ching, the shuffling of card decks or poker chips and the hand-clap emojis certainly are a constant background reminder that metaverse experience is aimed to be as realistic as you possibly can - and, moreover, there is real cash to be made.

Top Casinos On Decentraland
Decentraland has a number of crypto casinos you might want to explore:

Chateau Satoshi

Produced by Decentral Games, a distributed autonomous organization (DAO), and launched in the Decentraland metaverse world in 2019, Chateau Satotoshi is an art deco inspired casino spanning across three floors, including a casino, a nightclub and a theater. Here, gamblers can find all the traditional real-life casino games and use MANA or ETH to make their crypto fortunes.

Tominoya Casino

This Japanese-themed casino can be run by Decentral Games, but unlike other platforms, gamblers are greeted by real-life hosts rather than computer-generated bots. The casino recently continued a hiring spree and has on-boarded 20 part-time greeters and a full-time manager to greatly help with daily operations, according to Decentral Games founder Miles Anthony.

At Tominoya, users can try their hand at a variety of decentralized casino games including blackjack and poker using MANA, DAI, or simply free play. More risk averse bettors can also elect to place their crypto on games of chance just like the slot machines and roulette tables. Addititionally there is gameplay involving real estate NFTs by which holders can earn a passive income of around 30% as part of a leasing agreement with the casino.

Tominoya Casino also features a conference hall where live streaming events are frequently held. Given its vast gambling offers and its interactive live staff Tominoya has fast turn into a favorite metaverse gambling destination.

Serenity Island

Serenity Island is really a sprawling casino laid out across three floors, including a nightclub area, everything in a Monte Carlo-inspired architecture. Players must climb an enormous island (that's part of the fun, we promise) to enter this casino and unlike a few of the other virtual casinos featured in Decentraland, Serenity Island can come across more like a beach house experience rather than full-on casino. That?s a proposition that can certainly interest the more low-key players.

Atari Casino

This past year, iconic video and arcade game maker Atari partnered with Decentral Games to launch the Atari Casino in Decentraland. The project is yet to be fully launched but in accordance with Atari it will feature a amount of arcade games through which users will be able to find nostalgic titles along with some new games where gamblers must use a mix of luck and skill. Players may also be able to search for the gaming company?s exclusive wearables located through the entire casino. The platform is supported by Matic Network, a move aimed at making game transactions cheaper and quicker when compared to other casinos. The Atari Casino is likely to rake in $400 million over 2 years in bets alone. Gamers can play with a wide range of tokens, including ETH, DAI and Decentraland?s own cryptocurrency MANA. Moreover, a so-called ?gaming mining? program will reward gamblers with Decentral Games? governance token, $DG.

ICE Poker

The undisputed go-to metaverse poker parlor is ICE Poker, with all the real-life trappings of the poker life included. That?s because new players are expected to live up to the poker swag and buy at least one ICE Wearable before being accepted. Trouble is that they?ll have to cough up thousands just to have a foot in the door as the minimum price for such NFTs commands a minimum price of nearly $7000 on marketplaces like OpenSea. Fortunately, interested players can simply rent a wearable from other players who get yourself a generous cut of their profits, an arrangement that?s become ever more popular.

ICE Poker has become a favorite with Decentraland?s residents also because of its daily challenges, through which users can earn actual money prizes, also it?s poker tournaments. The casino attracts 6,000 daily poker players to its many poker halls where players can not only earn crypto tokens but also upgrade their wearable NFTs by beating opponents and completing in-game challenges. ICE Poker alone is bringing around $3.2 million in monthly revenue for Decentral Games, as the company claims to have paid some $15.4 million to players across its multiple casinos.

How to Start Playing In A Metaverse Casino
Gambling is fast becoming one of the top immersive experiences in the metaverse and platforms will work on rendering it as seamless as possible. One key aspect to bear in mind before entering the planet of crypto gambling is that different digital currency tokens and NFTs may be used by different casinos and over the multiple experiences they offer. The training curve can appear a little daunting at first, but once you get the hang of it, playing becomes much easier.

Below are a few steps you should follow:

1. Find the right metaverse casino for you personally
We?ve centered on Decentraland as that is the metaverse with the highest amount of casinos and one that is widely seen as the most trustworthy.There are other virtual worlds with great gambling platforms. However, you?re able to find casinos in other virtual worlds like The Sandbox. But, again, we?ll keep it down to Decentraland with regard to simplicity.

In the casinos we mentioned earlier, you should be able to find a range of games similar to those you?d typically encounter in a normal real-life casino, such as for example slot machines, poker, roulette and blackjack, and also proprietary games predicated on luck and skill.

Using the crowds they attract, each metaverse casino will have their own look and feel, and different rules. But when finding the right casino, we recommend you retain an eye out for a couple key features, including:

Security measures: Whenever personal and financial data is at play, online security is paramount. Metaverse casinos rely, as previously explained, on blockchain. This already ensures a high amount of security backed by cryptography, but feel free to ask the casino operator about any extra measures they may have in place to ensure the online safety of its users.

Game variety: Similar to in a real-life casino, players would want to have an exciting range of options to select from when gambling in the metaverse. An excellent casino will try to focus on the tastes of players from all backgrounds, offering games from the most common classics to newer options.

Attractive prizes, tournaments and promotions: You?ll desire to be engaged with a casino that puts effort into creating a tight community - and rewarding its members accordingly. A good telltale sign could be the welcoming package a casino gives to its newest players. With regards to games such as slots, for instance, players will also be given regular free spins. Other types of loyalty programs with plenty of benefits and rewards.

Reputation: Decentraland includes a large community of users it is simple to reach out to. In the event that you?re unsure of where to start, find a group of users you can chat with for his or her impressions of the metaverse?s casinos. You're sure to find other players who?re already well versed in the gambling scene and you?ll be in an improved position to see you about the best casinos on the platform.

2. Open a crypto wallet
All services and transactions within the metaverse go through some type of cryptocurrency. You?ll require a digital wallet so as to hold your cryptocurrency and there are plenty of secure and user-friendly platforms you should think about. We suggest you focus on Metamask, but really there are numerous of equally good wallets on the market.

3. Purchase crypto currency
You?ll need money to put bets and enter gambling events, and the currency itself will vary from casino to casino. Decentraland uses the MANA crypto currency token & most casinos may also accept ETH, so those are two safe currencies to load your digital wallet with. You?ll should do this via a crypto forex like Binance or Coinbase, amongst others.

As well as the steps mentioned, entering and playing in the metaverse will demand that you choose your personal avatar and customize it. That's also an excellent share of the knowledge to be a metaverse user and having fun, so we?ll leave all that to you.


Closing thoughts
The metaverse is now really removing, but virtual worlds are quickly becoming better, more immersive and dynamic while enabling high-quality experiences that may realistically mimic some of the emotions we enter real-life. In this sense, the metaverse is the perfect playing ground for something similar to gambling.

Traditional online gambling may be easy to jump into, but metaverse casinos are where in fact the most enthusiastic bettors are actually heading for the opportunity of hitting the jackpot. Decentraland?s Vegas City in particular is attracting enthusiastic players who enjoy having rewarding gaming experiences where, by using virtual reality and blockchain technology, they are often a lot more involved while experiencing highly immersive events.

Given the current popularity of metaverse casinos, we are able to expect to see decentralized gambling overtaking both real-life and online gambling sometime soon.
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