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  1. A more pragmatic reason for casinos using chips in place of cash at table games is to discourage players from grabbing back their bet and attempting to flee should their bet not win, because chips, unlike cash, must be redeemed at the casino cashier and have no value outside the casino in question. Lastly, the chips are.:
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  2. As Nico Zographos, dealer-extraordinaire for the 'Greek Syndicate' in Deauville, Cannes, and Monte Carlo in the s observed about casino gaming: . The odds bet in craps has zero house edge (although this bet cannot be made without making another negative expectation wager) and there are a few.:
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Superstition has long been a part of gambling - from both sides of the table. Superstitions can lead to irrational decisions that may hurt casino profits. For example, believing that a particular dealer is unlucky against a particular winning player may lead to a decision to change dealers. As many, if not most, players are superstitious.

At best, he may resent that the casino is trying to change his luck. At worst, the player may feel the new dealer is skilled in methods to "cool" the game. Perhaps he is even familiar with stories of old where casinos employed dealers to cheat "lucky" players. Understanding the mathematics of a game also is important for the casino operator to ensure that the reasonable expectations of the players are met. For most persons, gambling is entertainment. It provides an outlet for adult play.

As such, persons have the opportunity for a pleasant diversion from ordinary life and from societal and personal pressures. As an entertainment alternative, however, players may consider the value of the gambling experience. For example, some people may have the option of either spending a hundred dollars during an evening by going to a professional basketball game or at a licensed casino. If the house advantage is too strong and the person loses his money too quickly, he may not value that casino entertainment experience.

On the other hand, if a casino can entertain him for an evening, and he enjoys a "complimentary" meal or drinks, he may want to repeat the experience, even over a professional basketball game. Likewise, new casino games themselves may succeed or fail based on player expectations. In recent years, casinos have debuted a variety of new games that attempt to garner player interest and keep their attention.

Regardless of whether a game is fun or interesting to play, most often a player will not want to play games where his money is lost too quickly or where he has a exceptionally remote chance of returning home with winnings. Mathematics also plays an important part in meeting players' expectations as to the possible consequences of his gambling activities. If gambling involves rational decision-making, it would appear irrational to wager money where your opponent has a better chance of winning than you do.

Adam Smith suggested that all gambling, where the operator has an advantage, is irrational. He wrote "There is not, however, a more certain proposition in mathematics than that the more tickets [in a lottery] you advertise upon, the more likely you are a loser.

Adventure upon all the tickets in the lottery, and you lose for certain; and the greater the number of your tickets, the nearer you approach to this certainty. Even where the house has an advantage, however, a gambler may be justified if the amount lost means little to him, but the potential gain would elevate him to a higher standing of living.

He could save or gamble this money. Even if he did this for years, the savings would not elevate his economic status to another level. While the odds of winning are remote, it may provide the only opportunity to move to a higher economic class. Since the casino industry is heavily regulated and some of the standards set forth by regulatory bodies involve mathematically related issues, casino managers also should understand the mathematical aspects relating to gaming regulation.

Gaming regulation is principally dedicated to assuring that the games offered in the casino are fair, honest, and that players get paid if they win. Fairness is often expressed in the regulations as either requiring a minimum payback to the player or, in more extreme cases, as dictating the actual rules of the games offered. Casino executives should understand the impact that rules changes have on the payback to players to assure they meet regulatory standards.

Equally important, casino executives should understand how government mandated rules would impact their gaming revenues. The player's chances of winning in a casino game and the rate at which he wins or loses money depends on the game, the rules in effect for that game, and for some games his level of skill.

The amount of money the player can expect to win or lose in the long run - if the bet is made over and over again - is called the player's wager expected value EV , or expectation. When the player's wager expectation is negative, he will lose money in the long run. When the wager expectation is viewed from the casino's perspective i. For the roulette example, the house advantage is 5. The formal calculation is as follows: When this EV calculation is performed for a 1-unit amount, the negative of the resulting value is the house edge.

Here are the calculations for bets on a single-number in double-zero and single-zero roulette. Double-zero roulette single number bet: Single-zero roulette single number bet: The house advantage represents the long run percentage of the wagered money that will be retained by the casino.

It is also called the house edge, the "odds" i. Regardless of the method used to compute it, the house advantage represents the price to the player of playing the game. Because this positive house edge exists for virtually all bets in a casino ignoring the poker room and sports book where a few professionals can make a living , gamblers are faced with an uphill and, in the long run, losing battle.

There are some exceptions. Occasionally the casino will even offer a promotion that gives the astute player a positive expectation. These promotions are usually mistakes - sometimes casinos don't check the math - and are terminated once the casino realizes the player has the edge.

But by and large the player will lose money in the long run, and the house edge is a measure of how fast the money will be lost. The trick to intelligent casino gambling - at least from the mathematical expectation point of view - is to avoid the games and bets with the large house advantages.

Some casino games are pure chance - no amount of skill or strategy can alter the odds. These games include roulette, craps, baccarat, keno, the big-six wheel of fortune, and slot machines. Of these, baccarat and craps offer the best odds, with house advantages of 1. Roulette and slots cost the player more - house advantages of 5. Games where an element of skill can affect the house advantage include blackjack, video poker, and the four popular poker-based table games: Blackjack, the most popular of all table games, offers the skilled player some of the best odds in the casino.

The house advantage varies slightly depending on the rules and number of decks, but a player using basic strategy faces little or no disadvantage in a single-deck game and only a 0. Complete basic strategy tables can be found in many books and many casino-hotel gift shops sell color-coded credit card size versions.

Rule variations favorable to the player include fewer decks, dealer stands on soft seventeen worth 0. If the dealer hits soft seventeen it will cost you, as will any restrictions on when you can double down. Probability represents the long run ratio of of times an outcome occurs to of times experiment is conducted. Odds represent the long run ratio of of times an outcome does not occur to of times an outcome occurs.

The true odds of an event represent the payoff that would make the bet on that event fair. Confusion about Win Rate. There are all kinds of percentages in the world of gaming. Win percentage, theoretical win percentage, hold percentage, and house advantage come to mind.

Sometimes casino bosses use these percentages interchangeably, as if they are just different names for the same thing.

Admittedly, in some cases this is correct. House advantage is just another name for theoretical win percentage, and for slot machines, hold percentage is in principle equivalent to win percentage. But there are fundamental differences among these win rate measurements. The house advantage - the all-important percentage that explains how casinos make money - is also called the house edge, the theoretical win percentage, and expected win percentage. In double-zero roulette, this figure is 5.

In the long run the house will retain 5. In the short term, of course, the actual win percentage will differ from the theoretical win percentage the magnitude of this deviation can be predicted from statistical theory. The actual win percentage is just the actual win divided by the handle. Because of the law of large numbers - or as some prefer to call it, the law of averages - as the number of trials gets larger, the actual win percentage should get closer to the theoretical win percentage.

Because handle can be difficult to measure for table games, performance is often measured by hold percentage and sometimes erroneously called win percentage. Hold percentage is equal to win divided by drop. The drop and hold percentage are affected by many factors; we won't delve into these nor the associated management issues. House advantage and theoretical win percentage are the same thing, hold percentage is win over drop, win percentage is win over handle, win percentage approaches the house advantage as the number of plays increases, and hold percentage is equivalent to win percentage for slots but not table games.

Furthermore, the house advantage is itself subject to varying interpretations. In Let It Ride, for example, the casino advantage is either 3. Those familiar with the game know that the player begins with three equal base bets, but may withdraw one or two of these initial units. The final amount put at risk, then, can be one In the long run, the casino will win 3.

So what's the house edge for Let It Ride? Some prefer to say 3. Either way, the bottom line is the same either way: The question of whether to use the base bet or average bet size also arises in Caribbean Stud Poker 5. For still other games, the house edge can be stated including or excluding ties. The prime examples here are the player 1. Again, these are different views on the casino edge, but the expected revenue will not change. That the house advantage can appear in different disguises might be unsettling.

When properly computed and interpreted, however, regardless of which representation is chosen, the same truth read: Statistical theory can be used to predict the magnitude of the difference between the actual win percentage and the theoretical win percentage for a given number of wagers.

When observing the actual win percentage a player or casino may experience, how much variation from theoretical win can be expected? What is a normal fluctuation? The basis for the analysis of such volatility questions is a statistical measure called the standard deviation essentially the average deviation of all possible outcomes from the expected.

Together with the central limit theorem a form of the law of large numbers , the standard deviation SD can be used to determine confidence limits with the following volatility guidelines: Obviously a key to using these guidelines is the value of the SD. Computing the SD value is beyond the scope of this article, but to get an idea behind confidence limits, consider a series of 1, pass line wagers in craps.

they had both owned

In 19th-century America, there was enough of a tradition of using blue chips for higher values that "blue chip" in noun and adjective senses signaling high-value chips and high-value property are attested since and , respectively. Because eight is considered a lucky number in Chinese culture, chips denominated 8, 88, and e. They will sometimes contain an image of the animal associated with the year and are issued in a variety of colors.

Low-denomination yellow chips vary in value: Such chips are often yellow or orange. Casinos often use gaming plaques for these denominations: These plaques are about the size of a playing card, and must be marked with serial numbers.

Each casino has a unique set of chips, even if the casino is part of a greater company. This distinguishes a casino's chips from others, since each chip and token on the gaming floor has to be backed up with the appropriate amount of cash. In addition, with the exception of Nevada, casinos are not permitted to honor another casino's chips. The security features of casino chips are numerous.

Artwork is of a very high resolution or of photographic quality. Custom color combinations on the chip edge edge spots are usually distinctive to a particular casino. UV markings can be made on the inlay. Also, makers' marks are difficult to reproduce. Also being used by one manufacturer, Palm Gaming, is an audible taggant incorporated into the ceramic chip blank.

A simple handheld reader will beep if the gaming chip is authentic. Palm Gaming is even manufacturing custom made molds for their ceramic gaming chips- adding yet another high level of security to its gaming chip.

Counterfeit chips are rare. High levels of surveillance, along with staff familiarity with chip design and coloring, make passing fake chips difficult. Casinos, though, are prepared for this situation. All states require that casinos have a set of chips in reserve with alternate markings, [ citation needed ] though they may not be required to have exactly the same number of reserve chips as they do on the floor. Casino chips used in tournaments are usually much cheaper and of much simpler design.

Because the chips have no cash value, usually chips are designed with a single color usually differing in shade or tone from the version on the casino floor , a smaller breadth, and a basic mark on the interior to distinguish denominations; however, at certain events such as the World Series of Poker or other televised poker , chips approach quality levels of chips on the floor.

Several casinos, such as the Hard Rock Hotel and Casino in Las Vegas, issue "limited edition" varied-designed chips, commemorating various events, though retaining a common color scheme.

This encourages customers to keep them for souvenirs, at a profit to the casino. In certain casinos, such as the Wynn and Encore Casinos in Las Vegas, chips are embedded with RFID tags to help casinos keep better track of them, determine gamblers' average bet sizes, and to make them harder for counterfeiters to reproduce.

However, this technique is costly and considered by many to be unnecessary to profit. Also, this technology provides minimal benefits in games with layouts that do not provide gamblers with their own designated betting areas, such as craps. The first game show to use them, Duel , had a variation in which the contestants answer questions using oversized casino tokens.

The World Series of Poker at one time actually used its casino tokens for the poker tournaments, but in more recent years has had special Paulson WSOP clay sets made for the tournaments. From Wikipedia, the free encyclopedia. This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. November Learn how and when to remove this template message.

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In other projects Wikimedia Commons. As many, if not most, players are superstitious. At best, he may resent that the casino is trying to change his luck. At worst, the player may feel the new dealer is skilled in methods to "cool" the game. Perhaps he is even familiar with stories of old where casinos employed dealers to cheat "lucky" players.

Understanding the mathematics of a game also is important for the casino operator to ensure that the reasonable expectations of the players are met. For most persons, gambling is entertainment. It provides an outlet for adult play.

As such, persons have the opportunity for a pleasant diversion from ordinary life and from societal and personal pressures. As an entertainment alternative, however, players may consider the value of the gambling experience. For example, some people may have the option of either spending a hundred dollars during an evening by going to a professional basketball game or at a licensed casino.

If the house advantage is too strong and the person loses his money too quickly, he may not value that casino entertainment experience. On the other hand, if a casino can entertain him for an evening, and he enjoys a "complimentary" meal or drinks, he may want to repeat the experience, even over a professional basketball game.

Likewise, new casino games themselves may succeed or fail based on player expectations. In recent years, casinos have debuted a variety of new games that attempt to garner player interest and keep their attention. Regardless of whether a game is fun or interesting to play, most often a player will not want to play games where his money is lost too quickly or where he has a exceptionally remote chance of returning home with winnings. Mathematics also plays an important part in meeting players' expectations as to the possible consequences of his gambling activities.

If gambling involves rational decision-making, it would appear irrational to wager money where your opponent has a better chance of winning than you do. Adam Smith suggested that all gambling, where the operator has an advantage, is irrational. He wrote "There is not, however, a more certain proposition in mathematics than that the more tickets [in a lottery] you advertise upon, the more likely you are a loser.

Adventure upon all the tickets in the lottery, and you lose for certain; and the greater the number of your tickets, the nearer you approach to this certainty. Even where the house has an advantage, however, a gambler may be justified if the amount lost means little to him, but the potential gain would elevate him to a higher standing of living. He could save or gamble this money. Even if he did this for years, the savings would not elevate his economic status to another level.

While the odds of winning are remote, it may provide the only opportunity to move to a higher economic class. Since the casino industry is heavily regulated and some of the standards set forth by regulatory bodies involve mathematically related issues, casino managers also should understand the mathematical aspects relating to gaming regulation. Gaming regulation is principally dedicated to assuring that the games offered in the casino are fair, honest, and that players get paid if they win.

Fairness is often expressed in the regulations as either requiring a minimum payback to the player or, in more extreme cases, as dictating the actual rules of the games offered. Casino executives should understand the impact that rules changes have on the payback to players to assure they meet regulatory standards.

Equally important, casino executives should understand how government mandated rules would impact their gaming revenues. The player's chances of winning in a casino game and the rate at which he wins or loses money depends on the game, the rules in effect for that game, and for some games his level of skill.

The amount of money the player can expect to win or lose in the long run - if the bet is made over and over again - is called the player's wager expected value EV , or expectation.

When the player's wager expectation is negative, he will lose money in the long run. When the wager expectation is viewed from the casino's perspective i. For the roulette example, the house advantage is 5. The formal calculation is as follows: When this EV calculation is performed for a 1-unit amount, the negative of the resulting value is the house edge. Here are the calculations for bets on a single-number in double-zero and single-zero roulette.

Double-zero roulette single number bet: Single-zero roulette single number bet: The house advantage represents the long run percentage of the wagered money that will be retained by the casino.

It is also called the house edge, the "odds" i. Regardless of the method used to compute it, the house advantage represents the price to the player of playing the game. Because this positive house edge exists for virtually all bets in a casino ignoring the poker room and sports book where a few professionals can make a living , gamblers are faced with an uphill and, in the long run, losing battle.

There are some exceptions. Occasionally the casino will even offer a promotion that gives the astute player a positive expectation.

These promotions are usually mistakes - sometimes casinos don't check the math - and are terminated once the casino realizes the player has the edge. But by and large the player will lose money in the long run, and the house edge is a measure of how fast the money will be lost.

The trick to intelligent casino gambling - at least from the mathematical expectation point of view - is to avoid the games and bets with the large house advantages. Some casino games are pure chance - no amount of skill or strategy can alter the odds. These games include roulette, craps, baccarat, keno, the big-six wheel of fortune, and slot machines. Of these, baccarat and craps offer the best odds, with house advantages of 1.

Roulette and slots cost the player more - house advantages of 5. Games where an element of skill can affect the house advantage include blackjack, video poker, and the four popular poker-based table games: Blackjack, the most popular of all table games, offers the skilled player some of the best odds in the casino.

The house advantage varies slightly depending on the rules and number of decks, but a player using basic strategy faces little or no disadvantage in a single-deck game and only a 0. Complete basic strategy tables can be found in many books and many casino-hotel gift shops sell color-coded credit card size versions.

Rule variations favorable to the player include fewer decks, dealer stands on soft seventeen worth 0. If the dealer hits soft seventeen it will cost you, as will any restrictions on when you can double down. Probability represents the long run ratio of of times an outcome occurs to of times experiment is conducted. Odds represent the long run ratio of of times an outcome does not occur to of times an outcome occurs.

The true odds of an event represent the payoff that would make the bet on that event fair. Confusion about Win Rate. There are all kinds of percentages in the world of gaming. Win percentage, theoretical win percentage, hold percentage, and house advantage come to mind. Sometimes casino bosses use these percentages interchangeably, as if they are just different names for the same thing.

Admittedly, in some cases this is correct. House advantage is just another name for theoretical win percentage, and for slot machines, hold percentage is in principle equivalent to win percentage. But there are fundamental differences among these win rate measurements.

The house advantage - the all-important percentage that explains how casinos make money - is also called the house edge, the theoretical win percentage, and expected win percentage. In double-zero roulette, this figure is 5. In the long run the house will retain 5. In the short term, of course, the actual win percentage will differ from the theoretical win percentage the magnitude of this deviation can be predicted from statistical theory.

The actual win percentage is just the actual win divided by the handle. Because of the law of large numbers - or as some prefer to call it, the law of averages - as the number of trials gets larger, the actual win percentage should get closer to the theoretical win percentage. Because handle can be difficult to measure for table games, performance is often measured by hold percentage and sometimes erroneously called win percentage.

Hold percentage is equal to win divided by drop. The drop and hold percentage are affected by many factors; we won't delve into these nor the associated management issues.

House advantage and theoretical win percentage are the same thing, hold percentage is win over drop, win percentage is win over handle, win percentage approaches the house advantage as the number of plays increases, and hold percentage is equivalent to win percentage for slots but not table games. Furthermore, the house advantage is itself subject to varying interpretations. In Let It Ride, for example, the casino advantage is either 3. Those familiar with the game know that the player begins with three equal base bets, but may withdraw one or two of these initial units.

The final amount put at risk, then, can be one In the long run, the casino will win 3. So what's the house edge for Let It Ride? Some prefer to say 3. Either way, the bottom line is the same either way: The question of whether to use the base bet or average bet size also arises in Caribbean Stud Poker 5.

For still other games, the house edge can be stated including or excluding ties. The prime examples here are the player 1. Again, these are different views on the casino edge, but the expected revenue will not change.

That the house advantage can appear in different disguises might be unsettling. When properly computed and interpreted, however, regardless of which representation is chosen, the same truth read: Statistical theory can be used to predict the magnitude of the difference between the actual win percentage and the theoretical win percentage for a given number of wagers.

When observing the actual win percentage a player or casino may experience, how much variation from theoretical win can be expected? What is a normal fluctuation? The basis for the analysis of such volatility questions is a statistical measure called the standard deviation essentially the average deviation of all possible outcomes from the expected. Together with the central limit theorem a form of the law of large numbers , the standard deviation SD can be used to determine confidence limits with the following volatility guidelines: Obviously a key to using these guidelines is the value of the SD.

Computing the SD value is beyond the scope of this article, but to get an idea behind confidence limits, consider a series of 1, pass line wagers in craps. Since each wager has a 1. It can be shown calculations omitted that the wager standard deviation is for a single pass line bet is 1. Note that if the volatility analysis is done in terms of the percentage win rather than the number of units or amount won , the confidence limits will converge to the house advantage as the number of wagers increases.

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Vintage Las Vegas Themed Party. Our name is the big giveaway. Whether you are looking for an intimate 2 table Vegas experience or the full works we can provide the experience you are looking for. Table Footie World Cup. Table Footie World Cup Recreate a Champions League or World Cup table football tournament with group stages followed by the knockout rounds culminating in the grand final. Learn how to play in our structured tournament format complete with on-site instructor and tournament umpire.

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Plaques differ from chips in that they are larger, usually rectangular in shape and contain serial numbers. Money is exchanged for tokens in a casino at the casino cage, at the gaming tables, or at a cashier station. The tokens are interchangeable with money at the casino. They generally have no value outside of the casino, but certain businesses such as taxis or waiters—especially for tips in gambling towns may honor them informally.

Tokens are employed for several reasons. Because of the uniform size, shape, and patterns of stacks of chips, they are easier to tally compared to currency. This attribute also enables the pit boss or security to quickly verify the amount being paid, reducing the chance that a dealer might incorrectly pay a customer. The uniform weight of the casino's official tokens allows them to weigh great stacks or heaps of chips rather than tally them.

Though aids such as chip trays are far more common. Furthermore, it is observed that consumers gamble more freely with replacement currencies than with cash. Lastly, the chips are considered to be an integral part of the casino environment, and replacing them with some alternate currency would be unpopular.

Many casinos have eliminated the use of metal tokens and coins in their slot machines, in favor of paper receipts or pre-paid cards, which, while requiring heavy infrastructure costs to install, eliminate the coin handling expenses, jamming problems encountered in machines which took coins or tokens and can allow more game-specific technology in the space of a machine which would usually be dedicated to coin mechanisms.

Most casinos using receipts have automated machines at which customers may redeem receipts, eliminating the need for coin counting windows and decreasing labor costs. Casino chip collecting is a part of numismatics , more specifically as specialized exonumia collecting.

Several casinos sell custom-made sets of chips and one or two decks of cards stamped with the name of the casino on them. Each set is contained in a small briefcase or box. The ancestors of the modern casino token were the counters used to keep score in the card games Ombre and Quadrille. In , French Quadrille sets contained a number of different counters, known as jetons , fiches and mils. Unlike modern poker chips, they were colored differently only to determine player ownership for purposes of settling payments at the end of the game, with different denominations differentiated by different shapes that each counter type had.

In the early history of Poker during the 19th century, players seemed to use any small valuable object imaginable. Early poker players sometimes used jagged gold pieces, gold nuggets, gold dust, or coins as well as "chips" primarily made of ivory, bone, wood, paper, and a composition made from clay and shellac. Several companies between the s and the late s made clay composition poker chips. There were over designs from which to choose. Most chips were white, red, blue, and yellow, but they could be made in almost any color desired.

The vast majority of authentic casino chips are "clay" chips but can be more accurately described as compression molded chips. Modern clay chips are a composition of materials more durable than clay alone.

At least some percentage of the chips is of an earthen material such as sand, chalk, and clay similar to that found in cat litter. The process used to make these chips is a trade secret , and varies slightly by manufacturer, most being relatively expensive and time-consuming per chip. The edge spots, or inserts, are not painted on; to achieve this effect, this area of the clay is removed and then replaced with clay of a different color; this can be done to each chip individually or a strip can be taken out of a cylindrical block of material and replaced with the alternate color before the block is cut into chips.

The printed graphics on clay chips is called an inlay. Inlays are typically made of paper and are then clad with a plastic film applied to the chip prior to the compression molding process. During the molding process the inlay becomes permanently fastened to the chip and can not be removed from the chip without destroying the inlay.

Ceramic chips were introduced in the mid s as alternative to clay chips, and are also used in casinos, as well as being readily available to the home market. The ability to print lettering and graphics on the entire surface of the chip, instead of just the inlay, made them popular.

Ceramic chips are sometimes also referred to as clay or clay composite, but they are in fact an injection-molded chip made with a special plastic or resin formula that approximates the feel and sound of ceramic or porcelain.

There are less expensive chips for the home market, made from various forms of plastic and plastic covered metal slugs as well. There is no universally standardized color scheme for poker chip values, and schemes not only vary nationally and regionally, but even from venue to venue, or by event type within a single venue. Chip colors found in home sets typically include red, white, blue, and sometimes green and black; however, more recently a wide assortment of colors have become readily available, particularly in lower-cost ABS plastic chips.

Common additional colors are pink, purple, yellow, orange, and grey. Newer designs in home chips include three-color designs where a three-step molding process creates a chip with unique base, secondary, and detail colors. In casinos, uniform chip colors and sizes are sometimes specified by the local gaming control board for consistency.

For example, regulations in New Jersey [2] and Illinois [3] specify similar uniform colors. All US states where gambling is legal require that casino chips have a unique combination of edge spots for identification, the name and location of the casino and the chip's value, if any, impressed, printed, or molded onto the obverse and reverse of the token.

In 19th-century America, there was enough of a tradition of using blue chips for higher values that "blue chip" in noun and adjective senses signaling high-value chips and high-value property are attested since and , respectively.

Because eight is considered a lucky number in Chinese culture, chips denominated 8, 88, and e. They will sometimes contain an image of the animal associated with the year and are issued in a variety of colors. Low-denomination yellow chips vary in value:

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