Casino slot department
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Malfunctions are recorded and reported to slot mechanics, and other deviations are quickly detected and addressed. The slot monitor generates computer reports for each machine which reveal the amount of play, coins in, coins out, major jackpots, and player preference. As previously mentioned, slot machines periodically malfunction and require the services of another slot department employee--- the slot mechanic.
Top jackpots
Slot machine department
Today, in many gaming jurisdictions slots have become the leader in at least two areas: gaming revenue, and technology.
Slot machines were once thought to be a necessary evil, a diversion, something to keep the spouse happy while the real money was being wagered at the twenty-one, baccarat, or crap tables.
The slot department is headed by a slot manager or director of slot operations. This person analyzes daily slot revenues and is responsible for maximizing the layout, types, and denominations of machines on the casino floor.
Slot marketing and promotions are coordinated with this manager, and the success of each program is thoroughly scrutinized.
Comping policies for slot players are determined by the slot manager, who also establishes personnel policies and staffing requirements.
An assistant manager works in association with the slot manager. Day-to-day operations such as scheduling, employee disciplinary situations, and miscellaneous activities indigenous to the slot department are often handled by this employee.
Each shift is headed by a shift manager, who circulates on the casino floor, ensuring a smooth and efficient operation.
This manager constantly evaluates employee performance and verifies adherence to internal control procedures. Disputes with payouts are brought to the shift manager prior to being referred to the head of the department.
Larger casinos may employ an assistant shift manager.
The slot floorperson monitors the operation of slot machines makes sure change persons are circulating throughout the casino, and participates in the payment of 'handpay' jackpots.
Handpay jackpots exceed the slot machine's coin hopper capacity (1,200 to 1,500 coins in a quarter video poker machine) and are verified by the slot floorperson.
Slot jackpots won in the united states exceeding $1,200 require a tax declaration form, which is also handled by the slot floorperson.
When all the coins in a slot machine's hopper are dispensed, the floorperson does a hopper fill in conjunction with either casino security and/or change person, or shift manager.
Also, casinos allow floorpersons to attempt to fix minor slot machine malfunctions and specify a machine out of order if there is a major problem.
Casinos arrange special-attraction slot machines in a round or rectangular configuration known as a carousel and utilize a carousel attendant to dispense change, and draw attention to these machines.
Carousels are designed so that the attendant will be elevated within the configuration, which allows employee to move quickly and freely from machine to machine while keeping an eye on the entire bank. Carousel attendants' duties can best be described as a combination change person, booth cashier, and promoter.
The final coin-dispensing employee in the slot department is the changeperson. Using a change belt or a slot cart that holds rolls of coins, the changeperson circulates throughout the casino selling coin to slot patrons.
Changepersons either solicit sales by shouting 'change', or are called over and stopped by a slot player, or react to the change light (the 'candle' or 'lamp') on top of a machine, which has been activated by a player waiting for change.
Slot clubs are analogous to airline flier concepts. Slot players either enroll themselves in the club with a slot club attendant or are approached on the casino floor by a slot host.
Players who enroll are given a computerized card that can be inserted into any slot machine. An electronic message on the machine welcomes the player by name, and the computerized slot-tracking system records points for the player based on amounts wagered and duration of play.
Points are then redeemed by players for gifts or cash, depending on the casino's policy. Slot clubs come under the supervision of the director of slot marketing, who is responsible for designing additional slot promotions.
Slot tournaments involve invitations to frequent or preferred slot customers with a special bank of slot machines reserved for tournament play. Players play these machines, and the highest points totals/credits scored result in cash awards, or prizes.
As previously mentioned, slot machines periodically malfunction and require the services of another slot department employee--- the slot mechanic.
This employee normally is trained at a special school , or by the manufacturer of the various slot machines. This job is critical to the operation, since inoperative machines with prolonged downtimes can significantly impact slot revenues.
Additional duties include cleaning the interiors of the machines, installing new machines, and assisting in the movement of machines as directed by the slot manager.
One final employee found in this department is the slot monitor. This employee is employed only in highly computerized operations and monitors ongoing slot play, noting machines getting high-volume play and dispatching slot hosts to meet and greet players.
Malfunctions are recorded and reported to slot mechanics, and other deviations are quickly detected and addressed. The slot monitor generates computer reports for each machine which reveal the amount of play, coins in, coins out, major jackpots, and player preference.
These reports are used by the slot manager to alter the floor layout, moving less played machines into higher-traffic areas or removing machines that do not test well.
What does a slot attendant do?
Slot attendants play an important role in gambling casinos.
Erik snyder/photodisc/getty images
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Slot attendants serve as a link between a casino guest and the casino’s management. Each attendant looks after a number of slot machines, ensuring their proper functioning. The attendant also ensures the safety and comfort of the slot players. In some casinos, slot attendants pay players who have won a large amount of money and they promote special programs offered by the casino.
Machine function
A slot attendant ensures all the slot machines she is responsible for function properly. Casinos make no profit on slot machines that malfunction and prevent guests from using them. The attendant’s role is to alert machine repair mechanics to the problem to encourage rapid repair. In instances of minor issues, such as bill jams, an attendant may correct the malfunctions himself. Attendants must be aware of the model of all the machines in the casino, since guests will often have favorite models, such as video slots or reel slots, or favorite games, such as "double diamonds" or "video poker," and not know where to find them.
Safety and comfort
Slot attendants must also ensure all players are behaving properly. They circulate through the area of their machines and maintain surveillance of the players. Attendants call security when they see a guest who is making loud noises which annoy other players or behaving abusively toward guests or attendants. Attendants are called on to assist players who are disabled and need help. They often get requests for directions to restaurants or bathrooms. Slot attendants receive requests from other casino staff members to respond to guests’ complaints or special requests. Incumbent on slot attendants is the need to be knowledgeable about local gambling laws and rules established by the casino.
Pay big winners
Some casinos feature machines dedicated to slots which require a minimum $10 per spin and pay winnings with tokens. For large winnings on these slots and for others where large sums have been won, attendants supervise the payment of cash or the distribution of vouchers. Attendants also collect the required data from winners whose payments exceed the amount that must be reported to the internal revenue service.
Program promotion
Slot attendants proactively build relationships with guests. This helps them promote special programs of the casino. Among the commonly sponsored casino programs attendants help promote are hourly cash giveaways, monthly awards of new cars, free massages in the casino spa, rounds of golf, or meals in one of the casino restaurants. Attendants may be assigned to provide special service to wealthy players, called “high rollers,” who gamble large amounts of money.
Casino slot department
Slot machines
At casino copenhagen our guests can use over 140 slot machines, where the stakes can be varied between 1 dkk and up to about 200 dkk per game . That way there is something for everyone and every budget .
Mystery jackpot
A total of 42 machines are linked up to four new jackpots. The exciting thing about the four jackpots is that they all are released within a certain figure, shown on several displays.
To know when the jackpot latest is being triggered, contributes to a not insignificant intensity and excitement.
You know, when the jackpot is triggered - a the latest. For how long do you dare to wait. - only competitor is the other 41 machines.
Ticket in - ticket out
Almost all slot machines at casino copenhagen today is equipped with ticket in - ticket out.
This means that you as a guest can freely move your money between machines. You just press cash out and a small bar code ticket comes out, you can either exchange via an ATM for cash or use it in another machine.
Slot machines
The classic slot machine typically had 3 reels with different symbols ( horseshoes, bells , etc. ) and the game was activated with a pull in an " arm " . It was invented in the united states in the late 1800s.
Machines with fruit symbols appeared in early 1900s and the machines did not only pay out in real money - but also in chewing gum.
A lot has happened since the first slot machines appeared .
The modern machines available at casino copenhagen has a screen with virtual reels and buttons where you can decide how much you want to bet, how many lines you want to play. Often the slot machine contains quite a bit different games to choose from.
Pay outs
Coins are a part of history.
All slot machines at casino copenhagen accept cash and all major payments (over 10.000, - dkk.) will be issued by the casino staff who also will help answering any questions. The vast majority of transactions carried out by yourself via the ticket in - ticket out system. Before leaving the casino please exchang your tickets for cash.
You are always welcome to withdraw money in the casino or from an external ATM machine in the hotel lobby.
It is customary to give a share of payments to staff. On slot machines is usually 3%, which corresponds to the percentage on the gaming tables.
Casino: cage operations - the backbone of a casino
The casino cashierвђ™s cage is the operational nerve centre of casino operations. As a hub of activity, it performs many vital functions on a shift-by-shift, day-by-day basis. First, the cage, together with the vault, is responsible for the custodianship of and accountability for the casinoвђ™s bankroll. This involves the daily care, control, and accounting for thousands, hundreds of thousands, and even millions of dollars. After all, this is the casino industry we are talking about, with many high rollers playing for big money.
What is a casino cage?
To break things down, all transactions involving currency, coin, casino checks (chips), customer casino markers (ious), safekeeping funds, and customer front flow money to and from the cage and its related vault in a continuous cycle. Firstly, accurate recording procedures and adherence to sound internal controls are required to ensure bankroll safety and accountability at online casinos. Secondly, the cage provides a vital communication link to the casino pit or pit areas.
Services include providing check fills and credits to table games, as requested; supplying information regarding customer credit status; providing financing tabulations of table game activities documented by the master game report form; and keeping casino supervisors advised of the relevant information required for a smooth operation.
Thirdly, the cage deals with countless customer transactions. Front-line window cashiers handle casino chip exchanges for currency; cash personal, payroll, and travellerвђ™s checks; handle customer safekeeping and 'front money' transactions; receive customer marker payment; deal with casino promotional coupons, and provide information to customers.
The cashierвђ™s job
The main job of a casino cashier is to exchange casino chips for cash whenever the players bring their chips from tables like blackjack and craps. It is the cashierвђ™s job to greet the player, take the chips, break them down by denomination and pay the player the right amount. If the total being paid out is quite high, a casino supervisor may be called to verify the payout before the cashier transfers the money to the player.
While errors rarely happen during this process, it is possible, therefore, cashiers but be diligent and efficient when they handle casino chips as you wouldnвђ™t want either the casino or the player losing out. Cashiers would need basic math skills as well as the ability to distinguish the different chips used by the casino. If the casino makes use of slot machines that require players to insert coins, the cage and cashier will also have to accept and exchange these coin buckets.
The coins are taken to a coin sorter with the player in attendance, where the coins are counted. The total amount will be shown on the machine reader, and the cashier must pay this amount to the player. This not only saves time as the cashier does not have to manually count the coins but also prevents errors from taking place.
Cage cashiers must also handle a certain amount of paperwork when dealing with daily transactions, including balancing books and invoices. Cashiers may also need to run internal checks on gamblers who require credit or to process credit applications for new customers. They may also need to assist with cashing in tips for fellow employees.
It is important that the cashier have good people skills as you will be working with gamblers all day long. Cashiers must be able to satisfy the needs of all players, and be able to handle any negative or hostile situation that may arise. People may get antsy when money is involved, so it is important for cashiers to be able to control the situation and sort out any issues immediately and in the most professional manner. Many gamblers enjoy drinking while playing, therefore cashiers may also have to deal with intoxicated customers. Cashiers must be aware of all the relevant rules and regulations associated with the casino and gaming industry and be able to explain them when the situation arises.
The blood line of the casino
Fourthly, the cage interfaces with virtually every casino department--- for example, transmittal of key forms to the accounting department; involvement with the hard and soft count audit teams; receiving and issuing cashiers banks to casino revenue departments (bar banks, showroom banks, race and sports book banks, hotel front-desk banks, etc.); and working with the security department during the table game fill and credit process.
In some casinos, the cage supports the slot department by providing slot fills, supplying change persons with requested coins, and providing large jackpot payoffs. The cage is also charged with the responsibility of preparing and maintaining countless forms required for sound internal control procedures and safeguarding the casino's assets. Additionally, compliance with requirements and procedures of the bank secrecy act is a critical responsibility of casino cage personnel. However, many casinos locate the cage toward the rear of the casino property and away from customer exits.
Keeping it safe: window cage security
One reason for this is to minimise the chances of a successful cage robbery. A second reason for locating the cage in the rear is the psychological factor. A customer cashing out at the window must walk the length of the casino toward the exit. The temptation of 'one last slot pull' or 'one final play at the table' can decrease the amount of money the customer takes out the front door. A third consideration is the location of the pit or live gaming areas. There are a number of structural possibilities for the cage facade. Metal bars, others by plexiglas or shatterproof windows, protect some cages.
Still, others are 'open' cages with no protective barriers. It all depends on the environment and management's perceived need for physical security. A small cage operation will typically offer two customer service windows and an additional window to service casino, slot, or employee requests. The larger the operation, the more service windows required, but keep in mind that customers do not to stand in long lines to cash their chips. It is better to have too many operational windows and window cage security than too few.
Casino cage operations and cashiers may not be necessary for the future as more and more casinos are now using coinless slot machines, which has made things a lot easier. With no coins to count, things are less likely to go wrong, fewer employees will be needed and there will less room for error. Some slot machines print out a bar-coded voucher instead of coins or cash that can then be cashed out ATM-type machines or at the cashier cage.
The bar-code will indicate a legitimate voucher and is read using a reader, which will reveal the amount the player must be paid. The casino cage is one of the most important and highly functional aspects of a casino and needs to be treated as such. It is important to be respectful and civilised to your cashier at all times. Whenever you visit a casino, make sure to adhere to the rules of the establishment so that everyone can have an enjoyable experience.
Casino: cage operations - the backbone of a casino
The casino cashierвђ™s cage is the operational nerve centre of casino operations. As a hub of activity, it performs many vital functions on a shift-by-shift, day-by-day basis. First, the cage, together with the vault, is responsible for the custodianship of and accountability for the casinoвђ™s bankroll. This involves the daily care, control, and accounting for thousands, hundreds of thousands, and even millions of dollars. After all, this is the casino industry we are talking about, with many high rollers playing for big money.
What is a casino cage?
To break things down, all transactions involving currency, coin, casino checks (chips), customer casino markers (ious), safekeeping funds, and customer front flow money to and from the cage and its related vault in a continuous cycle. Firstly, accurate recording procedures and adherence to sound internal controls are required to ensure bankroll safety and accountability at online casinos. Secondly, the cage provides a vital communication link to the casino pit or pit areas.
Services include providing check fills and credits to table games, as requested; supplying information regarding customer credit status; providing financing tabulations of table game activities documented by the master game report form; and keeping casino supervisors advised of the relevant information required for a smooth operation.
Thirdly, the cage deals with countless customer transactions. Front-line window cashiers handle casino chip exchanges for currency; cash personal, payroll, and travellerвђ™s checks; handle customer safekeeping and 'front money' transactions; receive customer marker payment; deal with casino promotional coupons, and provide information to customers.
The cashierвђ™s job
The main job of a casino cashier is to exchange casino chips for cash whenever the players bring their chips from tables like blackjack and craps. It is the cashierвђ™s job to greet the player, take the chips, break them down by denomination and pay the player the right amount. If the total being paid out is quite high, a casino supervisor may be called to verify the payout before the cashier transfers the money to the player.
While errors rarely happen during this process, it is possible, therefore, cashiers but be diligent and efficient when they handle casino chips as you wouldnвђ™t want either the casino or the player losing out. Cashiers would need basic math skills as well as the ability to distinguish the different chips used by the casino. If the casino makes use of slot machines that require players to insert coins, the cage and cashier will also have to accept and exchange these coin buckets.
The coins are taken to a coin sorter with the player in attendance, where the coins are counted. The total amount will be shown on the machine reader, and the cashier must pay this amount to the player. This not only saves time as the cashier does not have to manually count the coins but also prevents errors from taking place.
Cage cashiers must also handle a certain amount of paperwork when dealing with daily transactions, including balancing books and invoices. Cashiers may also need to run internal checks on gamblers who require credit or to process credit applications for new customers. They may also need to assist with cashing in tips for fellow employees.
It is important that the cashier have good people skills as you will be working with gamblers all day long. Cashiers must be able to satisfy the needs of all players, and be able to handle any negative or hostile situation that may arise. People may get antsy when money is involved, so it is important for cashiers to be able to control the situation and sort out any issues immediately and in the most professional manner. Many gamblers enjoy drinking while playing, therefore cashiers may also have to deal with intoxicated customers. Cashiers must be aware of all the relevant rules and regulations associated with the casino and gaming industry and be able to explain them when the situation arises.
The blood line of the casino
Fourthly, the cage interfaces with virtually every casino department--- for example, transmittal of key forms to the accounting department; involvement with the hard and soft count audit teams; receiving and issuing cashiers banks to casino revenue departments (bar banks, showroom banks, race and sports book banks, hotel front-desk banks, etc.); and working with the security department during the table game fill and credit process.
In some casinos, the cage supports the slot department by providing slot fills, supplying change persons with requested coins, and providing large jackpot payoffs. The cage is also charged with the responsibility of preparing and maintaining countless forms required for sound internal control procedures and safeguarding the casino's assets. Additionally, compliance with requirements and procedures of the bank secrecy act is a critical responsibility of casino cage personnel. However, many casinos locate the cage toward the rear of the casino property and away from customer exits.
Keeping it safe: window cage security
One reason for this is to minimise the chances of a successful cage robbery. A second reason for locating the cage in the rear is the psychological factor. A customer cashing out at the window must walk the length of the casino toward the exit. The temptation of 'one last slot pull' or 'one final play at the table' can decrease the amount of money the customer takes out the front door. A third consideration is the location of the pit or live gaming areas. There are a number of structural possibilities for the cage facade. Metal bars, others by plexiglas or shatterproof windows, protect some cages.
Still, others are 'open' cages with no protective barriers. It all depends on the environment and management's perceived need for physical security. A small cage operation will typically offer two customer service windows and an additional window to service casino, slot, or employee requests. The larger the operation, the more service windows required, but keep in mind that customers do not to stand in long lines to cash their chips. It is better to have too many operational windows and window cage security than too few.
Casino cage operations and cashiers may not be necessary for the future as more and more casinos are now using coinless slot machines, which has made things a lot easier. With no coins to count, things are less likely to go wrong, fewer employees will be needed and there will less room for error. Some slot machines print out a bar-coded voucher instead of coins or cash that can then be cashed out ATM-type machines or at the cashier cage.
The bar-code will indicate a legitimate voucher and is read using a reader, which will reveal the amount the player must be paid. The casino cage is one of the most important and highly functional aspects of a casino and needs to be treated as such. It is important to be respectful and civilised to your cashier at all times. Whenever you visit a casino, make sure to adhere to the rules of the establishment so that everyone can have an enjoyable experience.
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MGM grand las vegas offers text alerts to consumers interested in receiving property discounts as well as event and information related to MGM grand las vegas. A message will be sent to your mobile device for verification.
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Work for carnival corporation casino department
Speedy global provides asian casino crew to the worlds largest international cruise line company.
Keywords: working, carnival corporation, global casino operations, casino, cruise ship casino, casino jobs
Introduction
- Speedy global is a specialist provider of asian casino workers to international cruise ships. We have supplied crew from all over asia and we are an official manning agent for carnival corporation global casino operations (GCO) for australia, cambodia, indonesia, japan, malaysia, myanmar, new zealand, singapore, south korea, taiwan, thailand and vietnam.
- Carnival corporation global casino operations (GCO) is responsible for the casino operations on all carnival corporation's cruise ships, regardless of brand. However, we only supply for the english-speaking ship brands, which includes: carnival cruise line, cunard, holland america line, P&O cruises, P&O australia, princess cruises and seabourn.
- Confirm our association at carnival corporation global casino operations' website.
Contracts
- All GCO’S jobs are contract-positions; however, candidates should look at them as permanent jobs. We are not looking for people who want to do one contract on a ship for fun but rather those who have a genuine desire to start a career working with international cruise lines.
- Contracts are normally between six (06) to eight (08) months long. You will then have one (01) week holiday for every month worked (i.E. If you have worked eight (08) months onboard, you would have eight (08) weeks off for vacation at home country). You would then return to another ship in the fleet on another six (06) to eight (08) month contract. This cycle will repeat for the whole of your career.
- Your next contract is normally issued to you before you complete the current one in order to allow you to know your exact start date, position, etc. In advance for your preparation. You can then get any requirements done for your next deployment and enjoy your holiday with the 1,000's of US dollars that you just save from your current one.
Benefits
- Be hired and paid according to your experience and qualification.
- Have opportunities to be recognized, trained and promoted internally onboard based on your performance.
- Have opportunities to attend various training courses onboard.
- Have free accommodation, meals and medical during the whole contract length.
- Travel to many attractive places around the world and make international friends.
- Work in a dynamic, multi-national, friendly, safe and professional working environment.
- Contracts are generally from six (06) to eight (08) months, followed by several weeks of vacation at home country.
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Dealer
Dealers (table gaming applicants) level 2 and 3
Position overview:
- A dealer has to be competent and floor-experienced in dice (or craps), blackjack, caribbean stud poker, three card poker and roulette before they can be recommended for the position of dealer 4.
- Dealer 4 staff must meet or surpass the required standard in all key areas of their performance (technical ability, adherence to procedures, guest service and attitude).
Objective:
- Ensure that all accounting operations are carried out to the highest standard of efficiency, security and customer service in accordance with GCO operations’ manual.
Requirements:
- Have at least one (01) year blackjack proficiency in any licensed casino.
- Possess good english communication skills (marlins english test result from 80%).
- Be from 21 international years of age.
- Have clear communication skills and good customer service.
- Be able to work well under high pressure and adapt quickly.
- Have high responsibilities and self-discipline.
- Love meeting many people and dealing with your teammates and colleagues from other departments onboard and guests from all over the world.
Primary job functions:
- Assist in any duties of a safety nature as requested by ship’s command, i.E. Safety drills; port manning or gangway duties.
- Possess a sound working knowledge of the GCO’s gaming manual.
- Deal all games to correct gaming procedures as laid down in the GCO’s gaming manual.
- Deal games in a non-intimidating, friendly and professional manner.
- Work cohesively as a team with casino management and supervisors, as well as work independently with little or no supervision.
- Keep supervisors informed by means of clear commentary on all operations and transactions.
- Liaise and co-operate with colleagues whilst dealing to ensure smoothness and efficiency when running the gaming tables.
- Report any discrepancies or incidents of a doubtful nature to the casino manager.
- Refer any dispute or argument concerning a guest to the immediate supervisor.
- Perform revenue counts as instructed by casino management, i.E. Soft count; stacker and /or coin counts.
- Participate in day to day operational needs as deemed necessary by the casino management.
Additional information regarding responsibilities:
- Assist the casino host with any promotional activity when necessary, i.E. Tournaments.
- Attend casino staff meetings as required.
- Transfer to other vessels within carnival corporation, when deemed necessary by members of the casino executive office.
Additional information regarding casino experience:
- The principal games dealt on GCO's ships are blackjack, american roulette, dice (or craps) and various poker games. Any applicant for a dealer position is required to have at least one (01) year experience in any licensed casino in blackjack and/ or roulette.
- Successful applicants will be interviewed, and table tested by a carnival casino representative.
Income:
| position name | daily pay rate | plus monthly tips or commission | notes |
|---|---|---|---|
| dealer 1 (level B) * | $10 | at least $500 USD per month |
|
| Dear 2 and 3 | $10 | at least $1,000 USD per month | full tip point |
| dealer 4 | $15 | at least $1,000 USD per month | full tip point |
* dealers are paid a day rate ( fixed) and tips ( variable). For this reason, the income for a month can vary depending upon the number of days in the month and the number of tips collected.
Clinton onboard carnival UK
Linda onboard holland america line
Myo myint onboard carnival cruise line
Slot technician
All levels of technical slots
Position overview :
- The difference in titles pertains to the fact that a technician 2 has full understanding, technical knowledge and practice in all fields of his/ her job description, as opposed to a technician 1 still accumulating this knowledge.
Objective :
- Assist the slot manager in the smooth running of the technical side of the casino operation, both with the slot machines and all other casino related equipment under the control of the slot manager.
Requirements :
- Have at least one (01) year of experience in the casino business and/ or relevant technical employment in the telecommunications/ I.T. Or electronics fields e.G.:
- experienced electronic engineers/ technicians who have a minimum of one (01) year experience in their field to repair and maintain slot machines onboard, OR
- experienced electronic engineers/ technicians who have a minimum of one (01) year experience in modern PC computer repair, local area networks and software installation and fault identification/correction, OR
- experienced network engineers/ technicians with modern TCP/ IP networks included wired and wireless.
- Possess good english communication skills (marlins english test result from 80%).
- Be from 21 international years of age.
- Have clear communication skills and good customer service.
- Be able to work well under high pressure and adapt quickly.
- Have high responsibilities and self-discipline.
- Love meeting many people and dealing with your teammates and colleagues from other departments onboard and guests from all over the world.
Primary job functions:
- Assist in any duties of a safety nature as requested by ship’s command, i.E. Safety drills; port manning or gangway duties.
- The casino slot technician is responsible for the upkeep, maintenance and security of all slot and video arcade machines, funds contained therein and their associated systems and further expected to provide the same degree of service maintenance for supplementary casino equipment.
- Gather analytical data from gaming machines as instructed by the casino executive office.
- Set-up, collect and carry out coin drop counts in accordance with established GCO's procedures per shipboard schedule.
- Assist in all hand paid jackpots, hopper fills and change machine fills according to GCO's policy and procedures and in the collection of machine bill stackers during slot revenue counts.
- Assist with all slot department configurations, conversions, installations as needed,
working on port days where scheduling has been deemed necessary. - Provide a high level of guest service.
- Refer any disputes or arguments concerning a guest to the casino manager and /or slot
manager.
Additional information regarding responsibilities:
- Assist in the repair and maintenance of the following equipment: tables and ancillary equipment, photocopiers, casino intercom systems and computer related products (when no computer/I.S. Officer is available)
- Install all casino safes, perma-vaults, key files etc.
- Attend casino staff meetings as required.
- Transfer to other vessels within carnival corporation, when deemed necessary by members of the casino executive office.
Income :
Position name
Daily pay rate
(min - max)
Plus monthly tips or commission
* slot managers do not get floor tips but they do get a share of on-board and fleet casino revenue.
Casino slot department
This guide, written by casino math professor robert hannum, contains a brief, non-technical discussion of the basic mathematics governing casino games and shows how casinos make money from these games. The article addresses a variety of topics, including house advantage, confusion about win rates, game volatility, player value and comp policies, casino pricing mistakes, and regulatory issues. Statistical advantages associated with the major games are also provided.
- Introduction
- Why is mathematics important?
- The house edge
- Probability versus odds
- Confusion about win rate
- Volatility and risk
- Player value and complimentaries
- Gaming regulation and mathematics
- Summary tables for house advantage
At its core the business of casino gaming is pretty simple. Casinos make money on their games because of the mathematics behind the games. As nico zographos, dealer-extraordinaire for the 'greek syndicate' in deauville, cannes, and monte carlo in the 1920s observed about casino gaming: "there is no such thing as luck. It is all mathematics."
With a few notable exceptions, the house always wins - in the long run - because of the mathematical advantage the casino enjoys over the player. That is what mario puzo was referring to in his famous novel fools die when his fictional casino boss character, gronevelt, commented: "percentages never lie. We built all these hotels on percentages. We stay rich on the percentage. You can lose faith in everything, religion and god, women and love, good and evil, war and peace. You name it. But the percentage will always stand fast."
Puzo is, of course, right on the money about casino gaming. Without the "edge," casinos would not exist. With this edge, and because of a famous mathematical result called the law of large numbers, a casino is guaranteed to win in the long run.
Why is mathematics important?
Critics of the gaming industry have long accused it of creating the name "gaming" and using this as more politically correct than calling itself the "gambling industry." the term "gaming," however, has been around for centuries and more accurately describes the operators' view of the industry because most often casino operators are not gambling. Instead, they rely on mathematical principles to assure that their establishment generates positive gross gaming revenues. The operator, however, must assure the gaming revenues are sufficient to cover deductions like bad debts, expenses, employees, taxes and interest.
Despite the obvious, many casino professionals limit their advancements by failing to understand the basic mathematics of the games and their relationships to casino profitability. One casino owner would often test his pit bosses by asking how a casino could make money on blackjack if the outcome is determined simply by whether the player or the dealer came closest to 21. The answer, typically, was because the casino maintained "a house advantage." this was fair enough, but many could not identify the amount of that advantage or what aspect of the game created the advantage. Given that products offered by casinos are games, managers must understand why the games provide the expected revenues. In the gaming industry, nothing plays a more important role than mathematics.
Mathematics should also overcome the dangers of superstitions. An owner of a major las vegas strip casino once experienced a streak of losing substantial amounts of money to a few "high rollers." he did not attribute this losing streak to normal volatility in the games, but to bad luck. His solution was simple. He spent the evening spreading salt throughout the casino to ward off the bad spirits. Before attributing this example to the idiosyncrasies of one owner, his are atypical only in their extreme. 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. For example, a person with an annual income of $30,000 may have $5 in disposable weekly income. He could save or gamble this money. By saving it, at the end of a year, he would have $260. Even if he did this for years, the savings would not elevate his economic status to another level. As an alternative, he could use the $5 to gamble for the chance to win $1 million. 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. For a $5 bet on the color red in roulette, for example, the expectation is -$0.263. On the average the player will lose just over a quarter for each $5 bet on red.
When the wager expectation is viewed from the casino's perspective (i.E., the negative of the player's expectation) and expressed as a percentage, you have the house advantage. For the roulette example, the house advantage is 5.26% ($0.263 divided by $5). The formal calculation is as follows:
EV = (+5)(18/38) + (-5)(20/38) = -0.263
(house advantage = 0.263/5 = 5.26%)
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):
EV = (+35)(1/38) + (-1)(37/38) = -0.053
(house advantage = 5.3%)
Single-zero roulette (single number bet):
EV = (+35)(1/37) + (-1)(36/37) = -0.027
(house advantage = 2.7%)
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.E., avoid games with bad odds), or just the "percentage" (as in mario puzo's fools die). Although the house edge can be computed easily for some games - for example, roulette and craps - for others it requires more sophisticated mathematical analysis and/or computer simulations. 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. 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 video poker machines that return greater than 100% if played with perfect strategy. 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. A player betting in a game with a 4% house advantage will tend to lose his money twice as fast as a player making bets with a 2% house edge. 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 1.2% and less than 1% (assuming only pass/come with full odds), respectively. Roulette and slots cost the player more - house advantages of 5.3% for double-zero roulette and 5% to 10% for slots - while the wheel of fortune feeds the casino near 20% of the wagers, and keno is a veritable casino cash cow with average house advantage close to 30%.
Games where an element of skill can affect the house advantage include blackjack, video poker, and the four popular poker-based table games: caribbean stud poker, let it ride, three card poker, and pai gow poker. For the poker games, optimal strategy results in a house edge in the 3% to 5% range (CSP has the largest house edge, PGP the lowest, with LIR and TCP in between). For video poker the statistical advantage varies depending on the particular machine, but generally this game can be very player friendly - house edge less than 3% is not uncommon and some are less than 1% - if played with expert strategy.
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 0.5% house edge in the common six-deck game. Despite these numbers, the average player ends up giving the casino a 2% edge due to mistakes and deviations from basic strategy. 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 0.2%), doubling after splitting (0.14%), late surrender (worth 0.06%), and early surrender (uncommon, but worth 0.24%). 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). If a card is randomly selected from a standard deck of 52 playing cards, the probability it is a spade is 1/4; the odds (against spade) are 3 to 1. The true odds of an event represent the payoff that would make the bet on that event fair. For example, a bet on a single number in double-zero roulette has probability of 1/38, so to break even in the long run a player would have to be paid 37 to 1 (the actual payoff is 35 to 1).
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 5.3%. In the long run the house will retain 5.3% of the money wagered. 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. In nevada, this figure is about 24% for roulette. The drop and hold percentage are affected by many factors; we won't delve into these nor the associated management issues. Suffice it to say that the casino will not in the long term keep 24% of the money bet on the spins of roulette wheel - well, an honest casino won't.
To summarize: 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.
· hold % = win/drop
· win % (actual) = win/handle
· H.A. = theoretical win % = limit(actual win %) = limit(win/handle)
· hold percentage ¹ house edge
Furthermore, the house advantage is itself subject to varying interpretations. In let it ride, for example, the casino advantage is either 3.51% or 2.86% depending on whether you express the advantage with respect to the base bet or the average bet. 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 (84.6% of the time assuming proper strategy), two (8.5%), or three units (6.9%), making the average bet size 1.224 units. In the long run, the casino will win 3.51% of the hands, which equates to 2.86% of the money wagered. So what's the house edge for let it ride? Some prefer to say 3.51% per hand, others 2.86% per unit wagered. No matter. Either way, the bottom line is the same either way: assuming three $1 base bets, the casino can expect to earn 3.5¢ per hand (note that 1.224 x 0.0286 = 0.035).
The question of whether to use the base bet or average bet size also arises in caribbean stud poker (5.22% vs. 2.56%), three card poker (3.37% vs. 2.01%), casino war (2.88% vs. 2.68%), and red dog (2.80% vs. 2.37%).
For still other games, the house edge can be stated including or excluding ties. The prime examples here are the player (1.24% vs. 1.37%) and banker (1.06% vs. 1.17%) bets in baccarat, and the don't pass bet (1.36% vs. 1.40%) in craps. 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: money) emerges: expected win is the same.
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:
Volatility analysis guidelines
· only 5% of the time will outcomes will be more than 2 SD's from expected outcome
· almost never (0.3%) will outcomes be more than 3 SD's from expected outcome
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 1,000 pass line wagers in craps. Since each wager has a 1.4% house advantage, on average the player will be behind by 14 units. It can be shown (calculations omitted) that the wager standard deviation is for a single pass line bet is 1.0, and for 1,000 wagers the SD is 31.6. Applying the volatility guidelines, we can say that there is a 95% chance the player's actual win will be between 49 units ahead and 77 units behind, and almost certainly between 81 units ahead and 109 units behind.
A similar analysis for 1,000 single-number wagers on double-zero roulette (on average the player will be behind 53 units, wager SD = 5.8, 1,000 wager SD = 182.2) will yield 95% confidence limits on the player win of 311 units ahead and 417 units behind, with win almost certainly between 494 units ahead and 600 units behind.
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. This is the result of the law of large numbers - as the number of trials gets larger, the actual win percentage should get closer to the theoretical win percentage. Risk in the gaming business depends on the house advantage, standard deviation, bet size, and length of play.
Player value and complimentaries
Using the house advantage, bet size, duration of play, and pace of the game, a casino can determine how much it expects to win from a certain player. This player earning potential (also called player value, player worth, or theoretical win) can be calculated by the formula:
Earning potential = average bet ´ hours played ´ decisions per hour ´ house advantage
For example, suppose a baccarat player bets $500 per hand for 12 hours at 60 hands per hour. Using a house advantage of 1.2%, this player's worth to the casino is $4,320 (500 ´ 12 ´ 60 ´ .012). A player who bets $500 per spin for 12 hours in double-zero roulette at 60 spins per hour would be worth about $19,000 (500 ´ 12 ´ 60 ´ .053).
Many casinos set comp (complimentary) policies by giving the player back a set percentage of their earning potential. Although comp and rebate policies based on theoretical loss are the most popular, rebates on actual losses and dead chip programs are also used in some casinos. Some programs involve a mix of systems. The mathematics associated with these programs will not be addressed in this article.
In an effort to entice players and increase business, casinos occasionally offer novel wagers, side bets, increased payoffs, or rule variations. These promotions have the effect of lowering the house advantage and the effective price of the game for the player. This is sound reasoning from a marketing standpoint, but can be disastrous for the casino if care is not taken to ensure the math behind the promotion is sound. One casino offered a baccarat commission on winning banker bets of only 2% instead of the usual 5%, resulting in a 0.32% player advantage. This is easy to see (using the well-known probabilities of winning and losing the banker bet):
EV = (+0.98)(.4462) + (-1)(.4586) = 0.0032
(house advantage = -0.32%)
A casino in biloxi, mississippi gave players a 12.5% edge on sic bo bets of 4 and 17 when they offered 80 to 1 payoffs instead of the usual 60 to 1. Again, this is an easy calculation. Using the fact that the probability of rolling a total of 4 (same calculation applies for a total of 17) with three dice is 1/72 (1/6 x 1/6 x 1/6 x 3), here are the expected values for both the usual and the promotional payoffs:
Usual 60 to 1 payoff: EV = (+60)(1/72) + (-1)(71/72) = -0.153
(house advantage = 15.3%)
Promotional 80 to 1 payoff: EV = (+80)(1/72) + (-1)(71/72) = +0.125
(house advantage = -12.5%)
In other promotional gaffes, an illinois riverboat casino lost a reported $200,000 in one day with their "2 to 1 tuesdays" that paid players 2 to 1 (the usual payoff is 3 to 2) on blackjack naturals, a scheme that gave players a 2% advantage. Not to be outdone, an indian casino in california paid 3 to 1 on naturals during their "happy hour," offered three times a day, two days a week for over two weeks. This promotion gave the player a whopping 6% edge. A small las vegas casino offered a blackjack rule variation called the "free ride" in which players were given a free right-to-surrender token every time they received a natural. Proper use of the token led to a player edge of 1.3%, and the casino lost an estimated $17,000 in eight hours. Another major las vegas casino offered a "50/50 split" blackjack side bet that allowed the player to stand on an initial holding of 12-16, and begin a new hand for equal stakes against the same dealer up card. Although the game marketers claimed the variation was to the advantage of the casino, it turned out that players who exercised the 50/50 split only against dealer 2-6 had a 2% advantage. According to one pit boss, the casino suffered a $230,000 loss in three and a half days.
In the gaming business, it's all about "bad math" or "good math." honest games based on good math with positive house advantage minimize the short-term risk and ensure the casino will make money in the long run. Players will get "lucky" in the short term, but that is all part of the grand design. Fluctuations in both directions will occur. We call these fluctuations good luck or bad luck depending on the direction of the fluctuation. There is no such thing as luck. It is all mathematics.
Gaming regulation and mathematics
Casino gaming is one of the most regulated industries in the world. Most gaming regulatory systems share common objectives: keep the games fair and honest and assure that players are paid if they win. Fairness and honesty are different concepts. A casino can be honest but not fair. Honesty refers to whether the casino offers games whose chance elements are random. Fairness refers to the game advantage - how much of each dollar wagered should the casino be able to keep? A slot machine that holds, on average, 90% of every dollar bet is certainly not fair, but could very well be honest (if the outcomes of each play are not predetermined in the casino's favor). Two major regulatory issues relating to fairness and honesty - ensuring random outcomes and controlling the house advantage - are inextricably tied to mathematics and most regulatory bodies require some type of mathematical analysis to demonstrate game advantage and/or confirm that games outcomes are random. Such evidence can range from straightforward probability analyses to computer simulations and complex statistical studies. Requirements vary across jurisdictions, but it is not uncommon to see technical language in gaming regulations concerning specific statistical tests that must be performed, confidence limits that must be met, and other mathematical specifications and standards relating to game outcomes.
Summary tables for house advantage
The two tables below show the house advantages for many of the popular casino games. The first table is a summary of the popular games and the second gives a more detailed breakdown.
| House advantages for popular casino games | |
| game | house advantage |
| roulette (double-zero) | 5.3% |
| craps (pass/come) | 1.4% |
| craps (pass/come with double odds) | 0.6% |
| blackjack - average player | 2.0% |
| blackjack - 6 decks, basic strategy* | 0.5% |
| blackjack - single deck, basic strategy* | 0.0% |
| baccarat (no tie bets) | 1.2% |
| caribbean stud* | 5.2% |
| let it ride* | 3.5% |
| three card poker* | 3.4% |
| pai gow poker (ante/play)* | 2.5% |
| slots | 5% - 10% |
| video poker* | 0.5% - 3% |
| keno (average) | 27.0% |
| *optimal strategy | |
| House advantages for major casino wagers | ||
| game | bet | HA* |
| baccarat | banker (5% commission) | 1.06% |
| baccarat | player | 1.24% |
| big six wheel | average | 19.84% |
| blackjack | card-counting | -1.00% |
| blackjack | basic strategy | 0.50% |
| blackjack | average player | 2.00% |
| blackjack | poor player | 4.00% |
| caribbean stud | ante | 5.22% |
| casino war | basic bet | 2.88% |
| craps | any craps | 11.11% |
| craps | any seven | 16.67% |
| craps | big 6, big 8 | 9.09% |
| craps | buy (any) | 4.76% |
| craps | C&E | 11.11% |
| craps | don't pass/don't come | 1.36% |
| craps | don't pass/don't come w/1X odds | 0.68% |
| craps | don't pass/don't come w/2X odds | 0.45% |
| craps | don't pass/don't come w/3X odds | 0.34% |
| craps | don't pass/don't come w/5X odds | 0.23% |
| craps | don't pass/don't come w/10X odds | 0.12% |
| craps | don't place 4 or 10 | 3.03% |
| craps | don't place 5 or 9 | 2.50% |
| craps | don't place 6 or 8 | 1.82% |
| craps | field (2 and 12 pay double) | 5.56% |
| craps | field (2 or 12 pays triple) | 2.78% |
| craps | hard 4, hard 10 | 11.11% |
| craps | hard 6, hard 8 | 9.09% |
| craps | hop bet - easy (14-1) | 16.67% |
| craps | hop bet - easy (15-1) | 11.11% |
| craps | hop bet - hard (29-1) | 16.67% |
| craps | hop bet - hard (30-1) | 13.89% |
| craps | horn bet (30-1 & 15-1) | 12.50% |
| craps | horn high - any (29-1 & 14-1) | 16.67% |
| craps | horn high 2, horn high 12 (30-1 & 15-1) | 12.78% |
| craps | horn high 3, horn high 11 (30-1 & 15-1) | 12.22% |
| craps | lay 4 or 10 | 2.44% |
| craps | lay 5 or 9 | 3.23% |
| craps | lay 6 or 8 | 4.00% |
| craps | pass/come | 1.41% |
| craps | pass/come w/1X odds | 0.85% |
| craps | pass/come w/2X odds | 0.61% |
| craps | pass/come w/3X odds | 0.47% |
| craps | pass/come w/5X odds | 0.33% |
| craps | pass/come w/10X odds | 0.18% |
| craps | place 4 or 10 | 6.67% |
| craps | place 5 or 9 | 4.00% |
| craps | place 6 or 8 | 1.52% |
| craps | three, eleven (14-1) | 16.67% |
| craps | three, eleven (15-1) | 11.11% |
| craps | two, twelve (29-1) | 16.67% |
| craps | two, twelve (30-1) | 13.89% |
| keno | typical | 27.00% |
| let it ride | base bet | 3.51% |
| pai gow | poker skilled player (non-banker) | 2.54% |
| pai gow poker | average player (non-banker) | 2.84% |
| red dog | basic bet (six decks) | 2.80% |
| roulette | single-zero | 2.70% |
| roulette | double-zero (except five-number) | 5.26% |
| roulette | double-zero, five-number bet | 7.89% |
| sic bo | big/small | 2.78% |
| sic bo | one of a kind | 7.87% |
| sic bo | 7, 14 | 9.72% |
| sic bo | 8, 13 | 12.50% |
| sic bo | 10, 11 | 12.50% |
| sic bo | any three of a kind | 13.89% |
| sic bo | 5, 16 | 13.89% |
| sic bo | 4, 17 | 15.28% |
| sic bo | three of a kind | 16.20% |
| sic bo | two-dice combination | 16.67% |
| sic bo | 6, 15 | 16.67% |
| sic bo | two of a kind | 18.52% |
| sic bo | 9, 12 | 18.98% |
| slots | dollar slots (good) | 4.00% |
| slots | quarter slots (good) | 5.00% |
| slots | dollar slots (average) | 6.00% |
| slots | quarter slots (average) | 8.00% |
| sports betting | bet $11 to win $10 | 4.55% |
| three card poker | pair plus | 2.32% |
| three card poker | ante | 3.37% |
| video poker | selected machines | -0.50% |
| *house advantages under typical conditions, expressed "per hand" and including ties, where appropriate. Optimal strategy assumed unless otherwise noted. | ||
Note: this summary is the intellectual property of the author and the university of nevada, las vegas. Do not use or reproduce without proper citation and permission.
Cabot, anthony N., and hannum, robert C. (2002). Gaming regulation and mathematics: A marriage of necessity, john marshall law review, vol. 35, no. 3, pp. 333-358.
Cabot, anthony N. (1996). Casino gaming: policy, economics, and regulation, UNLV international gaming institute, las vegas, NV.
Eadington, william R., and cornelius, judy (eds.) (1999). The business of gaming: economic and management issues, institute for the study of gambling and commercial gaming, university of nevada, reno, NV.
Eadington, william R., and cornelius, judy (eds.) (1992). Gambling and commercial gaming: essays in business, economics, philosophy and science, institute for the study of gambling and commercial gaming, university of nevada, reno, NV.
Epstein, richard A. (1995). The theory of gambling and statistical logic, revised edition, academic press, san diego, CA.
Feller, william (1968). An introduction to probability theory and its applications, 3rd ed., wiley, new york, NY.
Griffin, peter A. (1999). The theory of blackjack, 6th ed., huntington press, las vegas, NV.
Griffin, peter (1991). Extra stuff: gambling ramblings, huntington press, las vegas, NV.
Hannum, robert C. And cabot, anthony N. (2001). Practical casino math, institute for the study of gambling & commercial gaming, university of nevada, reno.
Humble, lance, and cooper, carl (1980). The world's greatest blackjack book, doubleday, new york, NY.
Kilby, jim and fox, jim (1998). Casino operations management, wiley, new york, NY.
Levinson, horace C. (1963). Chance, luck and statistics, dover publications, mineola, NY.
Millman, martin H. (1983). "A statistical analysis of casino blackjack," american mathematical monthly, 90, pp. 431-436.
Packel, edward (1981). The mathematics of games and gambling, the mathematical association of america, washington, D.C.
Thorp, edward O. (1984). The mathematics of gambling, gambling times, hollywood, CA.
Thorp, edward O. (1966). Beat the dealer, vintage books, new york, NY.
Vancura, olaf, cornelius, judy A., and eadington, william R. (eds.) (2000). Finding the edge: mathematical analysis of casino games. Institute for the study of gambling and commercial gaming, university of nevada, reno, NV.
Vancura, olaf (1996). Smart casino gambling, index publishing group, san diego, CA.
Weaver, warren (1982). Lady luck: the theory of probability, dover publications, new york, NY.
Wilson, allan (1970). The casino gambler's guide, harper and row, new york.
Bob hannum is a professor of risk analysis & gaming at the university of denver where he teaches courses in probability, statistics, risk, and the theory of gambling. His publications includepractical casino math (co-authored with anthony N. Cabot) and numerous articles in scholarly and gaming industry journals. Hannum regularly speaks on casino mathematics to audiences around the globe. (some of this guide has been excerpted from practical casino math.)
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