Odds

The odds in favor of an event or a proposition are expressed as the ratio of a pair of integers, which is the ratio of the probability that an event will happen to the probability that it will not happen. For example, the odds that a randomly chosen day of the week is a Sunday are one to six, which is sometimes written 1:6, or 1/6. In probability theory and statistics, where the variable p is the probability in favor of the event, and the probability against the event is therefore 1-p, the odds of the event are the quotient of the two, or p/(1-p). That value may be regarded as the relative likelihood the event will happen, expressed as a fraction if it is less than 1, or a multiple if it is equal to or greater than one of the likelihood that the event will not happen. In the example just given, saying the odds of a Sunday are one to six or, less commonly, one-sixth means the probability of picking a Sunday randomly is one-sixth the probability of not picking a Sunday. While the mathematical probability of an event has a value in the range from zero to one, the odds in favor of that same event lie between zero and infinity. The odds against the event with probability given as p are (1-p)/p.

The odds against Sunday are 6:1 or 6/1 = 6: it is 6 times as likely that a random day is not a Sunday. Hence 'odds' are an expression of relative probabilities. Generally 'odds' are quoted in this format odds against rather than as odds in favor of, because of the possibility of confusion of the latter with the fractional probability of an event occurring. E.g., the probability of a random day of the week is a Sunday is 'one-seventh' 1/7. A bookmaker may for his own purposes use 'odds' of 'one-sixth', but the overwhelming everyday use by most people is odds of the form 6 to 1, 6-1, 6:1, or 6/1 all read as 'six-to-one' where the first figure represents the number of ways of failing to achieve the outcome and the second figure is the number of ways of achieving a favorable outcome: thus these are odds against. In other words, an event with m to n odds against would have probability n/ m + n, while an event with m to n odds on would have probability m/ m + n. Even in probability theory, odds may be more natural or more convenient than probabilities. This is in particular the case in problems of sequential decision making as for instance in problems of how to stop online on a last specific event, which is solved by the odds algorithm.

In some games of chance, using odds against is also the most convenient way to understand what winnings will be paid if the selection is successful: the winner will be paid 'six' of whatever stake unit was bet for each 'one' of the stake unit wagered. For example, a winning bet of 10 at 6/1 will win '6 × 10 = 60' with the original 10 stake also being returned. Betting odds are skewed to ensure that the bookmaker makes a profit—if true odds were offered the bookmaker would break even in the long run—so the numbers do not represent the true odds.

Odds on means that the event is more likely to happen than not. This is sometimes expressed with the smaller number first 1:2 but more often using the word on 2:1 on meaning that the event is twice as likely to happen as not.

Decimal presentation

Taking an event with a 1 in 5 probability of occurring i.e. a probability of 1/5, 0.2 or 20%, then the odds are 0.2 / 1 − 0.2 = 0.2 / 0.8 = 0.25. This figure 0.25 represents the monetary stake necessary for a person to gain one monetary unit on a successful wager when offered fair odds. This may be scaled up by any convenient factor to give whole number values. For example, if a stake of 0.25 wins 1 unit, then scaling by a factor of four means a stake of 1 wins 4 units.

Ratio presentation

Fixed odds gambling tends to represent the probability as fractional odds, and excludes the stake. For example, 0.20 is represented as 4 to 1 against written as 4-1, 4:1, or 4/1, since there are five outcomes of which four are unsuccessful. Thus, the stake returned must be added to the odds to compute the entire return of a successful bet. In craps, the payout would be represented as 5 for 1, and in money line odds as +400 representing the gain from a 100 stake.

By contrast, for an event with a 4 in 5 probability of occurring i.e. a probability of 4/5, 0.8 or 80%, then the odds are 0.8 / 1 − 0.8 = 4. If one bets 4 units at these odds and the event occurs, one receives back 1 unit plus the original unit 4 units stake. This would be presented in fractional odds of 4 to 1 on'' written as 1/4 or 1–4 , in decimal odds as 1.25 to include the returned stake, in craps as 5 for 4, and in money line odds as −400 representing the stake necessary to gain 100.

Fixed odds are not necessarily presented in the lowest possible terms; if there is a pattern of odds of 5–4, 7–4 and so on, odds which are mathematically 3–2 are more easily compared if expressed in the mathematically equivalent form 6–4. Similarly, 10–3 may be stated as 100–30.

Gambling odds versus probabilities

In gambling, the odds on display do not represent the true chances that the event will occur, but are the amounts that the bookmaker will pay out on winning bets. In formulating his odds to display the bookmaker will have included a profit margin which effectively means that the payout to a successful bettor is less than that represented by the true chance of the event occurring. This profit is known as the 'over-round' on the 'book' the 'book' refers to the old-fashioned ledger in which wagers were recorded, and is the derivation of the term 'bookmaker' and relates to the sum of the 'odds' in the following way:

In a 3-horse race, for example, the true probabilities of each of the horses winning based on their relative abilities may be 50%, 40% and 10%. These are simply the bookmaker's 'odds' multiplied by 100% for convenience. The total of these three percentages is 100%, thus representing a fair 'book'. The true odds against winning for each of the three horses are 1-1, 3-2 and 9-1 respectively. In order to generate a profit on the wagers accepted by the bookmaker he may decide to increase the values to 60%, 50% and 20% for the three horses, representing odds against of 4-6, 1-1 and 4-1. These values now total 130%, meaning that the book has an over round of 30 130 − 100. This value of 30 represents the amount of profit for the bookmaker if he accepts bets in the correct proportions on each of the horses. The art of bookmaking is that he will take in, for example, $130 in wagers and only pay $100 back including stakes no matter which horse wins.

Profiting in gambling involves predicting the relationship of the true probabilities to the payout odds. Sports information services are often used by professional and semi-professional sports bettors to help achieve this goal.

The odds or amounts the bookmaker will pay are determined by the total amount that has been bet on all of the possible events. They reflect the balance of wagers on either side of the event, and include the deduction of a bookmaker’s brokerage fee vig or vigorish.

When the Stakes Turn Toxic

Anyone who’s bought a lottery ticket or played bingo has gambled. Gambling is any game of chance in which money changes hands. It’s common in most cultures around the world. Many people enjoy gambling as recreation without causing harm to themselves or others. Yet some people can’t control their impulse to gamble, even when it takes a terrible toll on their lives.         

For these gamblers and their families, researchers have been making progress in several areas. Scientists are learning why people have problems with gambling: how common it is, what goes on inside the gambler’s brain, which is at risk and what kinds of treatment can help.

Problem gambling is defined by some researchers as gambling that causes harm to the gambler or someone else, in spite of a desire to stop. Between 2% and 4% of Americans struggle with this condition. Problem gambling can progress to a recognized psychiatric diagnosis called pathological gambling.

Pathological gambling may affect from 0.4% to 2% of Americans. “Pathological gambling comes with a constellation of problems that contribute to chaos,” says Dr. Donald Black of the University of Iowa. “It’s associated with worse physical health, excessive smoking, excessive drinking, not exercising, not seeing primary care doctors and worse dental care. It also fuels depression, family dysfunction, crime, bankruptcy and suicide.”

Together, pathological and problem gambling may affect up to 5% of Americans. That number may rise, though. Laws in many states are creating more options for legal gambling, and internet gambling is becoming more common.

Still, gambling is often done in family settings, condoned or encouraged by parents. And the younger you start, the more likely you are to get into trouble later on. From 3% to 8% of adolescents have a problem with gambling.

Dr. John Welte of the University of Buffalo has found that, across the lifespan, gambling problems are even more common than alcohol dependence. They are also much more common in males, in young people, and in people who live in relatively poor neighborhoods. “That’s not true of the prevalence of alcoholism,” says Welte. “Alcoholism is much more democratic. So think about motives for gambling. People are hoping that winning will improve their lot. That makes them more vulnerable to developing a gambling problem.”

In a study of mostly African-American inner-city youth, Dr. Silvia Martins of Johns Hopkins University has found that about 15% have some form of problem gambling. Most at-risk were adolescents and young adults who began showing symptoms of depression at age 12. They were highly impulsive, although not hyperactive or aggressive. As the African-American boys developed into their teens and early adulthood, gambling appeared to be a separate risk factor for early fatherhood and criminal arrest.

“We are following up with these inner-city kids every single year as they enter adulthood,” says Martins.

But why is gambling irresistible to some folks and not others? Using advanced imaging techniques, Dr. Alexander Neumeister of Mount Sinai School of Medicine looked at the brains of people with gambling problems and alcohol problems. He measured the number of special receptors involved in regulating impulse control and other factors.          

“A key feature of addiction is impaired impulse control,” says Neumeister. “Abnormal function of the forebrain leads to reduced tolerance to waiting.” The resulting impatience may cause people to act without considering the consequences. “Our imaging clearly points toward the importance of impaired forebrain function in addiction.”

Pinpointing areas in the brain’s reward center, Neumeister’s team found that people with alcohol addiction and gambling problems show different functioning of these special receptors compared to healthy people. The differences were related to the severity of addiction. Other researchers are trying to develop drugs that could treat the affected areas.

Talk therapy can also help. Dr. Nancy Petry at the University of Connecticut Health Center works with pathological gamblers and people seeking treatment for drug use disorders. Gambling problems arise in about 10% to 20% of substance abusers. Petry compared the use of different types of talk therapy, including very brief interventions and cognitive-behavioral therapy CBT. CBT teaches people how to think differently about problems and then act on that knowledge.

“We found very brief interventions and CBT were effective in reducing gambling and gambling-related problems,” Petry says. “There was a significant improvement relative to usual care or standard forms of treatment like Gamblers Anonymous [a 12-step program].”

Anybody can have a gambling problem, and no one should feel ashamed or be afraid to seek treatment. “Pathological gambling is a medical disorder, not a sin or a vice,” says Dr. Carlos Blanco of Columbia University and the New York State Psychiatric Institute. “There is no stereotype. The main predictor of outcome is really motivation.”

In other words, what counts most is a strong drive or desire to take action. Blanco offers gamblers motivational interviewing, which helps them explore their mixed feelings about trying to quit gambling. This primes them to be ready and willing to begin CBT. Using both therapies together can be very effective.

If you have concerns about your gambling, ask for help. Your health provider can work with you to find the treatment that’s best for you.

Slot Machine Terminology

Bonus is a special feature of the particular game theme, which is activated when certain symbols appear in a winning combination. Bonuses vary depending upon the game. Some bonus rounds are a special session of free spins the number of which is often based on the winning combination that triggers the bonus, often with a different or modified set of winning combinations as the main game, and often with winning credit values increased by a specific multiplier, which is prominently displayed as part of the bonus graphics and/or animation. In other bonus rounds, the player is presented with several items on a screen from which to choose. As the player chooses items, a number of credits is revealed and awarded. Some bonuses use a mechanical device, such as a spinning wheel, that works in conjunction with the bonus to display the amount won.

Candle is a light on top of the slot machine. It flashes to alert the operator that change is needed, hand pay is requested or a potential problem with the machine.

Carousel refers to a grouping of slot machines, usually in a circle or oval formation.

Coin hopper is a container where the coins that are immediately available for payouts are held. The hopper is a mechanical device that rotates coins into the coin tray when a player collects credits/coins by pressing a Cash Out button. When a certain preset coin capacity is reached, a coin diverter automatically redirects, or drops, excess coins into a drop bucket or drop box. Unused coin hoppers can still be found even on games that exclusively employ Ticket-In Ticket-Out technology, as a vestige.

Credit meter is a visual LED display of the amount of money or credits on the machine. On video reel machines this is either a simulated LED display, or represented in a different font altogether, based on the design of the game graphics.

Drop bucket or drop box is a container located in a slot machine's base where excess coins are diverted from the hopper. Typically, a drop bucket is used for low denomination slot machines and a drop box is used for high denomination slot machines. A drop box contains a hinged lid with one or more locks whereas a drop bucket does not contain a lid. The contents of drop buckets and drop boxes are collected and counted by the casino on a scheduled basis.

EGM is used as shorthand for Electronic Gaming Machine.

Hand pay refers to a payout made by an attendant or at an exchange point cage, rather than by the slot machine itself. A hand pay occurs when the amount of the payout exceeds the maximum amount that was preset by the slot machine's operator. Usually, the maximum amount is set at the level where the operator must begin to deduct taxes. A hand pay could also be necessary as a result of a short pay.

Hopper fill slip is a document used to record the replenishments of the coin in the coin hopper after it becomes depleted as a result of making payouts to players. The slip indicates the amount of coin placed into the hoppers, as well as the signatures of the employees involved in the transaction, the slot machine number and the location and the date.

MEAL book Machine entry authorization log is a log of the employee's entries into the machine

Low Level or Slant Top slot machines include a stool so the player has sit-down access. Stand Up or Upright slot machines are played while standing.

Optimal play is a payback percentage based on a gambler using the optimal strategy in a skill-based slot machine game.

Pay line is a straight or zigzagged line that crosses through one symbol on each reel, along which a winning combination is evaluated. Classic spinning reel machines usually have up to nine pay lines, while video slot machines may have as many as one hundred.

Rollup is the process of dramatizing a win by playing sounds while the meters count up to the amount that has been won.

Short pay refers to a partial payout made by a slot machine, which is less than the amount due to the player. This occurs if the coin hopper has been depleted as a result of making earlier payouts to players. The remaining amount due to the player is either paid as a hand pay or an attendant will come and refill the machine.

Taste is a reference to the small amount often paid out to keep a player seated and continuously betting. Only rarely will machines fail to pay out even the minimum placed bet over the course of several pulls.

Display screen of a slot machine in tilt mode

Tilt Electromechanical slot machines usually include an electromechanical tilt switch, which makes or breaks a circuit if the machine is tilted or otherwise tampered with, and so triggers an alarm. While modern machines no longer have tilt switches, any kind of technical fault door switch in the wrong state, reel motor failure, out of paper, etc. is still called a tilt.

Theoretical Hold Worksheet A document provided by the manufacturer for all slot machines, which indicates the theoretical percentage that the slot machine should hold based on the amount paid in. The worksheet also indicates the reel strip settings, number of coins that may be played, the payout schedule, the number of reels and other information descriptive of the particular type of slot machine.

Weight count is an American term, referring to the dollar amount of coins or tokens removed from a slot machine's drop bucket or drop box and counted by the casino's hard count team through the use of a weigh scale.