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.

In most jurisdictions worldwide, gambling is limited to persons over the age of license in most countries where casinos are permitted.

Customers gamble by playing games of chance, in some cases with an element of skill, such as craps, roulette, baccarat, blackjack, and video poker. Most games played have mathematically determined odds that ensure the house has at all times an advantage over the players. This can be expressed more precisely by the notion of expected value, which is uniformly negative from the player's perspective. This advantage is called the house edge. In games such as poker where players play against each other, the house takes a commission called the rake. Casinos sometimes give out complimentary items to gamblers.

Payout is the percentage won by players.

Casinos in the USA say that a player staking money won from the casino is playing with house money.

Video Lottery Machines slot machines have become one of the most popular form of gambling in casinos. Recently, investigative reports have been calling into question whether the modern day slot machine is addictive. There are almost 900 casinos now in the United States, with that number steadily growing as more states seek to legalize casinos. 38 states now have some form of casino gambling. Relatively small places such as Las Vegas are best known for gambling; larger cities such as Chicago are not defined by their casinos in spite of the large turnover.

Las Vegas has the largest concentration of casinos in the United States. Based on revenue, Atlantic City, New Jersey ranks second and the Chicago region third.

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Acey Deucey

Acey Deucey, also known as In-Between or Sheets, is a simple card game that involves betting. Before the action, each player must add their ante into the pot. Two cards are then dealt face-up to one player. That player then bets from nothing to the amount that is in the pot at the time whether or not the third card will numerically fall in between the first two. If the third card falls in between the two other cards, the bettor takes the amount he bet out of the pot; if the third card falls outside of the two other cards, the bettor must add what he bet to the pot; and if the third card matches the numerical value of one of the other two cards, the bettor must add to the pot double what he bet. If two cards of the same value come up, e.g. 2,2 the bettor picks if the next card will be higher or lower and bets. If the next card is the same as the last two, i.e. a 2, the bettor must triple his/her bet.

The rules and specifics of the game often vary from region to region. For example in Liaoning province, northeast China the minimum number of players is 4 and each player is required to ante before the first card is turned. Two cards are then dealt face-up to one player. That player then bets from nothing to the amount that is in the pot at the time during the first time around the table players are only allowed to bet up to half of the pot whether or not the third card will numerically fall in between the first two.

If the third card falls in between the two other cards, the bettor takes the amount he bet out of the pot; if the third card falls outside of the two other cards, the bettor must add what he bet to the pot; and if the third card matches the numerical value of one of the other two cards, this is referred to as a Post and the bettor must add to the pot double his initial bet. If two cards of the same value come up, e.g. 2,2 the bettor picks if the next card will be higher or lower and bets. If the next card is the same as the last two, i.e. a 2, this is considered a Post and the player is required to pay double the bet for the hand.

In addition to this, there is a special rule for Aces. If the first card turned is an Ace the player may choose its value as either the high Ace or the low one. If an Ace comes up as the second card turned it is always considered the high Ace. If a player Posts on an Ace they are required to pay four times their bet for that hand. Aces also cause an automatic loss if it is the third card turned when the first two cards are a match, e.g. 6,6. The best spread in the game is considered to be a low Ace on the left and a high Ace on the right. This is also one of the worst hands to get as you run the risk of the third card being an Ace and having to pay four times your bet for the hand.

Another variation is to split the cards if two end cards are the same value. This requires the bettor to ante in for two hands and the dealer would draw one more card under each of the end cards. After this, the same rules apply.