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.

Bouillotte

Bouillotte, a vying 18th century French gambling card game of the Revolution, based on Brelan, very popular during the 19th century in France and again in America for some years from 1830. Bouillotte is regarded as one of the games that influenced the open-card stud variation in poker.

A piquet pack is used, from which, in case five play, the sevens are removed. When four the knaves, and when three the queens are omitted. The ace is the highest card in play and in cutting. Counters or chips, as in poker, are used. Before the deal each player antes one counter to the pot, after which each, the age passing, may raise the pot; those not seeing the raise being obliged to drop out.

Three cards are dealt to each player, and a thirteenth, called the retourné, when four play, turned up. Each player must then bet, call, raise or drop out. When a call is made the hands are shown and the best hand wins. The hands rank as follows:

Simple Brélan, three of a kind, ace being high.

Brélan Carré, four of a kind, one being the retourné.

Brélan Favori, three of a kind, one being the retourné.

If more than one player has a brélan, the best is one that matches the rank of the turn up a brélan carré, or squared-up brelan. If none matches, that of highest rank wins. Any player with a brelan receives a side-payment of one chip, two if it is a carré, from each opponent.

If no player holds a brélan, the hand holding the greatest number of pips wins. All hands are turned face up, including those of players who dropped. The face values of all these cards are totalled for each suit, ace counting 11, court cards 10 and numerals their face value. The best suit is the one with the highest visible total, and the player holding the highest card of it wins the pot, provided that he has not previously dropped. If he has, the winner is the player counting the greatest face value of cards in any other suit.

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Duplicate Poker

 

Duplicate poker is a variant of the popular card game poker. Duplicate poker is based on the principles of Duplicate Bridge but also involves some of the rules used for playing pot limit and no limit Texas hold'em.

Duplicate poker is a skill-based game in which there are two or more tables consisting of the same number of players. Each table is dealt with an identically shuffled deck of cards. Every player holds the same hand as the person seated in identical seats at other tables.

All players begin each hand with the ability to bet the same number of playing chips, regardless of prior performance in the previous rounds.

The object of Duplicate poker is to win more chips than your opponents sitting in corresponding seats at other tables. Ultimately, the winner is decided based on the total number of chips accumulated up until the end of the game, as compared with those held by all players in the same seats at the other tables. Conceivably, even a player who loses chips overall can win at the game if that player loses fewer chips than his opponents.

Duplicatepoker.com, the first poker room to use the format, closed down on October 5th 2008, citing the global financial crisis as the reason for the removal of services. It had previously been popular due to the fact that as a skill-based game it was legal in the U.S. While the game is more conducive to an automated online format because of pre-set decks and the need to record accurate scoring, Duplicate poker has also been played in a live format. The first-ever Duplicate poker tournament was held in April 2007 at the Cherokee Casino in Tulsa, Oklahoma.