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.

Dealing

 

In games where cards are distributed among players, the deal is the act of that distribution.

The dealer takes all of the cards in the pack, arranges them so that they are in a uniform stack, and shuffles them. In strict play, the dealer then offers the deck to the previous player in the sense of the game direction for cutting. If the deal is clockwise, this is the player to the dealer's right; if counterclockwise, it is the player to the dealer's left. The invitation to cut is made by placing the pack, face downward, on the table near the player who is to cut: who then lifts the upper portion of the pack clear of the lower portion and places it alongside. Normally the two portions have about equal size. Strict rules often indicate that each portion must contain a certain minimum number of cards, such as three or five. The formerly lower portion is then replaced on top of the formerly upper portion. Instead of cutting, one may also knock on the deck to indicate that on trusts the dealer to have shuffled fairly.

The actual deal distribution of cards is done in the direction of play, beginning with eldest hand. The dealer holds the pack, face down, in one hand, and removes cards from the top of it with his or her other hand to distribute to the players, placing them face down on the table in front of the players to whom they are dealt. The cards may be dealt one at a time, or in batches of more than one card; and all or a determined amount of cards are dealt out. The undealt cards, if any, are left face down in the middle of the table, forming the stock also called talon, widow or skat.

Throughout the shuffle, cut, and deal, the dealer should prevent the players from seeing the faces of any of the cards. The players should not try to see any of the faces. Should a player accidentally see a card, other than one's own, proper etiquette would be to admit this. It is also dishonest to try to see cards as they are dealt, or to take advantage of having seen a card. Should a card accidentally become exposed, visible to all, then, normally, any player can demand a redeal all the cards are gathered up, and the shuffle, cut, and deal are repeated.

When the deal is complete, all players pick up their cards, or 'hand', and hold them in such a way that the faces can be seen by the holder of the cards but not the other players, or vice versa depending on the game. It is helpful to fan one's cards out so that if they have corner indices all their values can be seen at once. In most games, it is also useful to sort one's hand, rearranging the cards in a way appropriate to the game. For example, in a trick-taking game it may be easier to have all one's cards of the same suit together, whereas in a rummy game one might sort them by rank or by potential combinations.

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Card Games Rules

A new card game starts in a small way, either as someone's invention, or as a modification of an existing game. Those playing it may agree to change the rules as they wish. The rules that they agree on become the house rules under which they play the game. A set of house rules may be accepted as valid by a group of players wherever they play, as it may also be accepted as governing all play within a particular house, café, or club.

When a game becomes sufficiently popular, so that people often play it with strangers, there is a need for a generally accepted set of rules. This need is often met when a particular set of house rules becomes generally recognized. For example, when Whist became popular in 18th-century England, players in the Portland Club agreed on a set of house rules for use on its premises. Players in some other clubs then agreed to follow the Portland Club rules, rather than go to the trouble of codifying and printing their own sets of rules. The Portland Club rules eventually became generally accepted throughout England and Western cultures.

It should be noted that there is nothing static or official about this process. For the majority of games, there is no one set of universal rules by which the game is played, and the most common ruleset is no more or less than that. Many widely played card games, such as Canasta and Pinochle, have no official regulating body. The most common ruleset is often determined by the most popular distribution of rulebooks for card games. Perhaps the original compilation of popular playing card games was collected by Edmund Hoyle, a self-made authority on many popular parlor games. The U.S. Playing Card Company now owns the eponymous Hoyle brand, and publishes a series of rulebooks for various families of card games that have largely standardized the games' rules in countries and languages where the rulebooks are widely distributed. However, players are free to, and often do, invent house rules to supplement or even largely replace the standard rules.

If there is a sense in which a card game can have an official set of rules, it is when that card game has an official governing body. For example, the rules of tournament bridge are governed by the World Bridge Federation, and by local bodies in various countries such as the American Contract Bridge League in the U.S., and the English Bridge Union in England. The rules of skat are governed by The International Skat Players Association and in Germany by the Deutscher Skatverband which publishes the Skatordnung. The rules of French tarot are governed by the Fédération Française de Tarot. The rules of Poker's variants are largely traditional, but enforced by the World Series of Poker and the World Poker Tour organizations which sponsor tournament play. Even in these cases, the rules must only be followed exactly at games sanctioned by these governing bodies; players in less formal settings are free to implement agreed-upon supplemental or substitute rules at will.