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.

California Card Rooms

State law requires that every owner, lessee or employee of a gambling establishment obtain and, thereafter, maintain a valid state gambling license. The Bureau of Gambling Control Bureau investigates the qualifications of individuals who apply for state gambling licenses to determine whether they are suitable and to ensure that gambling is conducted honestly, competitively and free from criminal and corruptive elements.
Gambling License

An owner of a gambling establishment must apply for and obtain a valid state gambling license from the Bureau and the California Gambling Control Commission. The Bureau's Licensing staff will conduct in-depth background investigations on applicants to determine whether they are suitable to hold a state gambling license. Suitability is determined by a number of factors including but not limited to the applicant's honesty, integrity, general character, reputation, habits, and financial and criminal history.
Additional Tables

The owner of a state-licensed gambling establishment who wishes to operate additional tables on a temporary or permanent basis must submit a request to operate additional tables to the Commission. The number of tables requested cannot exceed the total number of tables authorized under local and state law for the gambling establishment.
Game/Gaming Activity Approval

All controlled games pai-gow, poker, etc. and gaming activities jackpots, bonuses, tournaments, etc. must be approved by the Bureau and must comply with local gaming ordinances prior to their play at a licensed gambling establishment within California.

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Roulette Wheel

PlayingRoulette

To play you place your bet or bets on numbers (any number including the zero) in the table layout or on the outside, and when everybody at the table had a chance to place their bets, the croupier starts the spin and launches the ball. Just a few moments before the ball is about to drop over the slots, the croupier says 'no more bets'. From that moment no one is allowed to place - or change - their bets until the ball drops on a slot. Only after the croupier places the 'dolly' on the winning number on the table and clears all the losing bets you can then start placing your new bets while the croupier pays the winners. The winners are those bets that are on or around the number that comes up. Also the bets on the outside of the layout win if the winning number is represented.

The house advantage
On a single zero roulette tables the house advantage is 2.7%. On a double zero roulette table it is 5.26% (7.9% on the five-number bet, 0-00-1-2-3). The house advantage is gained by paying the winners a chip or two (or a proportion of it) less than what it should have been if there was no advantage.

The payouts
A bet on one number only, called a straight-up bet, pays 35 to 1. (You collect 36. With no house advantage it should be 36 to1).
A two-number bet, called split bet, pays 17 to 1.
A three-number bet, called street bet, pays 11 to 1.
A four-number bet, called corner bet, pays 8 to 1.
A six-number bet, pays 5 to 1.
A bet on the outside dozen or column, pays 2 to 1.
A bet on the outside even money bets, pays 1 to 1.

Object of the game
To win the player needs to predict where the ball will land after each spin. This is by no means easy. In fact, luck plays an important part in this game. Some players go with the winning numbers calling them 'hot' numbers and therefore likely to come up more times. Others see which numbers did not come up for some time and bet on them believing that their turn is now due. Some players bet on many numbers to increase their chances of winning at every spin, but this way the payout is considerably reduced. Other methodical players use systems or methods.