Boston

Boston is the capital and largest city of the Commonwealth of Massachusetts. The city is located in Suffolk County, Massachusetts, in the northeastern United States. The largest city in New England, Boston is considered the economic and cultural center of the entire region. The city, which had an estimated population of 616,535 in 2008, lies at the center of the Cambridge–Boston-Quincy metropolitan area—the 10th-largest metropolitan area (5th largest CSA) in the U.S., with a population of 4.5 million. In 1630, Puritan colonists from England founded the city on the Shawmut Peninsula. During the late eighteenth century Boston was the location of several major events during the American Revolution, including the Boston Massacre and the Boston Tea Party. Several early battles of the American Revolution, such as the Battle of Bunker Hill and the Siege of Boston, occurred within the city and surrounding areas. After American independence was attained Boston became a major shipping port and manufacturing center, and its rich history now attracts 16.3 million visitors annually. The city was the site of several firsts, including America's first public school, Boston Latin School (1635), and first college, Harvard College (1636), in neighboring Cambridge. Boston was also home to the first subway system in the United States.

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.

Financial betting refers to the wagering on the price development of a financial instrument at some later date relative to the current price or level of the instrument, against odds offered by a bookmaker. Maximum potential pay-off of the wager is known when the bet is taken and as a corollary risk is known beforehand by being limited to the initial stake.

Financial betting instruments are a type of digital option. The outcome of the wager at settlement is binary, that is, either a win or a loss. Settlement is executed in cash and there is no delivery of the underlying asset. At any point in time prior to the settlement date bets can often be sold, allowing for possibilities to bet on the accuracy of a market move within the fixed limits of zero win loss of the stake and maximum potential win. A fee might sometimes be charged for this service.

The main difference between financial betting and speculation on financial markets using products such as financial spread betting is that the bet must result in a simple binary win or loss based on an event on the underlying financial instruments. This triggers a fixed payout for a win, while with spread betting the payout or loss varies with the price level of the underlying instrument. Within financial floating odds the odds change for a given strike price as the price of the underlying changes. The floating odds company calculates odds for different strikes and how much can be won upon settlement depends on how much is bet at those odds.

Within financial fixed odds betting, the odds are fixed, while the strike price where a win is achieved relative the current level changes. The fixed odds company will calculate how much has to be bet to win a certain amount upon settlement if the conditions of the prediction become true.

Poker Jacks or Better Draw

Draw Poker Jacks or Better

Draw Poker Jacks or Better is played with a standard 52-card deck and one Joker. The Joker may be used as an Ace or as any card that completes a straight, flush, or a straight flush.

Players are dealt five cards face down, one at a time, in rotation. A round of betting begins (check, bet, call, raise, or fold). A player's hand must qualify with a pair of Jacks or better (higher) to open the pot. If no player has a pair of Jacks or better, the hand ends and the ante remains in the pot. A player who opens the pot must show openers, whether the hand is called or not, in order to win the pot. The remaining players may discard any number of their original cards and have the same number of cards replaced by the dealer. Another round of betting occurs. The player with the highest ranking five-card poker hand wins. Five Aces is the best possible hand (four Aces and the Joker). In the event of a tie, the pot is split equally.