Atlanta

Atlanta is the capital and the largest city in the state of Georgia with a population of 519,145, and the core city of the ninth most populous United States metropolitan area at 5,278,904, with a combined statistical area of 5,626,400. Atlanta is a world city that ranks as the 33rd-largest in the United States. It is the county seat of Fulton County, although a small portion of the city extends into DeKalb County. Residents of the city are known as Atlantans. Atlanta has in recent years undergone a transition from a city of regional commerce to a city of international influence, and has been among the fastest growing cities in the developed world for much of the 1990s and 2000s. Between 2000 and 2006, the metropolitan area grew by 20.5%, making it the fastest growing metropolitan area in the nation.

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.

Poker Crazy Pineapple

Crazy Pineapple

Crazy Pineapple Poker is played with a standard 52-card deck. Blinds are posted by players who sit in consecutive clockwise order from the button. Action is initiated on the first betting round by the player to the left of the person who posted blind clockwise from the button. The blinds act last on the first betting.

All players receive three cards dealt face down (hole cards) as their initial hand. The first round of poker betting occurs. Check and raises are permitted. Three cards are turned face up in the middle of the board simultaneously (flop). These board cards are community cards and available to all players. The second round of betting occurs. At this time poker players choose to keep two of their three cards hole cards from their initial hand and discard the third. The next two board cards are turned up one at a time with a round of betting after each card. After the final round of poker betting has been completed, a player may use any combination of five cards (for example, one hole card and four from the board, etc.) to determine their best hand. A player may use all of the board cards (playing the board). The winning poker hand must show both hole cards face up on the table. The best five-card poker hand wins the pot. In the event of a tie, the pot is split equally.

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Poker Omaha Hi-Low Split

Omaha Hi-Low Split

Omaha Hi-Low Split (8 or Better)

Omaha Hi-Low Split is a community card poker game that is played with a standard 52-card deck. In order for a hand to qualify for the low hand, it must contain an 8 or Better (lower) at showdown. The game starts to the left of the dealer button. The blind bets are made from the positions left of the dealer button and are forced bets which must be made before the cards are dealt.

Each player is dealt four cards, one at a time, in turn and face down (hole cards) as their initial hand. A round of betting occurs for players who are continuing to contend for the pot. Three board cards are turned face up (flop) in the middle of the table (community cards). The community cards are available for all players to use. The second round of betting occurs. The fourth community card is turned face up (the turn), followed by a third round of betting. A final community card (the river) is turned up and a fourth and final round of betting occurs. After the final round of betting has been completed, each player may use any two hole cards with three community cards to make the highest five-card poker hand, and any two hole cards with three community cards to make the lowest qualifying five-card poker hand. The lowest qualifying five-card poker hand is Ace, 2, 3, 4, 5. Players must qualify for the low hand with a hand containing an 8 or better (lower). The pot is split equally between the players with the highest ranking hand and lowest qualifying hand. If no player has a low qualifying hand, the player with the highest ranking five-card poker hand wins the entire pot. In the event of a tie, the pot, or portion of the pot, if the tie is for high or low hand only, is split equally.