New York State

New York is a state in the Mid-Atlantic and Northeastern regions of the United States and is the nation's third most populous. The state is bordered by New Jersey and Pennsylvania to the south, and Connecticut, Massachusetts and Vermont to the east. The state has a maritime border with Rhode Island east of Long Island, as well as an international border with the Canadian provinces of Quebec and Ontario to the northwest. New York is often referred to as New York State to distinguish it from New York City. New York covers 54,556 square miles and ranks as the 27th largest state by size. The Great Appalachian Valley dominates eastern New York, while Lake Champlain is the chief northern feature of the valley, which also includes the Hudson River flowing southward to the Atlantic Ocean. The rugged Adirondack Mountains, with vast tracts of wilderness, lie west of the valley. Most of the southern part of the state is on the Allegheny plateau, which rises from the southeast to the Catskill Mountains. The western section of the state is drained by the Allegheny River and rivers of the Susquehanna and Delaware systems. The Delaware River Basin Compact, signed in 1961 by New York, New Jersey, Pennsylvania, Delaware, and the federal government, regulates the utilization of water of the Delaware system. The highest elevation in New York is Mount Marcy in the Adirondacks.

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.

Hands for Poker

Best Poker Hands

Royal Flush: An Ace, King, Queen, Jack and Ten in the same suit.
In the event of a tie:
Two or more Royal Flushes
split the poker pot.

Straight Flush: Five cards in sequence, of the same suit.
In the event of a tie:
Highest rank at the
top of the sequence wins.

Four of a Kind: Four cards of the same rank, and one side card.
In the event of a tie:
Highest four of a kind wins.
In community card games where players have the same four of a kind, the highest fifth side card ("kicker") wins.

Full House: Three cards of the same rank, and two cards of a different, matching rank.
In the event of a tie:
Highest three matching cards wins the pot. In community poker card games where players have the same three matching cards, the highest value of the two matching cards wins.

Flush: Five cards of the same suit.
In the event of a tie:
The poker player holding the highest ranked card wins. If necessary, the second-highest, third-highest, fourth-highest, and fifth-highest cards can be used to break the tie.

Straight: Five cards in sequence.

In the event of a tie:
Highest ranking card at the top of the sequence wins. Note: The Ace may be used at the top or bottom of the sequence, and is the only card in poker which can act in this manner.

Three of a Kind: Three cards of the same rank, and two unrelated side cards.

In the event of a tie:
Highest ranking three of a kind wins. In community card games where players have the same three of a kind, the highest side card, and if necessary, the second-highest side card wins.

Two Pair: Two cards of a matching rank, another two cards of a different matching rank, and one side card.
In the event of a tie: Highest pair wins. If players have the same highest pair, highest second pair wins. If both players have identical pairs, highest side card wins.

One Pair: Two cards of a matching rank, and three unrelated side cards.
In the event of a tie: Highest pair wins. If poker players have the same pair, the highest side card wins, and if necessary, the second-highest and third-highest side card can be used to break the tie.

High Card: Any hand that does not qualify under a category listed above
In the event of a tie: Highest card wins, and if necessary, the second-highest, third-highest, fourth-highest and smallest card can be used to break the tie.

Poker Omaha

Omaha

According to Omaha Poker Rules, there are four betting rounds in a complete game - exactly the same as in Texas Holdem Poker. In Omaha Holden, the dealer deals each player their own four private cards face-down.

Each bet on the first two rounds of betting is set at the lower limit of the stakes structure. For example in a $5/$10 game, all bets and raises are $5 for the first two rounds (after private cards are dealt and once the flop is spread in center of table).

The last two rounds of betting (turn card and river) are set at the higher limit of the stakes structure. For example in a $5/$10 game, all bets and raises are $10 for the last two rounds.

One bet plus three raises (four total bets) are the maximum amount of bets allowed per betting round. This would consist of (1) a bet, (2) a raise, (3) a re-raise, and (4) a cap. The term cap is used to describe the 3rd raise in a round since betting is then capped and cannot be raised anymore. Once any player has made the third raise (capped the pot), then players will have only the option of calling or folding.

Check-raising is allowed in all online poker games.

Dealer Button

In order to designate which player is the theoretical dealer in Omaha high low poker games, a round disk is used. This disk is called the dealer button or simply "the button".
After each hand is completed, the button moves clockwise to the next active player and this player will be considered to be the dealer, and will act on their hand last on each betting round. This is also termed playing the button for that game.

Blinds
The player to the left of the button is first to receive a card and is required to post a small blind. The small blind is equal to half the lower limit bet rounded down to the nearest dollar. The player to the left of the small blind is required to post the big blind. The big blind is equal to the lower limit bet. These bets are referred to as blinds because players must post them before the dealer deals any cards to the players. These blinds are similar to the ante that is required in other games such as 7-Card Stud.

Omaha Poker Rules specify that both the small and the big blinds are considered live bets. They have the option of checking, calling, raising or folding when the betting action comes back around to their position. After the flop and after each subsequent betting round, the first active player left of the button is first to act.

When players first sit down to play, they will be required to post the equivalent of the big blind only once or they have the option to "sit out" until it is their natural turn to post the big blind. This rule is in place to ensure game fairness to all players, as it prevents the possibility of players entering games in late position and then leaving before they are required to post the big blind.

HOW TO PLAY
The dealer deals each player their own four private cards face-down.

First betting round

The dealer spreads three community boardcards face-up on the table. This is commonly called "the flop".

Second betting round

The dealer turns over a fourth boardcard face-up commonly called "the turn card".

Third betting round

The dealer turns over one final community boardcard commonly called "the river card".

Final betting round

Players show their hands. This is commonly called "the showdown".

When players show their hands, they MUST use exactly: two of their private cards plus three of the five board cards.