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Card Game Encyclopedia: Poker 
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 Poker is a card game, the most popular of a class of games called vying games, in which players with fully or partially concealed cards make wagers into a central pot, which is awarded to the remaining player or players with the best combination of cards. Poker can also refer to video poker which is a single-player game seen in casinos much like a slot machine.


In order to play, one must learn the basic rules and procedures of the game, the values of the various combinations of cards (see hand), and the rules about betting limits (see betting). Some knowledge of the equipment used to play (see poker equipment) is useful. There are also many variants of poker, loosely categorized as draw poker, stud poker, community card poker (a.k.a. "widow game"), and miscellaneous poker games. The most commonly played games of the first three categories are five-card draw, seven-card stud, and Texas hold 'em, respectively; each being a common starting point for learning games of the type. Dealer's choice is a way to play poker where the dealer chooses what type of poker to play.

History
The history of poker is a matter of some debate. The name of the game likely descended from the French poque, which descended from the German pochen ('to knock'), but it is not clear whether the origins of poker itself lie with the games bearing those names. It closely resembles the Persian game of as nas, and may have been taught to French settlers in New Orleans by Persian sailors. It is commonly regarded as sharing ancestry with the Renaissance game of primero and the French brelan. The English game brag (earlier bragg) clearly descended from brelan and incorporated bluffing (though the concept was known in other games by that time). It is quite possible that all of these earlier games influenced the development of poker as it exists now.

English actor Joseph Crowell reported that the game was played in New Orleans in 1829, with a deck of 20 cards, four players betting on which player's hand was the most valuable. Jonathan H. Green's book, An Exposure of the Arts and Miseries of Gambling (G. B. Zieber, Philadelphia, 1843), described the spread of the game from there to the rest of the country by Mississippi riverboats, on which gambling was a common pastime.


Soon after this spread, the full 52-card English deck was used, and the flush was introduced. During the American Civil War, many additions were made, including draw poker, stud poker (the five-card variant), and the straight. Further American developments followed, such as the wild card (around 1875), lowball and split-pot poker (around 1900), and community card poker games (around 1925). Spread of the game to other countries, particularly in Asia, is often attributed to the U.S. military.

The game and jargon of poker have become important parts of American culture and English culture. Such phrases as ace in the hole, ace up one's sleeve, beats me, blue chip, call one's bluff, cash in, high roller, pass the buck, poker face, stack up, up the ante, when the chips are down, wild card, and others are used in everyday conversation even by those unaware of their origins at the poker table.

Modern tournament play became popular in American casinos after the World Series of Poker began in 1970. It was also during that decade that the first serious strategy books appeared, notably The Theory of Poker by David Sklansky (ISBN 1880685000), Super System by Doyle Brunson (ISBN 0931444014), and The Book of Tells by Mike Caro (ISBN 0897461002).

Poker’s popularity has experienced an unprecedented spike in recent years, largely due to the introduction of online poker and the invention of the hole-card camera which finally turned the game into a spectator sport. Viewers can now follow the action and drama of the game, and broadcasts of poker tournaments such as the World Series of Poker and the World Poker Tour have brought in huge audiences for cable and satellite TV distributors.


Game play

The game of poker is played in hundreds of variations, but the following overview of game play applies to most of them.

Depending on the game rules, one or more players may be required to place an initial amount of money into the pot before the cards are dealt. These are called forced bets and come in three forms: antes, blinds, and bring-ins.

Like most card games, the dealer shuffles the deck of cards. The deck is then cut, and the appropriate number of cards are dealt face-down to the players. In a casino a "house" dealer handles the cards for each hand, but a button (any small item used as a marker, also called a buck) is rotated among the players to determine the order of dealing and betting in certain games. In a home game, the right to deal the cards typically rotates among the players clockwise, but a button may still be used.

After the initial deal, the first of what may be several betting rounds begins. Between rounds, the players' hands develop in some way, often by being dealt additional cards or replacing cards previously dealt. During a round of betting, there will always be a current bet amount, which is the total amount of money bet in this round by the player who bet last in this round. To keep better track of this, it is conventional for players to not place their bets directly into the pot (called splashing the pot), but rather place them in front of themselves toward the pot, until the betting round is over. When the round is over, the bets are then gathered into the pot.

After the first betting round is completed (every participating player having called an equal amount), there may be more rounds in which more cards are dealt in various ways, followed by further rounds of betting (into the same central pot). At any time during the first or subsequent betting rounds, if one player makes a bet and all other players fold, the deal ends immediately, the single remaining player is awarded the pot, no cards are shown, no more rounds are dealt, and the next deal begins. This is what makes it possible to bluff.

At the end of the last betting round, if more than one player remains, there is a showdown in which the players reveal their previously hidden cards and evaluate their hands. The player with the best hand according to the poker variant being played wins the pot.


Computer players

The game of poker (or at least most of the variants) is considered to be computationally intractable. However, methods are being developed to at least approximate perfect strategy from the game theory perspective in the heads-up (two player) game, and increasingly good systems are being created for the multi-player or ring game. Perfect strategy has multiple meanings in this context. From a game-theoretic optimal point of view, a perfect strategy is a minimax one that cannot expect to lose to any other player's strategy; however, optimal strategy can vary in the presence of sub-optimal players who have weaknesses that can be exploited. In this case, a perfect strategy would be one that correctly or closely models those weaknesses and takes advantage of them to make a profit. Some of these systems are based on Bayes theorem, Nash equilibrium, Monte Carlo simulation, and Neural networks. A large amount of the research is being done at the University of Alberta by the GAMES group led by Jonathan Schaeffer who developed Poki and PsOpt.

One major aspect of poker is being a game of imperfect information. Some cards in play are concealed, so the players cannot deduce the exact state the game is in. This fundamentally differs from games like chess where all information about the game's current state is public. A major part of the skill of live poker games, however, is guessing at the strength of a player's hand by identifying tells made by other players, while concealing one's own. As a computer would not make any tells, playing against a computer would fundamentally change the nature of the game far more than chess and similar games.

Although you cannot read a computer opponent, playing against computer opponents can still help you sharpen your skills by learning how to count outs and play the percentages. With the advancing technology of artificial intelligence, computer players can be created to incorporate bluffs and other human-like decisions.

Hand rankings

The most fundamental rules of poker concern the hand rankings, because the hand rankings determine the winner. While betting is extremely important to the game, players are wagering on whether they have won, therefore a complete understanding of hand rankings must come first. These hand rankings do not apply to games played "low", such as lowball or razz; see the section on "low hands" below.

The cards are ranked thus, from low to high: 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, Ace. An ace is the highest card, but it can also function as the lowest in completing a straight. The two is usually called a "deuce", and the three is sometimes called a "trey". Ten, Jack, Queen, King, and Ace are often abbreviated T, J, Q, K, and A, respectively, so that each card name has a single number or letter associated with it. This is commonly used in describing hands, for example, A-2-3-4-5 is a hand with an ace, a two ("deuce"), a three, a four, and a five — not necessarily in that order, but presenting them in that order makes it clear that the hand is a straight. A hand may also be written, say, A-A-x-x-x, where "x" means any card.

Ranks from lowest to highest
Rank name Also called Cards needed Example Names for example
High card No pair, nothing (Anything) A-x-x-x-x Ace high
Pair   Two cards of same rank A-A-x-x-x Aces; pair of aces
Two pair   Two pairs A-A-K-K-x Aces up; aces and kings; aces over kings
Three of a kind Trips, a set Three cards of same rank A-A-A-x-x Three aces; set of aces
Straight   Five cards in sequence T-J-Q-K-A Ace-high straight
Flush   All five cards same suit A♣-10♣-7♣-6♣ 4♣ Ace-high flush
Full house Boat, full boat Three of a kind plus a pair A-A-A-K-K Aces full; aces full of kings
Four of a kind Quads Four cards of same rank A-A-A-A-x Quad aces; four aces
Straight flush   Five cards forming straight and a flush T♠-J♠-Q♠-K♠-A♠ Ace-high straight flush

A-2-3-4-5 is considered a five-high straight, and it is called a wheel or bicycle; this is the only time an ace plays as a low card. An ace-high straight flush is called a royal flush and it cannot be beaten, but it can be tied. Higher cards always beat lower cards, for example, a pair of aces beats a pair of kings. If two players have the same pair, a kicker is used to break the tie if possible (more about them soon). When two players have two pair, the highest pairs are considered, for example, aces up always beats kings up, no matter the other pairs. If, for example, two players both have aces up, then the higher of the smaller pairs wins: aces over kings beats aces over queens. If, for example, both players have aces over kings, then the kicker card is considered. Kickers also come into play when more than one player has the same three or four of a kind (possible only in community card games or wildcard games). If players have the same straight, flush, full house, or straight flush, it is always a tie and the players split the pot.

A kicker is any card that you hold in your hand that does not make part of it, that is, an otherwise useless card. When two players hold the same pair, two pair, three of a kind, or four of a kind, the highest kicker wins, for example, A-A-K-x-x beats A-A-Q-x-x, A-A-K-Q-x beats A-A-K-J-x, and A-A-K-Q-J beats A-A-K-Q-T. A kicker can be higher than the rest of the hand, for example, K-K-A-x-x beats K-K-J-x-x, so an ace usually makes the best kicker.

 

Low hands

Some games have a high-low split, and some games such as lowball or razz are played low-only. In a high-low split game, typically a low hand must not have any cards ranked higher than eight and no cards must be paired, or it does not count as a low hand. In low-only games, any cards can be used. Many forms of poker do not use low hands, so you need not concern yourself with these until you intend to play games that do.

There are three common ways of ranking low hands: ace-to-five low, ace-to-six low, and deuce-to-seven low, named after the best possible hands in the respective systems. In all systems, paired cards are bad and cannot be used to beat any hand that does not have a pair. Likewise, a pair beats three of a kind, three of a kind beats a full house, and a full house beats four of a kind. The most common hand ranking system for low hands is ace-to-five, used almost universally in high-low split games and very common in other games. This means A-2-3-4-5 (called a wheel or bicycle, just as it is as a high hand) is the best possible low hand, and the ace is the lowest card. For a high-low split game, it also forms a high hand: a five-high straight. In order to avoid confusion, we will discuss only ace-to-five low at the moment.

When pairs and any other "bad" hands are not present, then the winner is the one whose highest card is lowest. For this reason, a low hand is usually described highest card first, to make it easier to tell which is lower. In ace-to-five, 8-4-3-2-A loses to 7-6-5-4-3 because the highest card in the first hand (eight) is higher than the highest card in the second hand (seven), even though all the other cards in the second hand are lower. If the highest cards are the same, then the next-highest cards are considered, and so on: 8-7-6-3-A loses to 8-7-5-4-2 because the second hand goes lower first.

In ace-to-six low, straights and flushes count for high (that is, they're bad), and the best possible hand is A-2-3-4-6 unsuited, since it's the lowest possible card combination that avoids pairing, straights, and flushes. Deuce-to-seven is identical except the ace is the highest card, so the best possible hand is 2-3-4-5-7 unsuited. Therefore, in deuce-to-seven low, the hand that would make the worst possible high hand in traditional poker is the best possible low hand, and vice versa: a royal flush is the worst possible hand.

Betting

Specifics of betting vary from game to game. Before a hand begins, most games either use an ante or a blind bet, and some games use both. An ante is usually a fraction of a normal bet size. Blind bets are used with games that have a dealer button (also called a puck or button), hereafter simply button to refer to both the button itself and to the player who holds it. With an ante, every player must toss a chip or coin of a given denomination into the pot before receiving his or her cards. Blind bets may also appear in the form of bring-in bets in stud games, where the player with the lowest (or highest) card showing on the first round must either "bring it in" for a set amount (usually half a small bet) or make a full small bet. The player making the bring-in cannot fold.

In games that use a dealer button, the most common structure is a two-blind structure. In this, the player to the button's left posts a small blind (usually half a bet, rounded either up or down if this results in an awkward bet size), and the person to the left of the small blind posts the big blind, generally a full bet size. The players then all receive their cards, the other players receiving them at no cost. The player to the big blind's left must then call, raise, or fold to the big blind, and betting continues normally. But what is normally?

In a normal betting round, there must be some means of determining who goes first. In games that use a button, it will always be the player to the button's left (except in the first betting round, in which case it is the player to the big blind's left; this position is called under the gun). Other games use various schemes. The player who goes first must check or bet. To check is to pass on the chance of betting, and the player to his or her left faces the same choice. If all players check, nobody may bet and the next round continues. When somebody bets, all other players must decide, one at a time (starting from the bettor's left) whether to call, raise, or fold. To call the bet is to put the same amount of money into the pot. To raise is to call and also add more money to the pot. To fold (lay down your hand) is to stop playing the hand, giving up any money invested in the pot. The round of betting ends when all players who have not folded have called the last raise (so each player who has not folded contributes the same amount to the pot). A player who bets and folds to a raise loses the bet he or she made, even though the player folded on the same betting round. For this reason, it is advantageous to act last; in a game with a dealer button, the player who has the button always acts last (except in the first betting round, since the blinds get the option to raise).

To confuse matters further, there are several ways to play betting rounds, which are usually unrelated to the game itself (for example, five card draw can be played spread limit, fixed limit, pot limit, or no limit).

  • Spread limit, also called straight limit, is a common method in home games: throughout a hand, there is a lower limit and an upper limit, for example, $1 to $5, and these limits usually do not change. Spread limit is rarely found in casinos.
  • Fixed limit means each bet and raise is a fixed size. A fixed limit table usually doubles the bet size for the last couple of betting rounds, so fixed limits are often described as, say, $2/4, which, if it describes a Texas hold'em game, means the small blind is $1 (half the big blind), the big blind is $2, the flop is $2, the turn is $4, and the river is $4.
  • Pot limit is like spread limit except the maximum bet size is always the size of the pot. Like fixed limit, the minimum bet size is often doubled at a certain point.
  • No limit means there is no upper limit at all. Like fixed limit, the minimum bet size is often doubled at a certain point.

Omaha hold'em is often played pot limit but is almost never played no limit. Stud poker is usually either spread limit or fixed limit. A beginning player is strongly urged not to play pot limit or no limit, no matter how low the stakes are, until at the very least the player is well acquainted with the rules to the game.

Expected value

The expected value (EV) or expectation of a wager is how much you will win in the "long run" by making that wager. For example, this situation comes up often in Texas hold'em: a player has four hearts on the turn, and needs to hit a heart on the next and final card to make a flush. He is absolutely certain he will win if he hits the flush and in so doing the board does not pair, because the board allows no possibility for a full house or better hand, and his flush will be the nut flush. Even if the board pairs, he has a good chance of winning, so he need not worry about other hands that much. The probability of catching the heart is about one in five. Therefore, he can expect to lose most of the time. However, the idea of continuing cannot be dismissed out of hand unless we know what his expectation is. If it will cost $5 to call a bet and the pot, including other bets and calls, is $50, our player actually has a very positive expectation and should pay to see the next card. The chance of hitting his hand is only one in five, the pot is ten times the bet size. The player expects to win on average two dollars for every dollar invested every time this situation occurs.

To make it easier to understand why this move is correct even though it usually loses, suppose you have a six-sided die. If you correctly guess what side it lands on, you will win $50. If you are wrong, you lose $5. You will be wrong five times out of six, but you stand to gain a lot over the long run! This is because the probability of guessing correctly is 1/6, sometimes expressed as odds, "5:1 against" (five losing possibilities, one winning possibility). However, the payoff odds are 50:5 ($50 won for a $5 bet), which can be reduced to 10:1, and 10:1 is twice as large as 5:1. The payoff odds are called pot odds in a poker game. Comparing the odds of winning to the pot odds is how you can estimate your expected value.

Ideally, you want to avoid all situations where you have a negative expectation. Even slightly negative situations can pile up and bleed away your bankroll.

Calculating expected value

You cannot always get a good idea of the chances of winning your hand — at least, not without knowing what your opponents have, and they're not going to tell you! However, you will often have a draw which, if you hit, you will very likely win the pot. The exact arithmetic involved varies from game to game. In Texas hold'em and Omaha, once you see the flop, the percent chance of making your hand within one card is generally your number of outs (cards that will make your hand) multiplied by two, and the odds of making your hand within two cards is your number of outs multiplied by four. For example, if you have four hearts and you need one more for a flush, you have nine outs, because there are thirteen hearts in the deck, and subtracting the four hearts you already have gives nine. 9 × 2 is 18, so you have about an 18% chance of making the hand in the next card, and 9 × 4 is 36, so you have about a 36% chance of making it in two cards.

To make this easy, you want to turn this percent chance into odds, like 5:1 against. Fortunately, they are easy enough to memorize:

50% =  1:1
33% =  2:1
25% =  3:1
20% =  4:1
16% =  5:1
14% =  6:1
12% =  7:1
11% =  8:1
10% =  9:1
 9% = 10:1
 8% = 11:1
 7% = 13:1
 5% = 20:1
 4% = 25:1

The odds in bold are the most important to commit to memory; the others can be easily estimated.

Now, take the x in the x:1 figure and multiply it by the bet size. For example, if the odds of making your hand are roughly 4:1, and the next bet costs $5, multiply 5 × 4 = 20. That means you want there to be at least $20 in the pot (be sure to include bets that have not been added to the pot proper yet!), preferably a bit more just in case unless you're certain to win if you hit your draw. If there is not at least $20 in the pot you will lay down your hand, unless you can check instead. If the table is really loose, and a lot of players are in the hand and are likely to stay in, and the pot will get really big, you may even want to raise. Normally, however, checking or calling is the correct move.

Notice we did not calculate the exact expected value. This is not necessary or indeed practical for most people. If it is negative, you get out, and if it is positive, you call. If you're a favorite to win the pot, you raise. However, as has been shown you can usually figure out if the value is only barely positive, for instance, the size of the pot is a dollar more than the odds of making your hand (and this dollar is small in proportion to the pot size). When faced with this situation, you might want to lay down your hand sometimes: you may be losing just a little money in the long run, but you keep your bankroll from taking big swings. But if you don't mind taking a gamble, by all means go for it!

 


 

 

 

 

 

 

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