When evaluating a hand before the flop, it’s useful to have some idea of how likely the hand is dominated. A dominated hand is a hand that is beaten by another hand (the dominant hand) and is extremely unlikely to win against it. Often the dominated hand has only a single card rank that can improve the dominated hand to beat the dominant hand (not counting straights and flushes.) For example, KJ is dominated by KQ—both hands share the king and the queen kicker is beating the jack kicker. Barring a straight or flush, the KJ will need a jack on the board to improve against the KQ (and will still be losing if a queen comes on the board also.) A pocket pair is dominated by a pocket pair of higher rank.
Pocket pairs
Barring a miracle straight or flush, a pocket pair needs to make three of a kind to beat a higher pocket pair.
To calculate the probability that another player has a higher pocket pair, first consider the case against a single opponent. The probability that a single opponent has a higher pair can be stated as the probability that the first card dealt to the opponent is a higher rank than the pocket pair and the second card is the same rank as the first. Where r is the rank of the pocket pair (assigning values from 2–10 and J–A = 11–14), there are (14 − r) × 4 cards of higher rank. Subtracting the two cards for the pocket pair leaves 50 cards in the deck. After the first card is dealt to the player there are 49 cards left, 3 of which are the same rank as the first. So the probability of a single opponent being dealt a higher pocket pair is
P = (((14-r)x4)/50) x (3/49)
The following approach extends this equation to calculate the probability that one or more other players has a higher pocket pair.
- Multiply the base probability for a single player for a given rank of pocket pairs by the number of opponents in the hand;
- Subtract the adjusted probability that more than one opponent has a higher pocket pair. (This is necessary because this probability effectively gets added to the calculation multiple times when multiplying the single player result.)
Where n is the number of other players still in the hand and Pma is the adjusted probability that multiple opponents have higher pocket pairs, then the probability that at least one of them has a higher pocket pair is
P = ((84-6r)/1225) x n – Pma.
The calculation for Pma depends on the rank of the player’s pocket pair, but can be generalized as
Pma = P where P The following table shows the probability that before the flop another player has a larger pocket pair when there are one to nine other players in the hand. The following table gives the probability that a hand is facing two or more larger pairs before the flop. From the previous equations, the probability Pm is computed as Pm = P From a practical perspective, however, the odds of out drawing a single pocket pair or multiple pocket pairs are not much different. In both cases the large majority of winning hands require one of the remaining two cards needed to make three of a kind. When holding a single ace (referred to as Ax), it is useful to know how likely it is that another player has a better ace—an ace with a higher second card. The weaker ace is dominated by the better ace. The probability that a single opponent has a better ace is the probability that they have either AA or Ax where x is a rank other than ace that is higher than the player’s second card. When holding Ax, the probability that the other player has AA is (3/50) x (2/49) ~ 0.00245. Where x is the rank 2–K of the second card (assigning values from 2–10 and J–K = 11–13) the probability that a single opponent has a better ace is calculated by the formula P = ((3/50) x (2/49)) + ((3/50) x (((13-x) x 4)/49) x 2) = (3/1225) + (12 x (13 – x))/1225 = (159 – 12x)/1225. The probability (3/50) x (((13-x) x 4)/49) of a player having Ay, where y is a rank such that x < y <= K, is multiplied by the two ways to order the cards A and y in the hand. This guide is licensed under the GNU Free Documentation License. It uses material from the Wikipedia. Need an webmaster? Click HERE When facing two opponents, for any given starting hand the number of possible combinations of hands the opponents can have is hands. For calculating probabilities we can ignore the distinction between the two opponents holding A♠ J♥ and and against three opponents is and against n opponents is where (2n − 1)!! (!! is the double factorial operator) is the number of ways to distribute 2n cards between n hands of two cards each. The following table shows the number of hand combinations for up to nine opponents. An exhaustive analysis of all of the match ups in Texas Hold ‘em of a player against nine opponents requires evaluating each possible board for each distinct starting hand against each possible combination of hands held by nine opponents, which is If you were able to evaluate one trillion (1012) combinations every second, it would take over 670 million years to evaluate all of the hand/board combinations. While it is possible to significantly reduce the total number of combinations by pruning combinations with identical properties, the total number of situations is still well beyond the number that can be evaluated by brute force. For this reason, most software programs compute probabilities and expected values for Hold ‘em poker hands against multiple opponents by simulating the play of thousands or even millions of hands to determine statistical probabilities. This guide is licensed under the GNU Free Documentation License. It uses material from the Wikipedia. Need an webmaster? Click HERE Play begins with each player being dealt one card face down, followed by one card face up (beginning as usual with the player to the dealer’s left). If played with a bring-in, the player with the lowest-ranking upcard must pay the bring in, and betting proceeds after that. If two players have equally ranked low cards, suit rankings may be used to break the tie. If there is no bring-in, then the first betting round begins with the player showing the highest-ranking upcard, who may check. In this case, suit should not be used to break ties; if two players have the same high upcard, the one first in clockwise rotation from the dealer acts first. After the first betting round is complete, another face-up card is dealt to each player (after a burn card, starting with the player to the dealer’s left, as will all subsequent rounds). Betting now begins with the player whose upcards make the best poker hand (since fewer than five cards are face up, this means no straights, flushes, or full houses). On this and subsequent betting rounds, the player to act first may check or bet up to the game’s limit. The second betting round is followed by a third upcard to each player and a third betting round, again starting with the player with the best poker hand showing (thus, the first player to act on each round may change). A fourth face-up card and fourth betting round is followed by a showdown, if necessary (it usually won’t be–most deals of five-card stud end early when a player bets and gets no calls). Here’s a sample deal. Assume that a game is being played by four players: Alice, who is dealing, Bob, who is sitting to her left, Carol to his left, and David to Carol’s left. Alice deals one card face down to each player, followed by one card face up to each player, beginning with Bob and ending with herself. Bob is dealt the ♠, Carol the K♦, David the ♦, and Alice the ♣. Because they had earlier agreed to play with a $1 bring-in, David is required to start the betting with a $1 bring-in (his ♦ is lower than Bob’s ♠ by suit). He has the option to open the betting for more, but he chooses to bet only the required $1. The bring-in sets the current bet amount to $1, so Alice cannot check. She decides to call. Bob folds, indicating this by turning his upcard face down and discarding his cards. Carol raises to $3. David folds (forfeiting his bring-in), and Alice calls. Alice now deals a second face-up card to each remaining player: Carol is dealt the J♣, and Alice the K♥. Alice’s two face-up cards make a poker hand of no pair, K-9 high, and Carol has K-J high, so it is Carol’s turn to bet. She checks, as does Alice, ending the betting round. Another face up card is dealt: Carol gets the ♥, and Alice gets the K♣. Alice now has a pair of kings showing, and Carol still has no pair, so Alice bets first. She bets $5, and Carol folds. Alice wins the pot without a showdown. This guide is licensed under the GNU Free Documentation License. It uses material from the Wikipedia. Need an webmaster? Click HERE Five-card draw is often the first poker variant learned by most players, and is very common in home games although it is now rare in casino and tournament play. The lowball variations make more interesting games and are more commonly played in casinos. Two to eight players can play. The descriptions below assume that you are familiar with the general game play of poker, and with hand values. They also make no assumptions about what betting structure is used. In casino play, it is common to use blinds; the first betting round thus begins with the player to the left of the big blind, and subsequent rounds begin with the player to the dealer’s left. In home games, it is typical to use an ante; the first betting round begins with the player to the dealer’s left, and the second round begins with the player who opened the first round. Play begins with each player being dealt five cards, one at a time, all face down. The remaining deck stub is placed aside, often protected by placing a chip or other marker on it. Players pick up the cards and hold them in their hands, being careful to keep them concealed from the other players. The first “before the draw” betting round occurs at this point, starting with the player to the dealer’s left (or to the left of the big blind if blinds are used). If more than one player remains after the first round, the “draw” phase begins. Each player specifies how many of his cards he wishes to replace, and discards that many from his hand. The deck stub is retrieved, and after a burn card is dealt, each player in turn beginning at the dealer’s left is dealt from the stub the same number of cards he discarded, so that each player again has five cards. It is important that each player discards the cards he wishes to replace before he takes any replacements, and that he take the same number of replacements as he discarded. A second “after the draw” betting round occurs after the draw phase, beginning with the player to the dealers left or else beginning with the player who opened the first round (the latter is common when antes are used instead of blinds). This is followed by a showdown if more than one player remains, in which the player with the best hand wins the pot. A common “house rule” in some places is that a player may not replace more than three cards, unless he draws four cards while keeping an ace (or wild card). This rule is only needed for low-stakes social games where many players will stay for the draw, and will help avoid depletion of the deck stub. In more serious games such as those played in casinos it is unnecessary and generally not used. A rule that is used by many casinos is that a player is not allowed to draw five consecutive cards from the deck stub. In this case, if a player wishes to replace all five of his cards, he is given four of them in turn, the other players are given their draws, and then the dealer returns to that player to give him his fifth replacement (if no later player drew, it is necessary to deal a burn card first). Another common house rule is that the bottom card of the deck is never given as a replacement, to avoid the possibility of someone who might have seen it during the deal using that information. If the deck stub is depleted during the draw before all players have received their replacements, the last players can receive cards chosen randomly from among those discarded by previous players. For example, if the last player to draw wants three replacements but there are only two cards remaining in the deck stub, the dealer gives the player the one top card he can give, then shuffles together the bottom card of the deck, the burn card, and the earlier players’ discards (but not the player’s own discards!), and finally deals two more replacements to the last player. The sample deal below assumes that a game is being played by four players: Alice, who is dealing in the examples; Bob, who is sitting to her left; Carol to his left; and David to Carol’s left. All four players ante $.25. Alice deals five cards to each player and places the deck stub aside. Bob opens the betting round by betting $1. Carol folds, David calls, and Alice calls, closing the betting round. Bob now declares that he wishes to replace three of his cards, so he removes those three cards from his hand and discards them. Alice retrieves the deck stub, deals a burn card, then deals three cards directly to Bob, who puts them in his hand. David discards one card, and Alice deals one card to him from the deck stub. Alice now discards three of her own cards, and replaces them with three from the top of the deck stub (Note: in a player-dealt casino game there is often a rule that the dealer must discard before picking up the deck stub, but this is a home game so we won’t worry about such details). Now a second betting round begins. Bob checks, David bets $3, Alice calls, and Bob folds, ending the second betting round. David shows a flush, and Alice shows two pair, so David takes the pot. This guide is licensed under the GNU Free Documentation License. It uses material from the Wikipedia. Need an webmaster? Click HERE For any given starting hand, there are 50 × 49 ÷ 2 = 1,225 hands that an opponent can have before the flop. (After the flop, the number of possible hands an opponent can have is reduced by the three community cards revealed on the flop to 47 × 46 ÷ 2 = 1,081 hands.) Therefore, there are (52/2)(50/2) -: 2 = 812.175 possible head-to-head match ups in Hold ‘em. (The number of total number of match ups is divided by the two ways that two hands can be distributed between two players to give the number of unique match ups.) However, since there are only 169 distinct starting hands, there are 169 × 1,225 = 207,025 distinct head-to-head match ups.[2] It is useful and interesting to know how two starting hands compete against each other heads up before the flop. In other words, we assume that neither hand will fold, and we will see a showdown. This situation occurs quite often in no limit and tournament play. Also, studying these odds helps to demonstrate the concept of hand domination, which is important in all community card games. This problem is considerably more complicated than determining the frequency of dealt hands. To see why, note that given both hands, there are 48 remaining unseen cards. Out of these 48 cards, we can choose any 5 to make a board. Thus, there are (48/5) = 1.712.304 possible boards that may fall. In addition to determining the precise number of boards that give a win to each player, we also must take into account boards which split the pot, and split the number of these boards between the players. The problem is trivial for computers to solve by brute force search; there are many software programs available that will compute the odds in seconds. A somewhat less trivial exercise is an exhaustive analysis of all of the head-to-head match ups in Texas Hold ‘em, which requires evaluating each possible board for each distinct head-to-head match up, or 1,712,304 × 207,025 = 354,489,735,600 (≈354 billion) results.[2] When comparing two starting hands, the head-to-head probability describes the likelihood of one hand beating the other after all of the cards have come out. Head-to-head probabilities vary slightly for each particular distinct starting hand matchup, but the approximate average probabilities, as given by Dan Harrington in Harrington on Hold’em [p.125], are summarized in the following table. These odds are general approximations only derived from averaging all of the hand matchups in each category. The actual head-to-head probabilities for any two starting hands vary depending on a number of factors, including: For example, A♠ A♣ vs. K♠ Q♣ is 87.65% to win (0.49% to split), but A♠ A♣ vs. ♦ ♦ is 76.81% to win (0.32% to split). The mathematics for computing all of the possible matchups is quite complex. However, a computer program can perform a brute force evaluation of the 1,712,304 possible boards for any given pair of starting hands in seconds. This guide is licensed under the GNU Free Documentation License. It uses material from the Wikipedia. Need an webmaster? Click HERE Five-card stud is probably the earliest form of the card game, stud poker, originating during the American Civil War, but is less commonly played today than seven-card stud and other games. It is still a popular game in a few locations such as South Africa (where it is played with a stripped deck). In Finland a specific version of five-card stud called Sökö (Canadian stud or Scandinavian stud) is still quite popular. The word sökö is also used for checking in Finland (“I check” = “minä sökötän”).Unlike seven-card stud, five-card stud plays very well at no limit and pot limit, though fixed limit and spread limit games are still more common (with higher limits in the later betting rounds). It is typical to use a small ante and a bring-in. The game can be played with low hand values, in which case the best low hand showing starts each betting round instead of the best high hand showing. Also, the highest-ranking card must pay the bring-in if it is played with a bring-in. If played high-low split, the highest showing hand always acts first. The fifth and final card is dealt face down in some games. Otherwise play is identical (the player who acted first on round three will therefore act first again on round four since no one’s exposed hand has changed). This game is described as “one down, three up, one down” or simply “1-3-1″, while traditional five-card stud is called “one down, four up”. This guide is licensed under the GNU Free Documentation License. It uses material from the Wikipedia. Need an webmaster? Click HERE Here is a sample deal involving our four players. The players’ individual hands will not be revealed until the showdown, to give a better sense of what happens during play: Compulsory bets: Alice is the dealer. Bob, to Alice’s left, posts a small blind of $1, and Carol posts a big blind of $2. First betting round: Alice deals four cards face down to each player, beginning with Bob and ending with herself. Ted must act first because he is the first player after the big blind. He cannot check, since the $2 big blind plays as a bet, so he folds. Alice calls the $2. Bob adds an additional $1 to his $1 small blind to call the $2 total. Carol’s blind is “live”, so she has the option to raise here, but she checks instead, ending the first betting round. The pot now contains $6, $2 from each of three players. First draw: Each player may now opt to draw up to four cards in an attempt to improve their hands. Bob, who is to the dealers immediate left, is given the first chance to draw. Bob discards two cards and receives two replacement cards from the top of the deck. Bob’s discarded cards are not added to the deck, but removed from play. Carol now chooses to also draw two. Finally, Alice chooses to draw one. Second betting round: Since there are no forced bets in later betting rounds, Bob is now first to act. He chooses to check, remaining in the hand without betting. Carol bets, adding $2 to the pot. Alice and Bob both call, each adding $2 to the pot. The pot now contains $12. Second draw: Bob draws one. Carol opts not to draw any cards, keeping the four she has (known as standing pat). Alice draws one. Third betting round: Bob checks again and Carol bets $4. Alice, this round, raises making the total bet $8. Bob folds and Carol calls the additional $4. The pot now contains $20. Third draw: Since Bob has folded Carol is now first to act, she opts to draw one. Alice stands pat (does not draw). Last betting round: Carol checks and Alice bets $4. Carol calls. Showdown: Alice shows 2♠4♣6♦9♥ for a nine-high badugi (or four card hand). Carol has 3♠5♦7♣8♥, an eight-high badugi. Carol wins the $28 pot. This guide is licensed under the GNU Free Documentation License. It uses material from the Wikipedia. Need an webmaster? Click HERE Another hold ‘em variant is Omaha hold’em. Each player is dealt four cards to his private hand instead of two. The betting rounds and layout of community cards is identical to Texas hold ‘em. At showdown, each player’s hand is the best five-card hand he can make from exactly three of the five cards on the board, plus exactly two of his own cards. The most popular form of the game is high-low split, called many different names such as “Omaha Eight or better”, “Omaha HiLo” or “Omaha8″. Each player, using the above rules, makes a separate five-card high hand and five-card low hand, and the pot is split between the high and low (which may be the same player). To qualify for low, a player must be able to play an 8-7-6-5-4 or lower. A few casinos play with a 9-low qualifier instead, but this is rare. When high hands only are used, the game is generally called “Omaha high” to avoid ambiguity. Omaha can be played fixed limit, pot limit (where it is often called “PLO”) or no limit. It is sometimes played where each player gets five cards instead of four. The same rules apply for showdown: each player must use two of his cards with three of the community cards. In the game of “Courcheval”, popular in Europe, instead of betting on the initial four cards and then flopping three community cards for the second round, the first community card is dealt before the first betting round, so that each player has four private cards and the single community card on his first bet. Then two more community cards are dealt, and play proceeds exactly as in Omaha. This guide is licensed under the GNU Free Documentation License. It uses material from the Wikipedia. Need an webmaster? Click HERE The probability of being dealt various starting hands can be explicitly calculated. In Texas Hold ‘em, a player is dealt two down (or hole) cards. The first card can be any one of 52 playing cards in the deck and the second card can be any one of the 51 remaining cards. This gives 52 × 51 ÷ 2 = 1,326 possible starting hand combinations. (Since the order of the cards is not significant, the 2,652 combinations are divided by the 2 ways of ordering two cards.) Alternately, the number of possible starting hands is represented as the binomial coefficient which is the number of possible combinations of choosing 2 cards from a deck of 52 playing cards. The 1,326 starting hands can be reduced for purposes of determining the probability of starting hands for Hold ‘em—since suits have no relative value in poker, many of these hands are identical in value before the flop. The only factors determining the strength of a starting hand are the ranks of the cards and whether the cards share the same suit. Of the 1,326 combinations, there are 169 distinct starting hands grouped into three shapes: 13 pocket pairs (paired hole cards), 13 × 12 ÷ 2 = 78 suited hands and 78 unsuited hands; 13 + 78 + 78 = 169. The relative probability of being dealt a hand of each given shape is different. The following shows the probabilities and odds of being dealt each type of starting hand. Here are the probabilities and odds of being dealt various other types of starting hands. This guide is licensed under the GNU Free Documentation License. It uses material from the Wikipedia. Need an webmaster? Click HERE Caribbean Stud Poker differs slightly in the United Kingdom, and most parts of Europe, from the US. The game is officially known as “Casino Five Card Stud Poker”, and not all casinos have the jackpot prize. Those which do have the prize, usually the large chain groups, officially call the game “Casino Jackpot Five Card Stud Poker”. In both instances, the game is commonly referred to as “Casino Stud Poker”. The basic rules are the same in the UK as the US, although the payouts differ – the maximum bet is generally £100 on the ante and £200 on the raise, and all payouts are paid on the raise, meaning the maximum payout can potentially be £10,000 (a Royal Flush pays at the same odds, 50:1, as a Straight Flush). Casinos offering the jackpot generally have the card shuffled by a card shuffling machine – the cards are then removed and dealt out by the dealer, or croupier. Independent and small casinos generally have the croupier shuffle the cards by hand. British casinos do not use the chip dropper system; instead, a £1 chip is placed on a small plastic circle on the table, which lights up. The croupier then presses a button on a panel infront of them, which keeps the lights lit up once the chips are removed. The dealer removes the chips, and can then tell which players are playing the jackpot game and which are not. If the dealer does not show an Ace/King, hands playing the jackpot must be turned over, face up, and shown to the dealer and table. If the player is not playing the jackpot prize, the cards are not shown. This guide is licensed under the GNU Free Documentation License. It uses material from the Wikipedia. Need an webmaster? Click HERE Badugi has a different ranking of hands than traditional poker. Although every player has four cards to use, the rules of the game require that certain cards be removed to construct a one, two, three or four card badugi hand. At the showdown (after all betting has concluded), a player is forced to remove the higher of any two suited cards and any paired cards from the four. This generates a badugi hand of one to four cards. Any four card badugi hand beats a three card badugi hand, three card badugi hands beat a two card badugi hand, and two card badugi hands beats a one card badugi hand. A four card badugi hand is often referred to simply as a “badugi”. Two badugi hands containing the same number of cards are evaluated by comparing the highest card in each hand (where ace is low). As in lowball, the hand with the lower card is superior. If there is a tie for the highest card, the second highest card (if there is one) is compared. If the ranks of all the cards in the badugi hand are the same the two hands tie. As with standard poker games, suits are irrelevant in comparison of two hands. Here are a few examples: This guide is licensed under the GNU Free Documentation License. It uses material from the Wikipedia. Need an webmaster? Click HERE The poker game called Chicago is one of the most popular card games in Sweden today. Relying on the keeping of score instead of the placing of bets, it is suitable even for environments such as schools, where gambling is often prohibited. The game exists in countless versions, so here a (somewhat arbitrarily chosen) basic game will be followed by a number of possible variations. The backbone of the game is that each poker hand has its own point value, as given in this table: One pair – 1 point. Chicago is played with a standard 52-card deck. Each player is dealt five cards. The objective is to reach 52 points. The players are allowed to exchange any number of their cards. If a player chooses to exchange one card only, he may choose “one up”, meaning that he is dealt one card faced up, which he can either accept, or instead take the next card unseen. After the exchanges, the player with the best hand (and only one player) gets points for his hand. Then follows another round of exchanges, but no hand scoring. Now, the first player begins by playing one card. Ordinary whist rules apply, but the players keep their cards collected by themselves. The player who wins the last trick gets 5 points. Also, the player with the best hand (whether it is the same player or not) gets points for his hand. After the second exchange, any player can choose to play Chicago. In this case, he pledges himself to win all the tricks of the game. If he does, he is awarded 15 points, but if he fails, the penalty is just as harsh: -15 points. This guide is licensed under the GNU Free Documentation License. It uses material from the Wikipedia. Need an webmaster? Click HERE This is the most popular community card game today. Each player is dealt two private cards, after which there is a betting round. Then three community cards are dealt face up (in no particular order or pattern), followed by a second betting round. A fourth community card is followed by a third betting round, a fifth community card and the fourth and final betting round. At showdown, each player plays the best five-card hand he can make using any five cards among the two in his hand and the five on the board. For double-board hold ‘em, two separate five-card boards are dealt, and the high hand using each board takes half of the pot. For example, after the first betting round, three community cards are dealt to each of two separate boards; after the second round, another community card is dealt to each board; and before the final round, a fifth community card is dealt to each board (so there will be in total ten community cards, comprising two separate five-card hold’em boards). This variant of Texas hold ‘em is sometimes called “double-flop hold’em”, which is a bit of a misnomer, since there are not just two flops, but also two turns and two rivers. This guide is licensed under the GNU Free Documentation License. It uses material from the Wikipedia. Need an webmaster? Click HERE Play begins with each player being dealt four cards face down. Each player may observe those four cards she is dealt, but not the cards dealt to other players. The hand begins with a “pre-draw” betting round, beginning with the player to the left of the big blind (or the player to the left of the dealer, if no blinds are used) and continuing clockwise. Each player must either call the amount of the big blind (put in an amount equal to the big blind), fold (relinquish any claim to the pot), or raise (put in more money than anyone else, thus requiring others to do the same). Once everyone has put the same amount of money in the pot or folded, play proceeds to the draw. Beginning with the first player still in the pot to the left of the dealer, each player may discard any number of cards and receive an equal number of replacement cards (called the “draw”). Replacement cards are dealt before the next player chooses the number of cards to draw. The discarded cards are not readded to the deck but are discarded from the game. The first draw is followed by a second betting round. Here players are free to check (not put in any money, but also remain in the hand) until someone bets. Again betting proceeds until all players have put in an equal amount of money or folded. After the second betting round ends, there is another draw followed by a third betting round. After that there is the final draw, followed by a fourth betting round and the showdown, if necessary. If at anytime all players but one have folded, the sole remaining player is awarded the pot. If there are more than one player remaining at the conclusion of the final betting round, the hands of those players are compared and the player with the best badugi hand is awarded the pot. This guide is licensed under the GNU Free Documentation License. It uses material from the Wikipedia. Video: How to play Badugi – Part 2 of 4 (Poker Video) Kuhn poker is a simplifed form of poker developed by Dr. Harold W. Kuhn, it is a zero sum two player game. The deck includes only three playing cards, for example a King, Queen, and Jack. One card is dealt to each player, then the first player must bet or pass then the second player may bet or pass. If any player chooses to bet the opposing player must bet as well (“call”) in order to stay in the round. After both players pass or bet the player with the highest card wins the pot. Kuhn demonstrated that there are many game theoretic optimal strategies for the first player this game, but only one for the second player, and that played optimally the first player should expect to lose at a rate of −1/18 per hand.In more conventional poker terms: This guide is licensed under the GNU Free Documentation License. It uses material from the Wikipedia. About the time of World War II, many modern poker games used community cards (also called “shared cards” or “window cards”), which are cards dealt face up to the center of the table and shared by all players. In these games, each player is dealt privately an incomplete hand (“hole cards”), which is then combined with the community cards to make a complete hand. The set of community cards is called the “board”, and may be dealt in a simple line or arranged in a special pattern. Rules of each game determine how they may be combined with each player’s private hand. The most popular community card game today is Texas hold ‘em, originating sometime in the 1920s. In home games, it is typical to use antes, while casinos typically use only blinds for these games. Fixed limit games are most common in casinos, while spread limit games are more common in home games. No limit and pot limit games are less common. Later betting rounds often have a higher limit than earlier betting rounds. Each betting round begins with the player to the dealer’s left (when blinds are used, the first round begins with the player after the big blind), so community card games are generally positional games. Most community card games do not play well with lowball hand values, though some do play very well at high-low split, especially with ace-to-five low values, making it possible to win both halves of a pot. When played high-low split, there is generally a minimum qualifying hand for low (often 8-high), and it is played cards speak. This guide is licensed under the GNU Free Documentation License. It uses material from the Wikipedia. In 1998, the movie Rounders starring Matt Damon and Edward Norton gave moviegoers a romantic view of poker as a way of life. Texas hold ‘em was the main game played during the movie and the no-limit variety was described, following Doyle Brunson, as the “Cadillac of Poker”. There was also a clip of the classic showdown between Johnny Chan and Erik Seidel from the 1988 World Series of Poker incorporated into the film. CommanderBond.net reports that the centerpiece card game in the next James Bond film, Casino Royale, will be no-limit Texas hold ‘em instead of Baccarat as in the original Ian Fleming novel. Hold ‘em first caught the public eye as a spectator sport in the United Kingdom with the Late Night Poker TV show in 1999. The popularity of the show led to lipstick cameras also being used for American poker programs. In 2003, hold ‘em exploded in popularity as a spectator sport in the United States. This was due to several factors, including the introduction of lipstick cameras that allowed the television audience to see the players’ hidden cards. ESPN’s coverage of the 2003 World Series of Poker featured the unexpected victory of Internet player Chris Moneymaker, an amateur player who gained admission to the tournament by winning a series of online tournaments. Moneymaker’s victory initiated a sudden surge of interest in the WSOP, based on the egalitarian idea that anyone – even a rank novice – can become a world champion. In 2003, there were 839 entrants in the WSOP Main Event. In 2004, that number tripled. The crowning of the 2004 WSOP champion, Greg “Fossilman” Raymer, a patent attorney from Connecticut whose trademark holographic sunglasses have become legendary, further fueled the popularity of the event among amateur (and particularly internet) players. In the 2005 Main Event, an unprecedented 5,619 entrants vied for a first prize of $7,500,000. The winner, Joseph Hachem of Australia, was a semi-professional player. The runner-up, Steve Dannenmann, an amateur from Maryland, opined that he was only “the fourth or fifth best player” in his regular home game. Two additional hold ‘em series debuted in 2003, the World Poker Tour and Celebrity Poker Showdown. All three of these shows are still currently in production and garner a large and loyal viewership. With the ability to edit a tournament that lasts days into just a few hours, ESPN’s World Series of Poker focuses on showing how various star players fared in each event. Key hands from throughout the many days of each event are shown, and similar, highly edited coverage of final tables is also provided. The World Poker Tour does not offer general coverage of the multi-day poker tournaments. Instead, WPT covers only the action at the final table of each event. With aggressive play and increasing blinds and antes, the important action from a single table can easily be edited into a two hour episode. Although the tournament fate of fewer stars are chronicled this way, it allows the drama to build more naturally toward the final heads up showdown. Celebrity Poker Showdown coverage is a single table like World Poker Tour, however, the players are much less skilled and are invited to participate instead of winning their way on. This guide is licensed under the GNU Free Documentation License. It uses material from the Wikipedia. Caribbean stud poker is a casino table game with rules similar to five card stud poker. However, unlike standard poker games, Caribbean stud is played against the house rather than against other players (and, like most such games, it cannot be beaten in the long run). There is no bluffing or other deception. For these reasons, most poker players do not consider it to be a form of poker. (They do not necessarily feel that it should not be called poker, but means merely that they will not refer to it as simply “poker”. For instance, a gambler might say “I played poker” if he played seven card stud, but probably would not if he played Caribbean stud.) The following rules are typical of U.S. casinos, but some of the details (the payouts and limits) vary from casino to casino. To play, every player places his ante on the layout where indicated; all ante wagers must be placed prior to the dealer announcing “No more bets“. Each player and the dealer will then receive 5 cards, face down. The dealer will turn over one of his cards, then push the cards toward the players, after which the players may look at their cards. They may only look at their own cards, and may not discuss what they have with any other player at the table. Players have the option to play or fold; if they choose to play, they place their bets (twice the amount of their respective ante) in the bet box. If they choose to fold, they forfeit their ante. After all the players have made their decisions, the dealer reveals his hole cards. The dealer only plays with an ace/king or higher; he then compares his cards to the players’ cards (individually, right to left), and the best poker hand wins. There are some major rules in Caribbean Stud Poker that must be observed at all times while playing: If a player’s cards beat the dealer’s cards, the player will receive even money (1-1) on the ante, and the following on his bet (with a maximum payout of $5,000 U.S. Dollars per hand on each bet wager): If the dealer does not have at least ace/king, all bet wagers will be void, and players will receive even money on their ante bet only. If the dealer’s cards beat a player’s cards, the dealer collects both the ante and bet. In addition, in Caribbean stud poker, players can also bet on their poker hands and win the “progressive feature”; this is done by dropping a 1.00 dollar gaming chip into the chip acceptor on the table after placing the ante. Players with a flush or higher win, regardless of the outcome of their table bets: Winning progressive payout hands are paid in accordance with the amount on the meter when it is the player’s turn to be paid. However, if more than one player at a table has a royal flush progressive payout hand, each player shares equally in the amount on the meter when the first player with a royal flush is to be paid. Using optimal strategy the house edge is 5.224% of the player’s ante bet. This strategy can be complicated and does not lend itself to practical use in a casino. Using a strategy of raising with Ace/King/Jack/8/3 or better the house edge is 5.316%, very close to the optimal strategy house edge. Knowledge of what other players hold can decrease the house edge. It has been estimated with the knowledge of 6 other player’s hands (30 cards) and associated optimal strategy the player can gain an edge of 2.3%. Given that sharing information is against the rules and that a computer would be needed to calculate the appropriate strategy it is unlikely this could ever be achieved in a real life casino. This guide is licensed under the GNU Free Documentation License. It uses material from the Wikipedia. Video: Poker Games : How to Play Caribbean Stud Poker The best hand in badugi, a four-high badugi. Badugi (also known as Badougi or Padooki) is a draw poker variant similar to triple draw, but with differing hand values than traditional poker. The betting structure and overall play of the game is identical to a standard poker game, but unlike traditional poker which involves a minimum of five cards, players’ hands contain only four cards at any one time. During each of three drawing rounds, players can trade zero to four cards from their hands for new ones from the deck, in an attempt to form the best badugi hand and win the pot. The object of Badugi is to win pots, the share of money put in by oneself and one’s opponents during the hand. The winner of the pot is the person, who has not folded, with the best badugi hand at the conclusion of play (known as the showdown). Originating in Asia, Badugi is becoming very popular in the United States. This guide is licensed under the GNU Free Documentation License. It uses material from the Wikipedia. Video: How To Play Badugi Web Design & Development Follow me on Twitter & Facebook Casino-Online.com (Gambling portal) + 2P + … + (n-1)Pn,
is the probability that exactly two players have a higher pair, P is the probability that exactly three players have a higher pair, etc. As a practical matter, even with pocket 2s against 9 opponents, P < 0.0015 and P < 0.00009, so just calculating P and P gives an adequately precise result.
Probability of facing a
larger pair when holdingAgainst 1
Against 2
Against 3
Against 4
Against 5
Against 6
Against 7
Against 8
Against 9
KK
0.0049
0.0098
0.0147
0.0196
0.0244
0.0293
0.0342
0.0391
0.0439
QQ
0.0098
0.0195
0.0292
0.0388
0.0484
0.0579
0.0673
0.0766
0.0859
JJ
0.0147
0.0292
0.0436
0.0577
0.0717
0.0856
0.0992
0.1127
0.1259
TT
0.0196
0.0389
0.0578
0.0764
0.0946
0.1124
0.1299
0.1470
0.1637
99
0.0245
0.0484
0.0718
0.0946
0.1168
0.1384
0.1593
0.1795
0.1990
88
0.0294
0.0580
0.0857
0.1125
0.1384
0.1634
0.1873
0.2101
0.2318
77
0.0343
0.0674
0.0994
0.1301
0.1595
0.1874
0.2138
0.2387
0.2619
66
0.0392
0.0769
0.1130
0.1473
0.1799
0.2104
0.2389
0.2651
0.2890
55
0.0441
0.0862
0.1263
0.1642
0.1996
0.2324
0.2623
0.2892
0.3129
44
0.0490
0.0956
0.1395
0.1806
0.2186
0.2532
0.2841
0.3109
0.3334
33
0.0539
0.1048
0.1526
0.1967
0.2370
0.2729
0.3040
0.3300
0.3503
22
0.0588
0.1141
0.1654
0.2124
0.2546
0.2914
0.3222
0.3464
0.3633
+ P + … + Pn.
♥
Probability of facing multiple
larger pairs when holdingAgainst 2
Against 3
Against 4
Against 5
Against 6
Against 7
Against 8
Against 9
KK
< 0.00001
0.00001
0.00003
0.00004
0.00007
0.00009
0.00012
0.00016
QQ
0.00006
0.00018
0.00037
0.00061
0.00091
0.00128
0.00171
0.00220
JJ
0.00017
0.00051
0.00102
0.00171
0.00257
0.00360
0.00482
0.00621
TT
0.00033
0.00099
0.00200
0.00335
0.00504
0.00709
0.00950
0.01226
99
0.00054
0.00164
0.00330
0.00553
0.00836
0.01177
0.01580
0.02045
88
0.00081
0.00244
0.00493
0.00828
0.01253
0.01769
0.02378
0.03084
77
0.00112
0.00341
0.00689
0.01160
0.01758
0.02487
0.03351
0.04353
66
0.00149
0.00454
0.00918
0.01550
0.02353
0.03335
0.04503
0.05861
55
0.00191
0.00583
0.01182
0.01998
0.03040
0.04318
0.05840
0.07619
44
0.00239
0.00728
0.01480
0.02506
0.03821
0.05438
0.07371
0.09635
33
0.00291
0.00890
0.01812
0.03075
0.04698
0.06699
0.09099
0.11919
22
0.00349
0.01068
0.02180
0.03706
0.05673
0.08107
0.11034
0.14484
Hands with one ace
Starting hands against multiple opponents in Texas Hold ‘em
♣ and the opponents holding ♥
♣ and A♠ J♥. The number of ways that hands can be distributed between n opponents is n! (pronounced n factorial). So the number of unique hand combinations H against two opponents is
Opponents
Number of possible hand combinations
1
1,225
2
690,900
3
238,360,500
4
56,372,258,250
5
≈9.7073 × 1012 (more than 9.7 trillion)
6
≈1.2620 × 1015 (more than 1.2 quadrillion)
7
≈1.2674 × 1017 (more than 126 quadrillion)
8
≈9.9804 × 1018 (almost 10 quintillion)
9
≈6.2211 × 1020 (more than 622 quintillion)
Five-card stud play
Five-card draw
Sample deal
Texas hold ‘em – Starting hands heads up
Head-to-head starting hand matchups
Favorite-to-underdog matchup
Probability
Odds for
Pair vs. 2 undercards
0.83
4.9 : 1
Pair vs. lower pair
0.82
4.5 : 1
Pair vs. 1 overcard, 1 undercard
0.71
2.5 : 1
2 overcards vs. 2 undercards
0.63
1.7 : 1
Pair vs. 2 overcards
0.55
1.2 : 1
Notes
Five-card stud
High-low and other variants
Example of hand in badugi poker
The blinds for this example hand
Community card poker – Omaha hold ‘em
Probability for starting hands in Texas Hold ‘em
Hand shape
Number
of handsPermutations
for each handCombinations
Pocket pair
13
(4/2) = 6
13 × 6 = 78
Suited cards
78
(4/1) = 4
78 × 4 = 312
Unsuited cards
78
(4/1)(3/1) = 12
78 × 12 = 936
Hand shape
Dealt specific hand
Dealt any hand
Probability
Odds
Probability
Odds
Pocket pair
/1326 ~ 0.00453
220 : 1
8/1326 ~ 0.0588
16 : 1
Suited cards
/1326 ~ 0.00302
12/1326 ~ 0.2353
331 : 1
3.25 : 1
Unsuited cards
2/1326 ~ 0.00905
110 : 1
36/1326 ~ 0.7059
0.417 : 1
Hand
Probability
Odds
AKs (or any specific suited cards)
0.00302
331 : 1
AA (or any specific pair)
0.00453
220 : 1
AKs, KQs, QJs, or JTs
0.0121
81.9 : 1
AK (or any specific non-pair)
0.0121
81.9 : 1
AA, KK, or QQ
0.0136
72.7 : 1
Suited cards, J or better
0.0181
54.3 : 1
AA, KK, QQ, JJ, or TT
0.0226
43.2 : 1
Suited cards, T or better
0.0302
32.2 : 1
Suited connectors
0.0392
24.5 : 1
Connected cards, T or better
0.0483
19.7 : 1
Any 2 cards with rank at least Q
0.0498
19.1 : 1
Any 2 cards with rank at least J
0.0905
10.1 : 1
Any 2 cards with rank at least T
0.143
5.98 : 1
Connected cards (cards of consecutive rank)
0.157
5.38 : 1
Any 2 cards with rank at least 9
0.208
3.81 : 1
Not connected nor suited, at least one 2-9
0.534
0.873 : 1
Caribbean Stud Poker in the United Kingdom
Hand evaluation in badugi poker
Chicago poker
Hand scores
Two pair – 2 points.
Three of a kind – 3 points.
Straight – 4 points.
Flush – 5 points.
Full House – 6 points.
Four of a kind – 7 points (but see Variations below).
Straight flush – 8 points (but see Variations below).Basic rules
Exchanges and hand scoring
The game
Chicago
Variations
Community card poker – Texas hold ‘em
Double-board hold ‘em
Poker probability for Texas hold ‘em
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Badugi play of the hand
Kuhn poker
References
Link
Community card poker
Texas hold ‘em in popular culture
Joe Hachem, winner of 2005 World Series of Poker main eventSpectator sport
Caribbean stud poker
Royal flush
100 to 1
Straight flush
50 to 1
Four of a kind
20 to 1
Full house
7 to 1
Flush
5 to 1
Straight
4 to 1
Three of a kind
3 to 1
Two pair
2 to 1
One pair or less
1 to 1
Royal Flush
100% of Progressive Meter
Straight Flush
10% of Progressive Meter
Four-of-a-Kind
$500
Full House
$100
Flush
$50
Player Strategy
Badugi
Titan PokerTranslator
Blogroll
Review
Internet Marketing & Advertising
English-Romanian Translation
Nicolae Sfetcu
E-mail, Tel.: 0745-526896
