The canonical community card game today is probably Texas hold'em (and variants thereof), originating sometime in the 1970s. That game is described in great detail on its own page, while most of the descriptions below are brief and refer to that more detailed page (a few other games merit their own page as well, such as Omaha hold'em).
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, but some games play particularly well with those structures. As with stud poker, 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.
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Described in more detail here, this is the most popular community card game today (2002), especially in the western US. Each player is dealt two private cards, after which there is a betting round. Then three community cards are deal 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.
Texas hold'em does not play well high-low split (Omaha hold'em is probably the best high-low community card game). It plays very well at no limit, and in fact the final game of the World Series of Poker, the tournament generally considered to be the world championship of the game of poker, is the $10,000 entry no limit Texas hold'em event.
These are variants of Texas hold'em in which each player is initially dealt three cards instead of two. In Pineapple, each player then immediately discards one of the three cards he is dealt, and the game proceeds exactly as in Texas hold'em. In Crazy Pineapple, the players discard their third card after the second betting round, before the fourth community card is dealt. In Tahoe, players keep all three cards through showdown, but may not use all three of them to make a hand--each player may use none, one, or two cards from his hand, combined with those on the board, to make his final five-card hand.
Crazy Pineapple and Tahoe are often played high-low split, and play reasonably well that way, though plain Pineapple does not.
A split-pot variant that can be applied to many games (but that is generally only applied to normal hold'em) is "double-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 popular and complex enough to deserve its own page. Briefly, each player is dealt four cards to his private hand instead of two. The betting rounds and layout of community cards are identical. 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. Unlike Texas hold'em, a player cannot play only one of his cards with four of the board, nor can he play the board, nor play three from his hand and two from the board, or any other combination. Each player must play exactly two of his own cards with exactly three of the commuity cards.
The most popular form of the game is high-low split, called "Omaha/8 or better", or just "Omaha/8". 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. This game is generally played at fixed limit.
When high hands only are used, the game is generally called "Omaha high" to avoid ambiguity. This game plays particularly well at pot limit, called "PLO".
Another variant is to deal each player 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.
One of the most popular games in Australian casinos is a Texas hold'em variant called "Manila" (also called "Seven-up" in some places). It is played with a Stripped deck in which all cards below the rank of 7 are removed (leaving 32 cards). Each player is dealt two private cards, and a single community card is dealt face up, followed by the first betting round. Then a second community card is followed by a second round, a third community card and a third round, and fourth community card and a fourth round, and finally a fifth community card, fifth betting round, and showdown. On showdown, unlike Texas hold'em (and more like Omaha), each player makes the best hand he can from both of his hole cards with exactly three of the five community cards.
Because of the stripped deck, a flush beats a full house. Also, an ace may not be played low for a straight (that is, the hand A-7-8-9-10 is not a straight in Manila). Manila and its variants are rarely played high-low split (in fact, very few stripped deck games are ever played low).
Common variations involve dealing three cards to each player, one of which can either be discarded at some point (like Pineapple, above), or else held to the end, but maintaining the requirement that each player play exactly two of his own cards with exactly three of the board. The three-card variant is sometimes played with 6s being restored to the deck, making it 36 cards.
Because Manila has five betting rounds, it does not play well at no limit or pot limit. This can be easily modified by eliminating the betting round between the second and third community cards. So, each player is dealt two private cards and a single community card is dealt to the board, followed by the first betting round. Then two community cards are dealt, followed by a second betting round. Then a fourth community card and third betting round, a fifth and final community card and fourth betting round, followed by a showdown as above.
The three-card variant can be played this way as well (as with Manila, the player must use exactly two of his three hole cards with three of the board cards to make a hand).
Although some of these games (notably Chowaha and Tic tac toe) have been played in formal casino settings, they are generally better suited to less serious low-stakes home games. They also lend themselves to ad-hoc variation, since the games themselves have not been time-tested for balanced play as have many casino games, so making variations is likely to make the game much worse.
Each player is dealt five hole cards, and then one community card is dealt face up to the table. After a first betting round, a second community card is dealt, followed by a second betting round. This continues until a fifth community card is dealt, followed by a fifth betting round and showdown. Each player plays the best five-card hand he can make from his five hole cards plus the five community cards in any combination. More sane variants are to restrict each player to using exactly two of his hole cards (as in Omaha) or no more than two (as in Pineapple).
Each player is dealt five hole cards, and then five community cards are dealt one at a time followed by a betting round, exactly as in Cincinatti. But they are dealt in a cross pattern with a center card (dealt last) and four other cards to its left, right, top, and bottom. Each player plays the best five-card poker hand he can make from his five hole cards plus the three cards from either the vertical arm or the horizontal arm of the cross. A common variant is to make the center card wild, or the center card and all of the same rank wild.
One can also make a better game by reducing to four betting rounds: one after the hole cards are dealt but before any community cards are, then another after the left and right cards of the cross are dealt at the same time, a third after the top and bottom cards of the cross are dealt, and a final round after the center card is dealt.
(Need graphics for this one)
In this game, each player will end up with two private cards, and there will be a board of nine cards arranged in a 3x3 square. Each player will make a five-card hand from a combination of his two cards plus any consecutive row of three on the board, either a horizontally, vertically, or diagonally (as in Tic tac toe). Variations exist in the number of betting rounds based on which community cards are revealed in what order. The simplest is probably to deal each player both hole cards then deal the three cards across the top of the 3x3 array before the first betting round; then deal the three cards across the bottom of the array followed by a second betting round; then deal the two cards on the left and right edge of the middle row, followed by a third round; and finally deal the center community card followed by a fourth betting round and showdown.
Another variation is to deal three or four hole cards to each player, though each player may still only play exactly two of them with any consecutive row of three from the grid.
(Need examples here)
A poker-like beginner's home game is also called "Tic tac toe"; it involves dealing each player two hole cards and then dealing the 3x3 grid face up, followed by a single betting round after which players announce the best hand they can make from their two cards plus any consecutive row, column, or diagonal of the board as above. Hole cards can be redealt several times to the same board of community cards. This is primarily for practice at recognizing and evaluating poker hands.
Three hole cards are dealt to each player, followed by a first betting round. Then a single community card is dealt, followed by a second betting round. Play continues with a single community card being added to the board followed by a betting round, until there are four community cards, for a total of five betting rounds. Upon showdown, the lowest-ranking card on the board, and all cards of that same rank either on the board or in players' hole cards, play as wild cards (thus, it is not possible to know exactly which cards will be wild until the end, unless a deuce appears on the board earlier than that). Each player makes his best five-card poker hand from his three hole cards plus the four community cards in any combination, with the low board card wild.
(Graphics would be good here too)
At showdown, each player will have two hole cards, and there will be six community cards on the board arranged in a circle (something like the even-hour marks on a clock). The rounds go like this: each player is dealt two hole cards, followed by the first betting round. Then two of the board cards at opposite sides of the circle (call them 12 o'clock and 6 o'clock) are dealt, followed by a second betting round. Two more opposite community cards are dealt (2 o'clock and 8 o'clock), followed by a third betting round. Finally, the 4 o'clock and 10 o'clock cards are dealt followed by a fourth and final betting round, and showdown.
At showdown, each player makes a hand by combining his two cards with any three consecutive cards of the board. That is, he can use 12, 2, and 4; or 2, 4, and 6; or 6, 8, and 10; etc. So cards dealt to opposite sides of the circle will never appear in the same final hand. With exactly two hole cards, there are only six possible choices for which hand to play. The game can be modified bit by dealing three hole cards, where each player is required to use exactly two of them plus three consecutive board cards.
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