Texas hold 'em
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.
Pineapple (and Crazy Pineapple, Tahoe)
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.
Double-board hold'em
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).
Omaha hold'em
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 community 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.

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