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Most variants of poker satisfy the following definition, but in a home game of course you are free to modify the rules as you see fit.
Poker is a card game in which players bet into a communal pot during the course of a hand, and in which the player holding the best hand at the end of the betting wins the pot. During a given betting round, each remaining player in turn may take one of four actions:
Betting usually proceeds in a circle until each player has either called all bets or folded. Different poker games have various numbers of betting rounds interspersed with the receipt or replacement of cards.
Poker is usually played with a standard 4-suit 52-card deck, but a joker or other wild cards may be added. The ace normally plays high, but can sometimes play low, as explained below. At the showdown, those players still remaining compare their hands according to the following rankings:
(* Such matchups are only possible in games where there are wild cards or where community cards are shared, such as Texas Holdem.)
Suits are not used to break ties, nor are cards beyond the fifth; only the best five cards in each hand are used in the comparison. In the case of a tie, the pot is split equally among the winning hands. For a more detailed explanation, see the section on splitting the pot.
Several variations are possible when playing for low. Some games permit the ace to play low and ignore straights and flushes, making 5432A the best possible low, even if it makes a straight flush. Other games just reverse the order used for high hands, making 75432 of mixed suits the best possible low. Still others count straights and flushes against you but let the ace play low, making 6432A best. Note that in most games in which the ace plays low, a pair of aces is lower than a pair of deuces, just as an ace is lower than a deuce.
When a joker is in play, it usually can only be used as an ace or to complete a straight or flush. It cannot be used as a true wild card, for example, as a queen to make QQ43X play as three queens. When playing for low, the joker becomes the lowest rank not already held, so 864AX is played as 8642A, with the joker used as a deuce.
Although true wild cards are rarely seen in a casino, they are a popular way to add excitement to a home game. Wild cards introduce an additional hand, five of a kind, which normally ranks above a straight flush. They can also cause confusion when two players hold the same hand composed of different wild card combinations. The standard rules of poker do not distinguish between such hands, but some players prefer to rank hands using fewer wild cards above less "natural" versions of the same hand.
You may find these comprehensive poker rulebooks helpful:
Caro and Cooke's Rules of Real Poker
Bob Ciaffone's "Robert's Rules of Poker"
Tournament Directors Association (TDA) Rules
2004 World Series of Poker (WSOP) Rules
If you are interested in learning all about online poker in particular, try the Beginners' Guide to Online Poker. It goes way beyond the basics to topics like record keeping software, site integrity, the law and taxes.