For "all poker variants", much depends on which kind of poker is meant. Poker at a casino comes in two very different forms. In house games such as three card poker or casino hold'em, each player faces the dealer and a paytable. In room games such as hold'em or Omaha, players compete with each other and the casino takes a small cut of each pot. The hand rankings are shared by all of them, and the other rules vary from game to game.
Every poker variant ranks hands the same way, from a high card at the bottom through a pair, two pairs, three of a kind, a straight, a flush, a full house and four of a kind, to a straight flush at the top. Three card games are the exception in one detail: with fewer cards, a straight beats a flush. The ranking chart is printed in the rules of every game and worth keeping open.
Three card poker deals three cards to the player and three to the dealer. After an ante, the player either folds or places a play bet equal to the ante. The dealer needs a queen high or better to qualify; if it does not, the ante pays even money and the play bet is returned. An optional pair plus bet pays on the player's own hand, whatever the dealer holds. Standard advice is to play any hand of queen, six, four or stronger.
After seeing two private cards and the first three shared ones, the player either folds or calls with a bet worth twice the ante.
Hold'em gives each player two private cards alongside five shared ones, while Omaha deals four private cards, exactly two of which must be used.
The order climbs from a high card through pairs, trips, straights, flushes, full houses and quads to the straight flush, though three card games place a straight above a flush.
The casino collects a rake, either a small share of each pot or a fixed fee per hour or per tournament, and has no stake in who wins.