What are the Texas Hold'em rules for determining which hand beats another in a showdown?

In Texas Hold'em, the hand rankings from highest to lowest are: Royal Flush, Straight Flush, Four of a Kind, Full House, Flush, Straight, Three of a Kind, Two Pair, One Pair, and High Card. In a showdown, the player with the highest-ranking hand wins. If two players have the same hand ranking, the player with the highest individual cards wins. If the highest individual cards are also the same, the pot is split.