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Frequently used when the exact odds are expressed. underfull A full house made where the three of a kind has lower-ranking cards than the pair. Compare with big full up When used with a card rank to describe a poker hand, refers to two pair with the named card being the higher pair. upcard A card that is played face up. See main article: upcard ...
Three of a kind, also known as trips or a set, is a hand that contains three cards of one rank and two cards of two other ranks (the kickers), such as 2 ♦ 2 ♠ 2 ♣ K ♠ 6 ♥ ("three of a kind, twos" or "trip twos" or a "set of twos"). It ranks below a straight and above two pair.
In statistics, this is called odds against. For instance, with a royal flush, there are 4 ways to draw one, and 2,598,956 ways to draw something else, so the odds against drawing a royal flush are 2,598,956 : 4, or 649,739 : 1. The formula for establishing the odds can also be stated as (1/p) - 1 : 1, where p is the aforementioned probability.
Thus, a run of four will contain two independent runs of three for 6 points; a run of five with three independent runs of 3 will be worth 9. Double runs of four will contain either 3 or 4 independent runs of three depending on whether the pair is at the end or the middle, garnering 9+2=11 or 12+2=14 points respectively.
A Farkle game in progress; a pair of three threes has been set aside, earning 300 points. Farkle, or Farkel, is a family dice game with varying rules. Alternate names and similar games include Dix Mille, Ten Thousand, Cosmic Wimpout, Chicago, Greed, Hot Dice, Volle Lotte, Squelch, Zilch, and Zonk.
Another variation is "six card bonus", in which the players are given a payout based on the best five-card poker hand that can be made using any combination of the player's three cards and the dealer's three cards. Payoff ranges from 5 to 1 for three of a kind to 1000 to 1 for royal flush. Payoffs are paid regardless of whether any other bets pay.
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Each one has an exact probability of 120 / 7776. Under these rules, a Straight beats a Full House (unlike in card poker, but correctly reflecting its probability) but does not beat a Four of a Kind (incorrectly reflecting its lower probability). A Flush beats a Four of a Kind (unlike in card poker, but correctly reflecting its lower probability).