Three of a Kind Definition – Probability of Three Cards of the Same Rank

What Is Three of a Kind in Poker?

Unlike some poker hands, three of a kind in poker is pretty self-explanatory.

It’s a hand containing three cards of the same rank in addition to two other, unrelated and irrelevant cards that only play the role of kickers.

Examples of 3 of a kind hands in Hold’em are A A A X X or 7 7 7 X X. You can make this poker hand one of two ways – holding just one of the cards in your hand and combining it with two community cards, or holding a pocket pair and finding the third card of the same rank on the board.

In the latter case, this type of a three of a kind hand is often referred to as a  set.

Without specific knowledge of poker math and odds, it’s somewhat of a natural question to ask whether three of a kind beats two pair. Both hands seem fairly difficult to get. However, it all high poker variations, three of a kind always beats two pair.

That said, it loses to all straights and better.

Probability of Three of a Kind

Three of a kind, or trips, is a relatively strong hand, but it’s often not the nuts. Thus, the probability of tree of a kind is naturally higher than that of other, stronger hands like flushes and full houses.

  • Making three of a kind on a flop with any two cards (pairs and unpaired hands): 1.9%
  • Odds of flopping three of a kind with a pocket pair: 10.8%
  • Probability of three of a kind with any unpaired hand: 1.35%

If you only have a single pair on the flop, whether with a flopped pair or holding a pocket pair, your odds of improving to three of a kind by the river are about 8.4%.

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