Three of a Kind is three cards of one rank plus two unrelated cards, the kickers. It is also called trips, or a set when it comes from a pocket pair. It is the seventh strongest hand in the poker hand rankings.
How it works
Three cards share a rank and the other two fill out the hand. In Texas Hold’em, how you make it changes how hidden it is.
Hold a pocket pair and hit a third card on the board and you have a set: only you know how strong your hand is. Make trips with one hole card while the board is paired and everyone can see the danger.
What beats three of a kind
Six hands beat it:
- Straight - five cards in sequence, 10,200 combinations.
- Flush - five cards of one suit, 5,108 combinations.
- Full House - three of a kind plus a pair, 3,744 combinations.
- Four of a Kind - four cards of one rank, 624 combinations.
- Straight Flush and Royal Flush - five suited cards in sequence, 36 and 4 combinations.
Two Pair, One Pair and High Card lose to it.
Does a straight beat three of a kind?
Yes. A set feels like the bigger hand and often wins the pot, but a Straight made by the board outranks it. A five-card deal holds 54,912 Three of a Kinds against 10,200 Straights, so the Straight is about five times rarer.
In Hold’em that margin nearly vanishes. Out of seven cards there are 6,461,620 Three of a Kinds and 6,180,020 Straights, a difference of just 5%. A Straight is no rarity at the table, even though it still ranks higher.
Set or trips: what is the difference
The two words describe the same hand strength but different ways of making it. A set is three of a kind built from a pocket pair plus a board card, so you hold two of the three. Trips are three of a kind built from one hole card plus a paired board.
A set is harder for opponents to read, because the card that completes it is one they have not seen twice.
Comparing two three of a kinds
Compare the rank of the three cards first. Three Kings beat three Queens. If both players share the same trips, the board supplied them, and the kickers decide in order. The highest kicker wins, then the second if that is also equal.
There are 858 distinguishable Three of a Kinds: thirteen ranks for the trips times the 66 pairs of ranks left for the kickers. Two Pair has exactly the same number of distinguishable hands, even though there are twice as many of them in total.
Probability
There are two ways to count it, and the numbers are far apart.
- In a five-card deal: 54,912 combinations out of 2,598,960 - that is 2.1128%, or about 1 in 47.
- In seven-card Hold’em: 6,461,620 out of 133,784,560 - that is 4.83%, or about 1 in 21 hands to the river.
The five-card number comes out like this:
- 13 ranks for the trips x 4 ways to pick three suits from four;
- 66 pairs of remaining ranks for the kickers x 16 suit arrangements;
- 13 x 4 x 66 x 16 = 54,912.
Three of a Kind is about twice as rare as Two Pair, which appears 123,552 times, and about five times more common than a Straight.