PHMAPALAD One Pair in Poker: Kickers and Frequency

A pair is two cards of the same rank, and one pair is a hand that holds exactly that, plus three cards that match nothing. It is the second-lowest category in the rank of cards poker order, above only a hand with no pair at all. Yet it is also the most common made hand, which is why ties between two players holding one pair come up constantly and why kickers matter.

One pair: what the hand is

The five cards are two of one rank and three of three different ranks, none of them matching the pair or each other. Three quick hands show the line:

Within the category, the higher pair wins, so 6-6-4-3-2 beats 5-5-A-K-Q. The unmatched cards only start to count when both players hold the same pair rank.

How kickers settle a tied one pair

A kicker is an unmatched card used to break a tie. When two hands have the same pair, compare their highest unmatched cards. If those are equal, compare the second highest, then the third.

1. Compare the pair rank. Higher wins.
2. If equal, compare the highest unmatched card.
3. If equal, compare the second highest unmatched card.
4. If equal, compare the lowest unmatched card.
5. If every card matches in rank, the pot is split, because suits do not rank in standard poker.

Example: K-K-A-7-4 beats K-K-Q-J-10, because the ace beats the queen at step 2 and the rest never gets looked at.

How often one pair is dealt

Out of all five-card hands, a count of exactly one pair is pure arithmetic. A 52-card deck gives C(52,5) = 52 x 51 x 50 x 49 x 48 / 120 = 2,598,960 hands.

1. Choose the pair rank: 13 ways.
2. Choose which 2 of its 4 suits: 6 ways, so 13 x 6 = 78.
3. Choose three different other ranks from the remaining 12: 220 ways, so 78 x 220 = 17,160.
4. Choose a suit for each of those three cards: 4 x 4 x 4 = 64 ways.
5. Multiply: 17,160 x 64 = 1,098,240 hands.

Divide 1,098,240 by 2,598,960 and you get 0.4226, or 42.26%. That is about 1 five-card hand in 2.37. Frequency tells you how common a hand is, and nothing about the next deal: each deal is a fresh draw from the deck.

Two pair: the next step up

Two pair is two cards of one rank, two of a different rank, and one unmatched card. Compare the higher pair first, then the lower pair, then the fifth card. Q-Q-5-5-2 beats J-J-10-10-A because the queens beat the jacks, so the aces never matter.

The count is also arithmetic: choose 2 ranks from 13 (78 ways), 6 suit choices for each pair (6 x 6 = 36), and a fifth card from the 44 that do not match either rank. That is 78 x 36 x 44 = 123,552 hands, or 4.75% of all hands, roughly 1 in 21.

A fixed order sits behind all of it, so you can see where one pair and two pair land among the nine categories on the rank of cards comparison for poker, baccarat and blackjack.

Why one pair loses more often than it feels

One pair is common because there are so many ways to make it, and every higher category beats it automatically. The gap is easy to count: 1,098,240 one-pair hands against 123,552 two-pair hands is about 8.9 to 1.

1. Start with the category: if the other hand is two pair or better, your pair loses whatever its rank.
2. Then compare pair ranks.
3. Then walk down the kickers.

Frequency changes nothing about your stake, so size any bet on the cards you hold. The page on when to check in poker covers the choices around a bet, and the two dice probability walkthrough counts outcomes the same way for dice.