3 Pair in Poker: Is It a Hand? Odds and Rules
3 pair is not a hand in poker. A poker hand is five cards, and three pairs would take six. In Texas Hold'em you can hold three pairs among your seven cards, and then you play the two highest pairs and the best other card, so it counts as two pair. It loses to a straight, a flush, a full house and three of a kind, and it can even lose to an ordinary two pair. You will have it on 1.85% of deals, about 1 in 54.1.
Is 3 pair a hand in poker? What it counts as
No. The hand rankings have one pair and two pair and nothing for three, because a hand is exactly five cards and five cards cannot hold three pairs. It comes up as a question because Hold'em gives you seven cards to choose from, so three pairs can sit in front of you at the same time. You still play only five of them. Three pairs count as two pair, the two highest, and nothing in the rules gives you credit for the third.
Which five cards play when you hold three pairs
Take the two highest pairs, then the highest card left over, which may be one card of the third pair or the odd seventh card. Your hole cards do not have to play at all:
| Board | Your cards | Five that play | What happened |
|---|---|---|---|
| K♦ 8♦ 4♥ 4♣ 2♠ | K♥ 8♠ | K-K-8-8-4 | Your two pair play. The board's fours are the kicker |
| K♠ K♦ Q♥ Q♣ 3♠ | 9♠ 9♥ | K-K-Q-Q-9 | Your nines are only the kicker |
| A♠ A♦ 7♥ 6♠ 2♣ | 7♦ 6♣ | A-A-7-7-6 | Your sixes are counterfeited: they are the kicker |
| K♠ K♦ Q♥ Q♣ 9♠ | 3♠ 3♥ | K-K-Q-Q-9 | Your threes do not play at all |
The third pair is the kicker in 25.00% of three-pair hands, an exact count, because the odd card is the lowest of the four ranks one time in four. The rest of the time the odd card plays and the third pair does nothing. The kicker guide explains the fifth card.
How often you get three pairs in Texas Hold'em
Choose three ranks (286 ways), two suits for each (216 ways) and one card from the ten other ranks (40 ways). That is 2,471,040 of the 133,784,560 possible seven-card hands: 1.85%, or 1 in 54.1. It is 7.86% of the 31,433,400 seven-card hands that are two pair. The same counts hold for seven-card stud. In Hold'em the same seven cards can reach you three ways, depending on which two are your hole cards:
| Your hole cards | Splits of the seven cards | Share of three pairs | Wins vs 1 |
|---|---|---|---|
| A pocket pair, with two pairs on the board | 3 of 21 | 14.29% | 51.24% |
| Both hole cards pair the board, which has a pair of its own | 12 of 21 | 57.14% | 74.55% |
| One hole card pairs the board, which has two pair | 6 of 21 | 28.57% | 57.18% |
Any seven cards split into two hole cards and five board cards 21 ways, which is where the second column comes from. The last column is an exact win rate against one random hand.
Does 3 pair beat a straight, two pair or a full house?
It is two pair, so it beats what two pair beats and loses to what beats two pair. It cannot be a straight or a flush at the same time: three pairs and a seventh card are only four ranks, a straight needs five, and a pair is always two suits, so no suit reaches five. Against another two pair, what decides it is the highest pair, then the second pair, then the kicker. The number of pairs does not count, so three pairs can lose to two:
| Against | Board | You | Them | Result |
|---|---|---|---|---|
| A straight | 9♠ 9♦ 6♥ 6♣ 5♠ | K♠ K♦ | 8♠ 7♠ | They win |
| A full house | 9♠ 9♦ 6♥ 6♣ 5♠ | K♠ K♦ | 9♥ 6♠ | They win |
| Three of a kind | 9♠ 9♦ 6♥ 4♣ 5♠ | 6♠ 4♦ | 9♥ A♣ | They win |
| Two pair, better kicker | K♠ K♦ Q♥ Q♣ 9♠ | 3♠ 3♥ | A♦ 2♣ | They win |
| Two pair, worse kicker | K♠ K♦ Q♥ Q♣ 3♠ | 9♠ 9♥ | 8♠ 8♦ | You win |
| One pair | K♦ 8♦ 4♥ 4♣ 2♠ | K♥ 8♠ | A♠ Q♠ | You win |
Your hand is three pairs in every row. In the fourth row both players have kings and queens: your threes do not play, and their ace is the kicker.
How strong three pairs are at showdown
A third pair adds almost nothing. Against one random hand three pairs win 66.26%, tie 4.31% and lose 29.43%, while two pair with no third pair win 64.08%: a gain of 2.18 points. What matters is whether your own cards are in the two pairs that play. If both hole cards pair the board and the board's own pair is the lowest of the three, you win 80.87%. If you hold a pocket pair below both board pairs, you win 4.50% and tie 24.97%, because you are nearly playing the board. The good hand guide has two pair against other hands, and aces and eights is a two pair with a story of its own, the dead man's hand.
| Hand | Wins vs 1 | Ties vs 1 | Loses vs 1 | Wins vs 3 |
|---|---|---|---|---|
| Two pair with no third pair | 64.08% | 5.29% | 30.63% | 33.6% |
| Three pairs, all of them | 66.26% | 4.31% | 29.43% | 36.2% |
| Both hole cards play, the board's pair is lowest | 80.87% | 0.40% | 18.72% | 53.8% |
| A pocket pair that plays | 74.62% | 0.10% | 25.28% | 40.9% |
| One hole card, and its pair plays | 74.35% | 1.33% | 24.31% | 39.9% |
| Both hole cards pair the board, one is counterfeited | 71.39% | 4.61% | 23.99% | 36.7% |
| One hole card, and its pair is below both others | 22.82% | 10.73% | 66.45% | 5.1% |
| A pocket pair below both board pairs | 4.50% | 24.97% | 70.53% | 0.6% |
Win rates, not equity: a tie is shown apart. The first three columns are an exact count: every (hand, board) deal, 2,598,960 boards with 1,081 holdings each, compared with all 990 opposing holdings. The last column is simulated, with one seeded random set of opponents per deal and a standard error under 0.03 points. Against the best quarter of holdings on each board three pairs win 10.27% and plain two pair 12.91%, so against a hand that has something the third pair is no help at all.
When the third pair decides the pot
Rarely. Against one random hand the opponent has your exact two pair in 15.46% of matchups, usually because both pairs are on the board, and then the kicker decides. In those battles you win 19.48%, split 27.88% and lose 52.65%. Only 1.39% of them are pots the third pair wins that your odd card would not have won, which is 0.21% of all matchups. A few more it turns from a loss into a split. Those figures are exact. The split pot rules cover what happens when the kickers tie.
Counterfeited: when the board pairs over your two pair
Every three-pair hand has a pair on the board, because your two hole cards can make at most two pairs, and a pair on the board belongs to everyone. Your two pair is counterfeited when the board pairs above your lower pair, so that pair stops playing. Hold 8♠ 7♠ on a turn of Q♦ 8♦ 7♣ 2♥: you have eights and sevens, and 6 of the 46 river cards (13.04%) give you a third pair. A queen or a deuce does that, and neither helps. Here is your record on three rivers, against all 990 holdings:
| River | Your hand | Wins | Ties | Loses |
|---|---|---|---|---|
| A blank | Eights and sevens, queen kicker | 95.45% | 0.40% | 4.14% |
| The queen pairs | Queens and eights, seven kicker | 79.39% | 4.24% | 16.36% |
| The deuce pairs | Eights and sevens, queen kicker | 75.15% | 0.40% | 24.44% |
A blank river leaves you winning 95.45%. The queen counterfeits your sevens: they drop to the kicker, and you win 79.39%. The deuce leaves your two pair as it was, but you win only 75.15%, because any queen and any pocket pair above your eights now makes a better two pair. That is why a third pair from the board is a warning, not a bonus. Across every deal, hands where the board's pair counterfeits one of your two pairs win 71.39% against one random hand, to 80.87% when it does not.
Three pair in Omaha, stud and pai gow
The answer changes a little from game to game.
- •Seven-card stud: you have seven cards of your own and play the best five, so three pairs are possible and count as two pair, just as in Hold'em, with the same count of hands. No card is shared, so the fifth card is always your own.
- •Omaha: you must use exactly two hole cards and three board cards, so the five that play are more restricted, and holding pairs among nine cards tells you little until you check which two hole cards you can use. See what Omaha is.
- •Pai gow poker: three pairs are worth more here. You split seven cards into a five-card hand and a two-card hand, so one pair can go in the two-card hand and the other two in the five-card hand, which has to rank higher. The Foxwoods house way, as Wizard of Odds prints it, puts the high pair in front, in the two-card hand.
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Frequently asked
Is 3 pair a thing in poker?
Not as a hand. A poker hand is five cards, so the pair hands stop at two pair. You can hold three pairs among seven cards in Hold'em or stud, and you then play the two highest pairs and the best other card.
Why is there no 3 pair in poker?
Because three pairs need six cards and a hand is five. The rankings were built for five cards, and five cards hold at most two pairs.
Does 3 pair beat a straight?
No. Three pairs count as two pair, and a straight beats two pair. They cannot be the same seven cards either: three pairs and an odd card are only four ranks, and a straight needs five.
Does 3 pair beat 2 pair?
Only if its two highest pairs and its kicker beat the other hand's. The third pair earns nothing by itself, so a hand holding three pairs can lose to one holding two.
Does 3 pair beat a full house?
No. Three pairs are two pair, and a full house beats two pair, three of a kind, a straight and a flush.
Can you have 3 pairs in Texas Hold'em?
Yes: 2,471,040 of the 133,784,560 seven-card hands hold three pairs, 1.85%, or 1 in 54.1. Only two of them play.
What does counterfeit mean in poker?
Your hand is counterfeited when the board pairs and a pair you held stops playing, or stops being worth what it was. With two pair, a higher pair on the board can push your lower pair out of the best five.
Terms used in this article
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