Full house #4 of 10

Three cards of one rank and two of another. It beats a flush and everything below it, and loses to four of a kind and everything above.

ExampleQ♦Q♥Q♠5♣5♦

in five cards0.14%3,744 / 2,598,960

as a frequency1 in 694on average

odds against693 to 1misses to hits

hold'em, by the river2.60%3,473,184 / 133,784,560

How often, card by card

Chance that a full house is the best hand
Cards dealt	Probability	1 in	Odds against	Count
5 cards: the flop, or five-card draw	0.14%	694	693 to 1	3,744 / 2,598,960
6 cards: the turn	0.82%	123	122 to 1	165,984 / 20,358,520
7 cards: the river in hold'em, or seven-card stud	2.60%	38.5	37.5 to 1	3,473,184 / 133,784,560

“Best hand” means exactly this hand and nothing better: a full house also contains a pair, but it counts once, as a full house. These are the odds for any two hole cards; your own starting hand moves them, which is the grid further down.

The working

Full house, five cards: trips rank × its suits × pair rank × its suits
13 × C(4,3) × 12 × C(4,2) = 13 × 4 × 12 × 6 = 3,744
enumerated by the engine: 3,744 of 2,598,960
probability: 3,744 / 2,598,960 = 0.14%

There are 156 different full house hands once suits are ignored: 13 × 12 = 156: the trips rank, then the pair rank. Every one of them can still be your best hand with seven cards.

When two players both have a full house

The higher three of a kind wins; if those match, the higher pair.

Two full houses: the three of a kind decides

BoardQ♠Q♦7♣7♥3♠

7♦3♣	7♣7♦7♥Q♦Q♠	Full house, sevens full of queens	Loses
Q♣3♦	Q♣Q♦Q♠7♣7♥	Full house, queens full of sevens	Wins

Open in the checker →

Check your own showdown in the hand checker →

Full house by starting hand

The chance each of the 169 starting hands ends the river with a full house as its best hand, from every one of its 2,118,760 boards. 13 hands tie for most often (8.55%): AA, KK, QQ and 10 more; 156 hands tie for least often (2.22%): AKs, AQs, AJs and 153 more. Averaged over their combinations: pocket pairs 8.55%, suited hands 2.22%, offsuit hands 2.22%.

AA8.5 AKs2.2 AQs2.2 AJs2.2 ATs2.2 A9s2.2 A8s2.2 A7s2.2 A6s2.2 A5s2.2 A4s2.2 A3s2.2 A2s2.2 AKo2.2 KK8.5 KQs2.2 KJs2.2 KTs2.2 K9s2.2 K8s2.2 K7s2.2 K6s2.2 K5s2.2 K4s2.2 K3s2.2 K2s2.2 AQo2.2 KQo2.2 QQ8.5 QJs2.2 QTs2.2 Q9s2.2 Q8s2.2 Q7s2.2 Q6s2.2 Q5s2.2 Q4s2.2 Q3s2.2 Q2s2.2 AJo2.2 KJo2.2 QJo2.2 JJ8.5 JTs2.2 J9s2.2 J8s2.2 J7s2.2 J6s2.2 J5s2.2 J4s2.2 J3s2.2 J2s2.2 ATo2.2 KTo2.2 QTo2.2 JTo2.2 TT8.5 T9s2.2 T8s2.2 T7s2.2 T6s2.2 T5s2.2 T4s2.2 T3s2.2 T2s2.2 A9o2.2 K9o2.2 Q9o2.2 J9o2.2 T9o2.2 998.5 98s2.2 97s2.2 96s2.2 95s2.2 94s2.2 93s2.2 92s2.2 A8o2.2 K8o2.2 Q8o2.2 J8o2.2 T8o2.2 98o2.2 888.5 87s2.2 86s2.2 85s2.2 84s2.2 83s2.2 82s2.2 A7o2.2 K7o2.2 Q7o2.2 J7o2.2 T7o2.2 97o2.2 87o2.2 778.5 76s2.2 75s2.2 74s2.2 73s2.2 72s2.2 A6o2.2 K6o2.2 Q6o2.2 J6o2.2 T6o2.2 96o2.2 86o2.2 76o2.2 668.5 65s2.2 64s2.2 63s2.2 62s2.2 A5o2.2 K5o2.2 Q5o2.2 J5o2.2 T5o2.2 95o2.2 85o2.2 75o2.2 65o2.2 558.5 54s2.2 53s2.2 52s2.2 A4o2.2 K4o2.2 Q4o2.2 J4o2.2 T4o2.2 94o2.2 84o2.2 74o2.2 64o2.2 54o2.2 448.5 43s2.2 42s2.2 A3o2.2 K3o2.2 Q3o2.2 J3o2.2 T3o2.2 93o2.2 83o2.2 73o2.2 63o2.2 53o2.2 43o2.2 338.5 32s2.2 A2o2.2 K2o2.2 Q2o2.2 J2o2.2 T2o2.2 92o2.2 82o2.2 72o2.2 62o2.2 52o2.2 42o2.2 32o2.2 228.5

most often (8.55%) less oftennumber = % of the 2,118,760 boards

Starting hands most and least likely to end with a full house
Starting hand	Full house by the river	1 in
AA	8.55%	12
KK	8.55%	12
QQ	8.55%	12
JJ	8.55%	12
TT	8.55%	12
99	8.55%	12
88	8.55%	12
77	8.55%	12
66	8.55%	12
55	8.55%	12
…
32o	2.22%	45
42o	2.22%	45
43o	2.22%	45

Full house beats

Flush 3.03% by the river
Straight 4.62% by the river
Three of a kind 4.83% by the river
Two pair 23.5% by the river
One pair 43.8% by the river
High card 17.4% by the river

Full house loses to

Royal flush 0.0032% by the river
Straight flush 0.028% by the river
Four of a kind 0.17% by the river

Making a full house: the odds pages

// how these numbers were computed

Every five-, six- and seven-card hand was dealt and classified by the site's engine (tools/build-rankings.mjs). The five-card count must equal the formula above or the build fails; the six- and seven-card counts must equal the standard published tables.
The starting-hand figures deal each hand every possible board. Suits are interchangeable, so one deal of each hand gives the exact figure for all its combinations.
The showdowns above were scored by the same engine; the build fails if any of them comes out differently from what its title says.
Back to all ten hands. Raw data: rankings.json.