Full House Odds: Boat Probability in Texas Hold'em

Last updated: May 15, 2026

A pocket pair flops a full house 0.98% of the time (1 in 102) and makes a full house by the river 7.46% (1 in 13.4). Once you flop a set, the path widens: 33.4% complete to a full house by the river. Two pair improves to a full house 16.74% of the time. Across all starting hands, full house at showdown happens 2.60% of hands — roughly 6× more common than flush in single 5-card draws.

Pocket Pair Pathway to a Boat

The cleanest path to a full house starts with a pocket pair. Flop a set (11.8%), then catch a board-pairing card on the turn or river (33.4% combined). End result: 7.46% of pocket pairs become full houses by the river.

Pocket-pair → full-house pathways

Scenario	Probability	Odds	Detail
Pocket pair → flop full house	0.98%	1 in 102	Two of your rank flop, plus the board pairs another rank. 3,944 / 19,600 flops favour you.
Pocket pair → flop set, complete FH by river	33.4%	1 in 3.0	Once you flop a set, you have 10 outs (3 pair + 1 four of a kind) over 2 streets.
Pocket pair → full house by river (all paths)	7.46%	1 in 13.4	Combines all set-completion paths plus runner-runner board-pair scenarios.
Pocket pair flops a set	11.76%	1 in 8.5	Prerequisite to most full-house pathways. 33.4% × 11.76% ≈ 3.93% of pocket pairs flop set AND complete.

From Two Pair or Set to a Boat

Improving made hands to full house

Scenario	Probability	Odds	Detail
Two pair → full house on turn (1 card)	8.51%	1 in 11.8	4 outs out of 47 unseen cards. Rule of 2 estimate: 4 × 2 = 8%.
Two pair → full house by river (2 streets)	16.74%	1 in 6.0	Rule of 4 estimate: 4 × 4 = 16% — accurate.
Set → full house on turn	21.28%	1 in 4.7	10 outs out of 47. Set has 7 board-pair outs + 1 quad out + ... = 10 effective improvement outs.
Set → full house by river	33.4%	1 in 3.0	Rule of 4 estimate: 10 × 4 = 40% — slightly overestimated due to overlap.

Full House Compared to Other Hands

Hand frequency in 5-card vs 7-card poker

Scenario	Probability	Odds	Detail
Full House in 5-card hand	0.1441%	1 in 694	Foundation probability — exactly 3,744 of 2,598,960 hands.
Full House in 7-card (Texas Hold'em)	2.60%	1 in 38.5	Across 7 cards (2 hole + 5 board) the chance rises 18×.
Flush in 7-card hand	3.03%	1 in 32.5	More common than full house in Texas Hold'em despite being less common in 5-card.
Straight in 7-card hand	4.62%	1 in 21.6	Most common 'big' hand in Hold'em.
Three of a kind (set or trips) in 7-card	4.83%	1 in 20.7	Similar frequency to straights.

Definitions

Full House

Three of a kind plus a pair (e.g., AAA-KK, called 'aces full of kings' or 'aces full'). Higher trips wins; ties broken by the pair.

Boat

Poker slang for a full house. Used interchangeably with 'full house' in commentary and casual play.

Underfull

The lower of two full houses in a showdown. KKK-AA loses to AAA-22 because the trips determine the winner — KKK is the 'underfull' to AAA.

Trips → Full House

When trips (3 of a kind made with 1 hole card + paired board) improves to a full house by another board card pairing. 4 outs on the flop, 33% by river.

Frequently Asked Questions

What are the odds of making a full house in Texas Hold'em?

Across all hands, the probability of any player making a full house by showdown is approximately 2.60% — about 1 in 38.5 hands seen to showdown. Starting from a pocket pair, the rate is 7.46% (1 in 13.4). The classic '5-card hand' probability is 0.144% — about 1 in 694.

How does a set become a full house?

A set (e.g., 888 on 8♠8♥6♦) becomes a full house when the board pairs any other rank. Outs: 3 sixes (the other rank on the board) + 3 sevens + 3 fives + ... wait, only board-pairing cards count. With one board pair the set has 1 board-pair out × 7 remaining ranks + the 4th 8 for quads = 10 'improvement outs', producing 33.4% by river.

What is the probability of two pair becoming a full house?

16.74% by the river — about 1 in 6. Two pair has 4 outs: each remaining card of either pair improves to a full house. With 4 outs over two streets, the Rule of 4 gives 16% — almost exactly correct.

Why is full house more common than flush in 7-card hands?

It's the opposite — flush is slightly more common in 7-card. 7-card full house: 2.60%. 7-card flush: 3.03%. The reason: flushes need only 5 of 7 cards to be same suit, while full house requires specific 3-of-a-kind + pair structure. Many 'three of a kind' hands don't pair up to become full houses.

How does a full house beat a flush?

Full house beats flush in standard poker hand rankings. Full house (e.g., AAA-KK) is rarer than a single-pair-plus-flush hand in 5-card poker (0.144% vs 0.197%), so it ranks higher. In 7-card Texas Hold'em, full house is actually slightly less common than flush (2.60% vs 3.03%) but ranking is fixed by 5-card probability rules.

Can a full house lose to a higher full house?

Yes. Full house is ranked by the trips first, then the pair. AAA-22 beats KKK-AA because aces full beats kings full. This is why pocket aces with a board like A-K-K-x-x can lose to KKK with KQ (kings full of queens vs trips). The lower full house is called the 'underfull' and is a common cooler in Hold'em.

What are the odds of flopping a full house?

With a pocket pair: 0.98% (1 in 102). With unpaired hole cards: ~0.09% — extremely rare and requires the board to come as XXX or XX-Y where one of your hole cards matches. The board itself comes as a paired flop (e.g., 9-9-6) 17.0% of the time, but you only make a full house if your hole cards match the right ranks.

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