Does a full house beat three of a kind?
Yes. A full house beats three of a kind in poker — every time. In the ranking of 10 hand categories, full house is #4 and three of a kind is #7. Categories are compared first: even deuces full of threes beats three aces — the category always decides first.
Three of a kind plus a pair.
Three cards of the same rank ("trips").
How rare is each hand?
Rarity is exactly why the order is what it is. Out of 2,598,960 possible five-card hands, a full house shows up in 0.144% of them (3,744 combinations), while three of a kind appears in 2.11% (54,912 combinations). The harder a hand is to make, the higher it ranks.
Does three of a kind ever beat a full house?
No — never. The category comparison is absolute: the highest possible three of a kind still loses to the lowest possible full house. Ranks inside a category only matter when both players hold the same category.
Prove it to yourself
Which hand wins? Tap it.