Two Pair vs Three of a Kind: Which Wins?
Short answer
Three of a kind beats two pair. Even three twos beat aces and kings. A straight beats both.
Three of a kind (wins)
Two pair (loses)
Why trips beat two pair
In five-card poker there are 123,552 two pair hands and 54,912 three of a kinds, so trips are more than twice as rare.
Two pair vs two pair
Compare the higher pair first, then the lower pair, then the fifth card (the kicker).
Queens and sevens (wins)
Queens and fours (loses)
More on this in what is a kicker in poker.
Does a straight beat three of a kind?
Yes. The order from here up is three of a kind, then straight, then flush, then full house.
FAQ
Does two pair beat three of a kind?
No. Three of a kind always beats two pair.
Does a straight beat three of a kind?
Yes. A straight ranks one place above three of a kind.
Does two pair beat a straight?
No. A straight beats two pair.
What if both players have the same two pair?
The fifth card, the kicker, decides it. If that matches too, the pot is split.