Does a full house beat a flush?
Yes. A full house ranks above a flush because it is rarer: 3,744 of the five-card hands are full houses and 5,108 are flushes. By the river in Hold'em the gap narrows (2.60% against 3.03%) but the order never changes.
Does a full house beat a straight?
Yes, and a flush beats a straight too. Straights are the most common of the three: 10,200 five-card hands, and 4.6% of Hold'em deals by the river.
Does four of a kind beat a full house?
Yes. Four of a kind is the third-best hand, behind only the straight flush and the royal flush, and you make it by the river about once in 595 deals. When two players have the same kind of hand, the higher ranks win: kings full of nines beat queens full of aces. When those match too, the , the best unpaired card, decides. If all five cards tie, the pot is split; suits never break a tie.
The odds of a royal flush
You are dealt a royal flush in five cards once in 649,740 hands. In Hold'em, with seven cards to choose from, you make one by the river once in 30,940 deals. To see how often your own hand improves, use the poker odds calculator, which shows what each hand makes by the river, or the outs calculator for a draw.