Why does 3 ace beat 67810 of clovers?

6–7–8–10 of clovers has no value in it self (no straight, no flush). If you had a 9 or another clover then you would beat the three of a kind. read more

But in this case three of a kind will beat two of a kind or a pair. It does not matter if its aces or any other face card. The chances of a making a pair on the flop when playing poker is roughly 32.43 percent, which is about a third. If you have pocket aces, there are still five outs available to other people to beat you. read more

An ace can be counted as low, so 5-4-3-2-A is a straight flush, but its top card is the five, not the ace, so it is the lowest type of straight flush. The highest type of straight flush, A-K-Q-J-10 of a suit, is known as a Royal Flush. read more