Cards are dealt one face-down to each player, followed by two face-up to each player. The dealer will determine beforehand if there is a betting round preceding the first card dealt face-up, but at the very least, one betting round will ensue the dealing of each of the two face-up cards.
There are a number of ways to determine what hand beats what hand in Three-Card Monte, but below are three common examples:
Version #1 (based only on possible poker hands with three cards)
Version #2 (based on the conventional rank of poker hands, with the exception of the Straight Flush)
Version #3 (based on the actual odds of being dealt each hand)