Four winning patterns in a sea of hands
A royal flush is the ace-high version of a straight flush: 10, jack, queen, king and ace, all in one suit. Because a standard deck has four suits, there are only four possible royal flushes. By contrast, a five-card hand can be dealt in 2,598,960 different combinations. That makes the chance of being dealt one in a single five-card deal about 1 in 649,740.
The key is that the cards must line up in two ways at once. They have to form an uninterrupted run, and every card has to share a suit. Getting four of the needed ranks—or getting the right sequence split across suits—doesn’t count.
The game changes the odds
Those odds apply to a random five-card hand. In games such as Texas hold’em, players can use their two private cards and five shared cards to make their best five-card hand, so they have more opportunities to assemble the pattern. Even then, the chance of making a royal flush by the river is only about 1 in 30,940.
A royal flush is also the highest straight flush, not a separate kind of hand that beats it. Its rarity comes from the narrow route to that top-ranked sequence: only one exact five-card pattern per suit. In most games, a player can go a long time without seeing one—and may never be dealt one at all.
