Royal flush

A royal flush is the ace, king, queen, jack and ten of a single suit. It is the highest hand in standard high poker and it cannot be beaten, only tied.

Where it sits in the rankings

A royal flush is simply the best possible straight flush — ace-high. It is listed separately because it is the one hand that nothing else can beat, and because of that it is the only holding in poker a player can bet without any risk of being outdrawn.

The odds, exactly

There are 2,598,960 distinct five-card hands in a 52-card deck and exactly four of them are royal flushes, one per suit. That is one in 649,740 — the figure usually quoted, and the right one for a five-card game.

Most poker today is played with seven cards available, as in hold'em and seven-card stud, and that changes the number considerably. Of the 133,784,560 possible seven-card combinations, 4,324 contain a royal flush, which is one in roughly 30,940. Still rare, but about twenty times more likely than the headline figure suggests.

In hold'em specifically the player only chooses two of those seven cards, so the practical rate is lower again: the board has to cooperate. A player needs two of the five royal cards in hand and the other three on the board, or to be playing a board that contains four of them.

Split pots

Because suits have no rank in standard poker, two royal flushes are equal. In hold'em that can only happen when all five royal cards of one suit are on the board, in which case every player still in the hand holds the same royal flush and the pot is split evenly.

Jackpots and bad-beat promotions

Many live rooms pay a bonus for a royal flush, sometimes requiring that both hole cards be used. These promotions are funded by a separate drop taken from pots, so they are not free money — players collectively pay for them. The terms are worth reading, because the "both cards used" condition excludes a large share of the royals that actually occur.

A note on play

Holding the absolute nuts changes the problem from winning the hand to maximising what is won. The common mistake is betting large enough that every worse hand folds. With a holding that cannot lose, the only question is which line extracts the most from an opponent who still believes they are ahead.