Probabilidade Royal Flush

The Royal Flush Probability Calculator computes the chance of being dealt a royal flush in a 5-card poker hand, using a standard 52-card deck. The royal flush is the rarest and most valuable hand, consisting of Ace, King, Queen, Jack, and 10 of the same suit. The probability is extremely low, with only 4 possible combinations out of 2,598,960 total hands.

The calculation is straightforward: divide the number of royal flush combinations (4, one per suit) by the total number of 5-card combinations from a 52-card deck, which is C(52,5) = 2,598,960. The result is a probability of approximately 0.00000154, or 1 in 649,740. The tool displays this value in decimal, percentage, and fraction formats.

Use this calculator when you want to understand the rarity of a royal flush, whether out of curiosity, for probability lessons, or to analyze poker games. It is useful for comparing with other hands (like straight flush or four of a kind) and for demonstrating combinatorial concepts. Remember that the probability is for a single hand; in a real game, factors like number of players and discarded cards change the odds.

Important caveats: the calculator assumes a perfectly random deck with no jokers. It does not account for draw poker or variants like Texas Hold'em, where the final hand uses 7 cards. In those cases, the probability of a royal flush differs. Use the tool only for the classic 5-card scenario.