Avaliador Mão Poker (5 cartas)

5-card poker hand ranking

A standard 52-card deck gives you C(52,5) = 2,598,960 possible 5-card hands. Ranked from best to worst, they go: Royal Flush (A-K-Q-J-10 of one suit, only 4 such hands, roughly 1 in 649,740), then Straight Flush, Four of a Kind, Full House, Flush, Straight, Three of a Kind, Two Pair, One Pair, and finally High Card. Take A♠ K♠ Q♠ J♠ 10♠: that's a Royal Flush, the rarest hand you can hold without wild cards. When two hands share a rank, the higher card (the kicker) settles it.

Applications

This shows up across poker variants like Texas Hold'em, Omaha and Stud, where a player builds the best 5-card hand out of 7 available cards. Online rooms such as PokerStars and GGPoker lean on it to score hands on the fly. So do the AI bots that made headlines: DeepStack and Libratus in 2017, then Pluribus in 2019, all of which beat top pros. You'll also find it behind equity calculators and odds tools, and in any course that touches game theory or combinatorial probability.

FAQ

Is A-2-3-4-5 a valid straight? It is. People call it the "wheel" or "five-high straight," and here the ace plays low. At the other end, A-K-Q-J-10 is the highest straight, known as Broadway.

Flush vs Straight, which wins? The flush takes it. That's because a flush turns up less often (~1 in 509) than a straight (~1 in 254).

How does Texas Hold'em use this? A player holds 2 hole cards and shares 5 community cards, for 7 in total. The engine then finds the strongest 5-card combination among those 7, which means checking C(7,5) = 21 combinations per hand.