The number of distinct poker hands is even smaller. For example, 3 ♣ 7 ♣ 8 ♣ Q ♠ A ♠ and 3 ♦ 7 ♣ 8 ♦ Q ♥ A ♥ are not identical hands when just ignoring suit assignments because one hand has three suits, while the other hand has only two—that difference could affect the relative value of each hand. In poker, players form sets of five playing cards, called hands, according to the rules of the game. Each hand has a rank, which is compared against the ranks of other hands participating in the showdown to decide who wins the pot. In high games, like Texas hold 'em and seven-card stud, the highest-ranking hands win. Italian restaurant near meadows casino.
Number Of Distinct Poker Hands Signals
Number Of Distinct Poker Hands Signals
Deuces wild - or, for that matter, any other game where any of the existing 52 cards are wild - will not change the mapping of the 2,598,960 hands to the 134,459 'unique' hands. What will change, of course, is the types of hands those 134,459 hands become. For example, in deuces wild, the unique hand, 'four deuces and a six' is a 'four deuces' hand, while 'ace and deuce of one suit, ace of a second suit, deuce of a third suit, and five of the remaining suit' becomes 'four of a kind' (instead of 'two pair' in games without wild cards).
On the other hand, if you add a joker, the number of total hands is now (53)C(5) = 2,869,685, and there are more than 134,459 unique hands as you have to include all of the unique hands that include a joker - for example, 'joker and four aces,' 'joker and A-K-5-3 suited,' and 'joker, a pair of kings, a three matching one of the kings' suits, and a six that does not match either king's suit.'
I think there are 16,432 additional unique hands if there is one joker in the deck:
Number Of Distinct Poker Hands Held
Joker and four of a kind - 13 hands
Joker, three of a kind, and a card matching one of the suits in the three - 156 x 12 hands (13 values for the three of a kind, 12 for the value of the fourth card, 4 sets of three suits for the three of a kind, and 3 possible suits for the fourth card)
Joker, three of a kind, and a card not matching one of the suits in the three - 156 x 4 hands (13 values for the three of a kind, 12 for the value of the fourth card, and 4 sets of three suits for the three of a kind; there is only one possible suit for the fourth card in this case)
Joker and two pair, where the suits in the higher pair match the suits in the lower pair - 78 x 6 hands
Joker and two pair, where one suit in the higher pair matches a suit in the lower pair - 78 x 24 hands
Joker and two pair, where no suits in the higher pair match the suits in the lower pair - 78 x 6 hands
Joker, pair, and two singles, where the singles are the same suit and it is one of the suits in the pair - 858 x 12 hands
Joker, pair, and two singles, where the singles are the same suit but it is not of the suits in the pair - 858 x 12 hands
Joker, pair, and two singles, where the singles are different suits and both suits match the suits in the pair - 858 x 12 hands
Joker, pair, and two singles, where the singles are different suits and the higher single's suit matches a suit in the pair - 858 x 24 hands
Joker, pair, and two singles, where the singles are different suits and the lower single's suit matches a suit in the pair - 858 x 24 hands
Joker, pair, and two singles, where the singles are different suits and neither suit matches a suits in the pair - 858 x 12 hands
For the hands that are a joker and four different values:
715 x 4 hands have the four cards in the same suit
715 x 12 x 4 hands have three cards suited but the fourth is a different suit
715 x 12 x 3 hands have two cards of one suit and two cards of another
715 x 24 x 6 hands have two cards of one suit, one of a third suit, and the remaining card the remaining suit
715 x 24 hands have the four cards be all different suits
