For three of a kind, the hand will look like x,x,x,y,z for some distinct values x,y,z in A,2,3,ldots,.
(We'll just look at the numerical values to start, and look at suits later).
The types of 5-card poker hands are straight flush 4-of-a-kind full house flush straight 3-of-a-kind two pairs a pair high card, most poker games are based on 5-card poker hands so the ranking of these hands is crucial.Thus, there are possible sets of ranks from which we remove the 10 sets of the form.Total 100.00 22100, there are two types of bets in 3 Card Poker (Ante and PairPlus) and therefore there are two payout schedules for each 3 Card Poker table.We could determine the number of high card hands by removing the hands which have already been counted in one of the previous categories.The actual payout tables may vary in the different casinos.Of these, 10 are straight flushes whose removal leaves 1,277 flushes of a given suit.Brian Alspach, abstract: We determine the number of 5-card poker hands.Hand number, probability dragon age origins extra dog slot mod straight flush.0022 3-of-a-kind.0024 straight 720.0326 flush 1,096.0496 pair 3,744.1694 high card 16,440.7439 Home Publications Preprints mitacs Poker Digest Graph Theory Workshop Poker Computations Feedback website by the Centre for Systems Science last updated.There are 4 ways of choosing the triple of a given rank and 6 ways to choose the pair of the other rank.Instead, let us count them independently and see if the numbers sum to 22,100 which will serve as a check on our arithmetic.Thus, there are 3-card hands with a single pair.A triple, this hand has the pattern aaabc where A, B, and C are from distinct kinds.Hence, there are 40 straight flushes.
TWO pair, this hand has the pattern aabbc where A, B, and C are from distinct kinds.
The ranks of the cards in a straight have the form x, x 1, x 2, where x can be any of 12 ranks.

There are choices for the ranks of the other 3 cards and 4 choices for each of these 3 cards.The probability is the probability of having the hand dealt to you when dealt 3 cards.The ranks of the cards in a straight have the form x, x 1, x 2, x 3, x 4, where x can be any of 10 ranks.Now we count the number of hands with a pair.Here is a table summarizing the number of 3-card poker hands.A straight flush is completely determined once the smallest card in the straight flush is known.If we sum the preceding numbers, we obtain 2,598,960 and we can be confident the numbers are correct.A single pair, this the hand with the pattern aabcd, where A, B, C and D are from the distinct "kinds" of cards: aces, twos, threes, tens, jacks, queens, and kings (there are 13 kinds, and four of each kind, in the standard 52 card.The probability.
In forming a 4-of-a-kind hand, there are 13 choices for the rank of the quads, 1 choice for the 4 cards of the given rank, and 48 choices for the remaining card.