To calculate the frequency of four of a kind, first note that there are 13 different ranks in which you can get four of a kind. For any given rank, the possible hands that give four of a kind in that rank all include the four cards of that rank as well as any three additional cards. There are C48,3 = 17,296 different ways of choosing these three additional cards, so we have a total of 13 · 17,296 = 224,848 different four of a kind hands. This gives a frequency of (224,848/133,784,560) = 0.0017.
Texas Holdem Royal Flush Probability
To find the frequency of straight flushes, sort all straight flush hands by the high card of the highest straight flush in the hand. For ace high straight flushes in any of the four suits you need the A - K - Q - J - 10 of the given suit and then any 2 of the remaining 47 cards. This gives a total of C47,2 = 1,081 distinct hands. For straight flushes that are not ace high the same argument holds except that one of the remaining 47 cards would give you higher straight flush if it were in your hand (for example, if you have 10 - 9 - 8 - 7 - 6 in hearts, if one of your two other cards was a jack of hearts you would have a jack high straight flush). Therefore, in these cases there are only C46,2 Texas holdem blind calculator. = 1,035 distinct straight flush hands. So the total number of straight flush hands is (1,081 · 4) + (1,035 · 4 · 9) = 41,584 hands (the nine in the second parenthesis comes from the fact that there are nine different possible non-ace high cards for straights - a 2,3, or 4 high straight can not occur). The corresponding frequency is then (41,584/133,784,560) = 0.00031.
To count the number of full house hands, we divide up the types of full houses by looking at the two cards that are not used as part of the final hand. These two cards can either be a pair (but of a different rank than the triple or the pair you are using for the full house, or else you would have four of a kind), one of the two cards could be of the same rank as your pair (giving you two triples and one card of some different rank), or the two cards could be of different ranks from each other, the triple, and the pair.
- We first consider the case of the unused cards being a pair. We can choose the rank for the triple in 13 ways. Once a rank is chosen we can pick the three cards for the triple in C4,3 = 4 ways. We can then choose the two ranks for the two pairs in C12,2 = 66 ways. For each pair, once we have chosen the rank we can choose the cards for the pair in C4,2 = 6 ways. So we have a total of 13 · 4 · 66 · 62 = 123,552 full house hands of this type.
- Now we consider the case of two triples. We can choose the ranks for the triples in C13,2 = 78 ways, and for each triple we can then choose the cards for the triple in C4,3 = 4 ways. There are then 44 remaining cards from which to choose the last card of the hand, so we have a total of 78 · 42 · 44 = 54,912 hands of this type.
- Finally we consider the case of two cards of different rank from each other, the triple, and the pair. As above, the cards for the triple can be chosen in 13 · C4,3 = 52 ways and the cards for the pair can then be chosen in 12 · C4,2 = 72 ways. We can choose the two ranks for the remaining two cards in C11,2 = 55 ways, and for each rank we can choose any of the four cards of that rank. This gives a total of 52 · 72 · 55 · 42 = 3,294,720 hands of this type.
Six Plus Hold'em is an exciting and fun poker variant based on Texas Hold'em where the game is played with a deck of 36 cards as opposed to the usual 52 cards in traditional hold'em. Deuces through fives are removed from the deck giving the game its name Six Plus Hold'em/6+ or Short Deck Poker. And the odds of making a royal flush is 649,739 to 1. This is correct assuming that every game plays to the river. In poker terms, the river is the name for the fifth card dealt, face-up on the board. In total, there are 2,598,960 possible poker hands with 52 cards. The odds of getting four of a kind in Texas Hold ‘Em is 4164 to 1.
For example, whenever you hold four cards to a nut flush on the turn in a Texas Hold'em game, there are 46 unknown cards, (52 minus your two pocket cards and four on the board). Of those 46 cards, 37 cards won't help you, but those other nine cards are the same suit as your flush draw and any one of them will give you the nut flush. The odds of flopping a flush when holding two suited cards is 118/1, and the odds of flopping a flush draw when holding two suited cards is 8/1. You should proceed cautiously here, as any player with a higher card of the same suit as your flush has slightly higher than a 2:1 chance of hitting another card on the turn or river to beat you. While the probability of flopping a one card Flush draw with an unsuited starting hand is always 2.24%, it's worth remembering that non-nut one-card Flush draws are not especially valuable holdings. For the most part, we prefer our one card Flush draws to be to the nuts. Odds of Making a Flush on the Later Streets.
Therefore, we have a total of 3,473,184 full house hands. This gives a frequency of (3,473,184/133,784,560) = 0.02696.
Therefore, we have a total of 3,473,184 full house hands. This gives a frequency of (3,473,184/133,784,560) = 0.02696.
Texas Holdem Flush Probability Calculator
For additional calculations, as well as the frequencies for 5-card poker hands (which tend to be significantly easier to calculate), see for example Wikipedia.