• Poker Probability Straight Flush Valve
• Poker Probability Straight Flush Lines
• Poker Probability Straight Flush Rules
• Poker Probability Straight Flush Video Poker
• Probability Of Straight Flush Poker

8921675656

• Playing situations; Drawing hands probabilities Odds Percent; Double wraparound straight draw (e.g. Hand: 9-8-5-4, flop: 7-6-x) 0.48-1: 68%: Wraparound straight draw (e.g. Hand: 8-5-4-x, flop: 7-6-x).
• Straight Flush To have a straight flush the hand must consist of all five cards being of the same suit and all in numerical order. There are 10 possible sequences: A – 5, 2 – 6, 9 – K, and 10 – A. Since there are 4 suits, then the number of straight flushes possible is just 10. 4 = 40, with the highest four (each a straight flush.
• B) Probability of seeing three legs of a straight in the flop (without the possibility of a straight flush) You subtract the 48 possible combinations that would also be part of a straight flush, since you only want to know the probability of seeing three legs of a normal straight on the flop.
• Probability tables for five card poker hands dealt from a single 52-card deck or from multiple decks.% straight flush 0.001539% straight flush 0.024010% 4 of a.

1800 5726 991

Poker Probability Straight Flush Valve

Discover the numbers, strategy and odds behind the Straight Flush and the poker odds of flopping the top-best hand in poker.

• Beginners Guide
• How to Play
• Leaderboards
  • Current Events
  • Past Events
• Promotions
• Support

Straight Flush Poker Hand Ranking

Straight Flush means any of the 5 cards in numerical order, all of identical suits. In the event of a tie, Highest rank at the top of the sequence wins the game. The best possible straight flush is known as a royal flush that consists of the ace, king, queen, jack and ten of a suit. There are two types of Straight. Straight flush. Any 5 cards of the same suit in sequence, such as 5♥, 6♥, 7♥, 8♥, 9♥. Ordinary straight. Five cards in sequence, with at least two cards of different suits. Ace can be high or low, but not both. Thus, A♠, 2♥, 3♦, 4♣, 5♥ and 10♠, J♥, Q♦, K♣, A♥ are valid straights; but Q♠, K♥, A♦, 2♣, 3♥ is not.

What is a Straight Flush?

Let's work out the analytical plan to find the probability of a straight flush

• First, we have to count the number of five-card hands that can be dealt from a standard deck of 52 cards. This is a combination problem. The number of combinations is n! / r!(n - r)!. We have 52 cards in the deck so n = 52. And we want to arrange them in unordered groups of 5, so r = 5. Thus, the number of combinations is: 52C5 = 52! / 5!(52 - 5)! = 52! / 5!47! = 2,598,960 Hence, there are 2,598,960 distinct poker hands.
• After that, we have to count the number of ways that five cards can be dealt to produce a straight flush. A straight flush consists of 5 cards in sequence, each card in the same suit. It requires two independent choices to produce a straight flush:
  • Choose the rank of the lowest card in the hand. For a straight, the lowest card can be an ace, 2, 3, 4, 5, 6, 7, 8, 9, or 10. So, we choose one rank from a set of 10 ranks. The number of ways to do this is 10C1.
  • Choose one suit for the hand. There are four suits, from which we choose one. The number of ways to do this is 4C1.
• The number of ways to produce a straight flush (Numsf) is equal to the product of the number of ways to make each independent choice. Therefore, Numsf = 10C1 x 4C1 = 10 x 4 = 40

Conclusion: There are 40 different poker hands that fall in the category of straight flush.

• Finally, we compute the probability. There are 2,598,960 unique poker hands. Of those, 40 are straight flushes. Therefore, the probability of being dealt a straight flush (Psf) is: Psf = 40 / 2,598,960 = 0.00001539077169

The probability of being dealt a straight flush is 0.00001539077169. On average, a straight flush is dealt one time in every 64,974 deals.

The Poker Hands Ranking are listed below,

• Royal Flush
• Straight Flush
• Four of a Kind
• Full House
• Flush
• Straight
• Three of a Kind
• Two Pair
• Pair
• High Card

Copyright © Vollbet Network Pvt Ltd All Rights Reserved

POKER PROBABILITIES

• Texas Hold'em Poker
  Texas Hold'em Poker probabilities
• Omaha Poker
  Omaha Poker probabilities
• 5 Card Poker
  5 Card Poker probabilities

POKER CALCULATOR

• Poker calculator
  Poker odds calculator

POKER INFORMATION

• Poker hand rankings
  Ranking of poker hands

In poker, the probability of each type of 5-card hand can be computed by calculating the proportion of hands of that type among all possible hands.

Frequency of 5-card poker hands

The following enumerates the (absolute) frequency of each hand, given all combinations of 5 cards randomly drawn from a full deck of 52 without replacement. Wild cards are not considered. The probability of drawing a given hand is calculated by dividing the number of ways of drawing the hand by the total number of 5-card hands (the sample space, five-card hands). The odds are defined as the ratio (1/p) - 1 : 1, where p is the probability. Note that the cumulative column contains the probability of being dealt that hand or any of the hands ranked higher than it. (The frequencies given are exact; the probabilities and odds are approximate.)

The nCr function on most scientific calculators can be used to calculate hand frequencies; entering ​nCr​ with ​52​ and ​5​, for example, yields as above.

Poker Probability Straight Flush Lines

The royal flush is a case of the straight flush. It can be formed 4 ways (one for each suit), giving it a probability of 0.000154% and odds of 649,739 : 1.

When ace-low straights and ace-low straight flushes are not counted, the probabilities of each are reduced: straights and straight flushes each become 9/10 as common as they otherwise would be. The 4 missed straight flushes become flushes and the 1,020 missed straights become no pair.

Note that since suits have no relative value in poker, two hands can be considered identical if one hand can be transformed into the other by swapping suits. For example, the hand 3♣ 7♣ 8♣ Q♠ A♠ is identical to 3♦ 7♦ 8♦ Q♥ A♥ because replacing all of the clubs in the first hand with diamonds and all of the spades with hearts produces the second hand. So eliminating identical hands that ignore relative suit values, there are only 134,459 distinct hands.

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 when there are more cards to come. However, even though the hands are not identical from that perspective, they still form equivalent poker hands because each hand is an A-Q-8-7-3 high card hand. There are 7,462 distinct poker hands.

Derivation of frequencies of 5-card poker hands

of the binomial coefficients and their interpretation as the number of ways of choosing elements from a given set. See also: sample space and event (probability theory).

• Straight flush — Each straight flush is uniquely determined by its highest ranking card; and these ranks go from 5 (A-2-3-4-5) up to A (10-J-Q-K-A) in each of the 4 suits. Thus, the total number of straight flushes is:
  • Royal straight flush — A royal straight flush is a subset of all straight flushes in which the ace is the highest card (ie 10-J-Q-K-A in any of the four suits). Thus, the total number of royal straight flushes is

    or simply . Note: this means that the total number of non-Royal straight flushes is 36.

• Four of a kind — Any one of the thirteen ranks can form the four of a kind by selecting all four of the suits in that rank. The final card can have any one of the twelve remaining ranks, and any suit. Thus, the total number of four-of-a-kinds is:

• Full house — The full house comprises a triple (three of a kind) and a pair. The triple can be any one of the thirteen ranks, and consists of three of the four suits. The pair can be any one of the remaining twelve ranks, and consists of two of the four suits. Thus, the total number of full houses is:

• Flush — The flush contains any five of the thirteen ranks, all of which belong to one of the four suits, minus the 40 straight flushes. Thus, the total number of flushes is:

• Straight — The straight consists of any one of the ten possible sequences of five consecutive cards, from 5-4-3-2-A to A-K-Q-J-10. Each of these five cards can have any one of the four suits. Finally, as with the flush, the 40 straight flushes must be excluded, giving:

• Three of a kind — Any of the thirteen ranks can form the three of a kind, which can contain any three of the four suits. The remaining two cards can have any two of the remaining twelve ranks, and each can have any of the four suits. Thus, the total number of three-of-a-kinds is:

• Two pair — The pairs can have any two of the thirteen ranks, and each pair can have two of the four suits. The final card can have any one of the eleven remaining ranks, and any suit. Thus, the total number of two-pairs is:

• Pair — The pair can have any one of the thirteen ranks, and any two of the four suits. The remaining three cards can have any three of the remaining twelve ranks, and each can have any of the four suits. Thus, the total number of pair hands is:

• No pair — A no-pair hand contains five of the thirteen ranks, discounting the ten possible straights, and each card can have any of the four suits, discounting the four possible flushes. Alternatively, a no-pair hand is any hand that does not fall into one of the above categories; that is, any way to choose five out of 52 cards, discounting all of the above hands. Thus, the total number of no-pair hands is:

Poker Probability Straight Flush Rules

• Any five card poker hand — The total number of five card hands that can be drawn from a deck of cards is found using a combination selecting five cards, in any order where n refers to the number of items that can be selected and r to the sample size; the '!' is the factorial operator:

Poker Probability Straight Flush Video Poker

This guide is licensed under the GNU Free Documentation License. It uses material from the Wikipedia.

Probability Of Straight Flush Poker

Home > 5 Card Poker probabilities