Probability
  1. Poker Probability Straight Flush Rules
  2. Poker Probability Straight Flush Video Poker
  3. Probability Of Straight Flush Poker
Poker probability straight flush valve

Poker Probability Straight Flush Rules

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Straight Flush Poker Hand Ranking

  1. Discover the numbers, strategy and odds behind the Straight Flush and the poker odds of flopping the top-best hand in poker.
  2. In the example of the four-flush, the player’s probability of filling the flush is approximately 36% after the flop (9 outs x 4) and 18% after the turn (9 outs x 2). Pot Odds Another important concept in calculating odds and probabilities is pot odds.

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?

Poker Probability Straight Flush

The next two tables show the probabilities in 5-card stud with one wild card. The first table is for a partially wild card that can only be used to complete a straight, flush, straight flush, or royal flush, otherwise it must be used as an ace (same usage as in pai gow poker). The second table is for a fully wild card.

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

Poker Probability Straight Flush Video Poker

  • 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

Probability Of Straight Flush Poker

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