• Straight Flush Poker Story
• Straight Flush Poker Night At The Inventory
• Straight Flush Poker Hand
• Straight Flush Poker Tour

Knowing the hand ranks gives a player a quick signpost for their strength when betting into a pot. A successful online poker player needs a detailed knowledge of the hand rankings. When I say you need to know the poker hands, I’m not talking about whether a pair of aces beats a pair of kings.

What Is A Straight Flush In A Poker Game? A Straight Flush is a five-card hand containing five sequential cards, all of the same suit. Certain named hands-such as the Royal Flush or the Wheel-are actually Straight Flushes that have earned nicknames. An ace high straight flush, such as Ad Kd Qd Jd 10d is called a royal flush, and is the highest ranked hand in standard poker, without wild cards. Four of a kind Also known as quads, four of a kind is a hand like 7h 7s 7c 7d 2s, that has four cards of the same rank, and one other card.

I’m talking about that mass of card combinations between the best and worst hands. Whenever you hold any set of cards, a gambler needs to know its strength relative to the rest of the possibilities. To do this, card players should study hand ranking charts not much different than what you would study in blackjack.

Several experts have made tables which detail the playable hands in Texas hold’em, Omaha, seven-card stud, razz, and the various hi/lo 8-or-better variants of the games already mentioned. Study these for the game or variant you want to master. That way, you know which hands to play and which to fold.

Even if you decide to play a hunch or make a bluff, you do so with the knowledge that you’re diverging from classic poker strategy. Predicate all you do in poker on a firm understanding of the hand ranks.

In the standard game of poker, each player gets5 cards and places a bet, hoping his cards are 'better'than the other players' hands.

The game is played with a pack containing 52 cards in 4 suits, consisting of:

13 hearts:
13 diamonds
13 clubs:
13 spades:

♥ 2 3 4 5 6 7 8 9 10 J Q K A
♦ 2 3 4 5 6 7 8 9 10 J Q K A
♣ 2 3 4 5 6 7 8 9 10 J Q K A
♠ 2 3 4 5 6 7 8 9 10 J Q K A

The number of different possible poker hands is found by counting the number of ways that 5 cards can be selected from 52 cards, where the order is not important. It is a combination, so we use `C_r^n`.

The number of possible poker hands

`=C_5^52=(52!)/(5!xx47!)=2,598,960`.

Royal Flush

The best hand (because of the low probability that it will occur) is the royal flush, which consists of 10, J, Q, K, A of the same suit. There are only 4 ways of getting such a hand (because there are 4 suits), so the probability of being dealt a royal flush is

`4/(2,598,960)=0.000 001 539`

Straight Flush

The next most valuable type of hand is a straight flush, which is 5 cards in order, all of the same suit.

For example, 2♣, 3♣, 4♣, 5♣, 6♣ is a straight flush.

For each suit there are 10 such straights (the one starting with Ace, the one starting with 2, the one starting with 3, ... through to the one starting at 10) and there are 4 suits, so there are 40 possible straight flushes.

The probability of being dealt a straight flush is

`40/(2,598,960)=0.000 015 39`

[Note: There is some overlap here since the straight flush starting at 10 is the same as the royal flush. So strictly there are 36 straight flushes (4 × 9) if we don't count the royal flush. The probability of getting a straight flush then is 36/2,598,960 = 0.00001385.]

The table below lists the number ofpossible ways that different types of hands can arise and theirprobability of occurrence.

Ranking, Frequency and Probability of Poker Hands

Question

The probability for a full house is given above as 0.001441. Where does this come from?

Answer

Explanation 1:

Probability of 3 cards having the same denomination: `4/52 xx 3/51 xx 2/50 xx 13 = 1/425`.

(There are 13 ways we can get 3 of a kind).

The probability that the next 2 cards are a pair: `4/49 xx 3/48 xx 12 = 3/49`

(There are 12 ways we can get a pair, once we have already got our 3 of a kind).

The number of ways of getting a particular sequence of 5 cards where there are 3 of one kind and 2 of another kind is:

`(5!)/(3!xx2!)=10`

Straight Flush Poker Story

So the probability of a full house is

`1/425 xx 3/49 xx 10 ` `= 6/(4,165)` `=0.001 440 6`

Explanation 2:

Number of ways of getting a full house:

`(C(13,1)xxC(4,3))` `xx(C(12,1)xxC(4,2))`

`=(13!)/(1!xx12!)` `xx(4!)/(3!xx1!)` `xx(12!)/(1!xx11!)` `xx(4!)/(2!xx2!)`

`=3744`

Number of possible poker hands

`=C(52,5)` `=(52!)/(47!xx5!)` `=2,598,960`

So the probability of a full house is given by:

Straight Flush Poker Night At The Inventory

`P('full house')`

`='ways of getting full house'/'possible poker hands'`

`= (3,744)/(2,598,960)`

Straight Flush Poker Hand

Straight Flush Poker Tour

`=0.001 441`