## 5 6 7 8 9 In Poker

## Playing 9-7, 9-7s and below in Texas Holdem.

2 3 4 5 6 7 8 9 10 J Q K A Possible Poker Hands 1-Straight Flush; 2-Four of a Kind; 3-Full House; 4-Flush; 5-Straight 6-Three of a Kind; 7-Two Pair; 8-One. Enjoy playing the most popular poker games at the touch of a button with the Classic Games Collection Mega Screen 7-in-1 Poker Game. This device has seven different games installed, including Draw, 2's Wild, Bonus Poker, Double Bonus Poker, Double Bonus Poker.

These hands are examples of one-gap connectors. In the case of unsuited one-gap connectors like 97, they are completely unplayable when they are below a Ten except in the blinds. They cannot be played for a profit in limit Texas holdem or in no limit Texas holdem. For this reason, all of the advice contained here is pertaining to 97s, which is a suited one-gap connector.

In addition, I do not recommend playing the 97s in no limit Texas holdem until you have gained a good deal of experience. It will never be able to form the best possible flush, and will only rarely form the best possible straight, so you can get trapped in a hand where you hit your draw and still lose your entire stack. In limit play, you may get trapped in a hand, but you can often control the betting to only lose a small pot instead of a large one if it looks like an opponent may have a better flush or straight.

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### Early Position

I do not recommend playing these hands from early position at any time. The possibility of a raise behind you when combined with the very low percentage of times you will be able to win make these hands very poor from early position.

### Middle Position

For the exact same reasons as listed in early position, these hands are not playable in middle position. Once you become a much more experienced player, you will find certain situations where 97s may be played from middle position, but it is very rare.

### Late Position

When the pot has not been raised and there are three or more players already in, I will usually limp into the pot from late position with 97s. You need many opponents in the pot to make it large enough when you win to make up for the majority of the time you will lose. If the pot has been raised or there are only one or two other players, it is a clear folding situation.

### Blind Play

In no limit play, I always fold 97 from the small blind and fold both the 97 and 97s from the big blind when there has been a raise. In limit play, from the big blind when there has been a raise, I fold the 97 and if the raiser is a solid player will also fold the 97s. If he or she is a loose raiser, I will call with 97s most of the time if it looks like at least three other players will see the flop with me.

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

### What Is 5 6 7 8 9 In Poker

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

Hand | No. of Ways | Probability | Description |

Royal Flush | 4 | 0.000002 | Ten, J, Q, K, A of one suit. |

Straight Flush | 36 | 0.000015 | A straight is 5 cards in order. (Excludes royal and straight flushes.) An example of a straight flush is: 5, 6, 7, 8, 9, all spades. |

Four of a Kind | 624 | 0.000240 | Example: 4 kings and any other card. |

Full House | 3,744 | 0.001441 | 3 cards of one denominator and 2 cards of another. For example, 3 aces and 2 kings is a full house. |

Flush | 5,108 | 0.001965 | All 5 cards are from the same suit. (Excludes royal and straight flushes) For example, 2, 4, 5, 9, J (all hearts) is a flush. |

Straight | 10,200 | 0.003925 | The 5 cards are in order. (Excludes royal flush and straight flush) For example, 3, 4, 5, 6, 7 (any suit) is a straight. |

Three of a Kind | 54,912 | 0.021129 Fps browser games. | Example: A hand with 3 aces, one J and one Q. |

Two Pairs | 123,552 | 0.047539 | Example: 3, 3, Q, Q, 5 |

One Pair | 1,098,240 | 0.422569 | Example: 10, 10, 4, 6, K |

Nothing | 1,302,540 | 0.501177 | Example: 3, 6, 8, 9, K (at least two different suits) |

### 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`

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:

### 5 6-7 8 9 In Poker

`P('full house')`

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

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

`=0.001 441`