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Today, when someone asks if you play poker, they generally mean Texas Hold ‘Em – a game that's become increasingly popular over the past decade thanks to the World Series of Poker and movies like 'Rounders.'

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Typically, five or seven cards are dealt to each player. Players attempt to form the best five-card poker hand possible (see below). For every poker game, the same hierarchy of hands exists, and the better hands are rarer and more difficult to achieve than the lesser hands. Individual cards are ranked from best to worst. Poker is any of a number of card games in which players wager over which hand is best according to that specific game's rules in ways similar to these rankings.Often using a standard deck, poker games vary in deck configuration, the number of cards in play, the number dealt face up or face down, and the number shared by all players, but all have rules which involve one or more rounds of betting.

But there are many versions and variations of poker, the main types being stud, draw and community card games. At 'friendly' tables, the dealer often has the choice of deciding the type of game. More structured tournaments usually specify the format from the get-go.

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Below are a few of the most popular versions of poker that you may encounter at your weekly dealer's-choice poker game. If you don't know these, you'll be at a disadvantage when something wild (like FOLLOW THE QUEEN!) is called.

Common terms you should know

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Before we dive in to the specific games, there are a few terms every player (and prospective player) needs to know:

Ante – the minimum amount you must gamble to get into the action of the game.

Blinds – money (generally in chip form) put on the table before the cards are dealt; there are typically two blinds (called the 'small' and the 'big') and ensure money is being wagered with each hand; blinds rotate from player to player with each new deal.

Call – when a new wager has been placed, a 'call' indicates that player's willingness to match the raised amount.

Check – if no new wager has been made and the player doesn't wish to raise, they may 'check'.

Raise – the player wishes to increase the table bet.

For a more complete list of poker terms, check out Wikipedia's glossary of poker terms.

Popular poker games

In 'stud' games, players are dealt a number of cards (typically 5 or 7) and must use those original cards to make their best hand.

In 'draw' games, the players may decide to trade in some of their cards (generally up to 3) in an effort to improve their hand.

In 'community card' games, the players are dealt 'hole cards' face down (cards that are uniquely theirs) then play off the community cards to make their best hand. What makes them 'community cards?' The other players at the table also may play off them.

Texas Hold ‘Em

Played in the World Series of Poker, Texas Hold ‘Em is easily the most popular poker game in America today. In Texas Hold ‘Em, players are dealt two 'pocket' or 'hole cards' then wait for 5 community cards to be revealed.

Betting takes place in four rounds: once after the hole cards are dealt, once after the first three community cards are revealed (referred to as 'the flop'), once after the fourth community card is revealed ('the turn') and lastly after the fifth community card is flipped ('the river'). Players must make their best hands with any combination of 5 cards (their hole cards and the communal).

Checking gives one the option to raise, call, fold or even check again later on in the betting round. When one checks, they do not have to put anything into the pot unless they are playing in a. Poker rules check call raise.

Omaha

Omaha is another type of Hold ‘Em that can be played by 2-10 players at a time. Like Texas Hold ‘Em, there are four rounds of betting, but unlike that version, each player is dealt four hole cards and the five community cards are immediately revealed. Players must make their best 5-card hands from two of their hole cards and three of the common.

7-Card Stud

In 7-Card Stud, each player is dealt 7 cards, three down and four up. Players must make best possible 5-card hand from their 7.

5-Card Draw

Each player is dealt 5 cards, but on the initial go around, the player may choose to trade in up to 3 of them.

High / Low Chicago

This stud game can be played for the highest hand or the lowest. In High Chicago, the player with the highest spade face-down wins half the pot. In Low Chicago, the player with the lowest spade face-down wins half the pot.

The other half of the pot is won by the player with the best hand. If someone, however, has the best hand and the winning spade (high or low, depending on version), that player will win the entire pot.

This game can be added to, and played simultaneously with, many other poker variations.

Follow the Queen

This is a 7-card stud poker game in which the wild card is designated to be the next exposed card after a queen is flipped. If no queens are flipped, there are no wild cards that hand.

And keep in mind there are almost infinite ways to win at poker, and many rules are malleable. It is important to know the specific guidelines of the game you're in…

For example, be sure to know:

• If a high hand or low hand wins in your game (some games offer hi/low, in which the high hand and the low hand split the pot).
• If an Ace is high or low.
• If there are wild cards.
• If there is a pot limit (how much money can be wagered on any single hand).
• If the deck is a typical 52 or some other amalgamation (for example, a 'royal deck' uses two decks but only cards 9-A, which results in a deck of 48).

Call – when a new wager has been placed, a 'call' indicates that player's willingness to match the raised amount.

Check – if no new wager has been made and the player doesn't wish to raise, they may 'check'.

Raise – the player wishes to increase the table bet.

For a more complete list of poker terms, check out Wikipedia's glossary of poker terms.

Popular poker games

In 'stud' games, players are dealt a number of cards (typically 5 or 7) and must use those original cards to make their best hand.

In 'draw' games, the players may decide to trade in some of their cards (generally up to 3) in an effort to improve their hand.

In 'community card' games, the players are dealt 'hole cards' face down (cards that are uniquely theirs) then play off the community cards to make their best hand. What makes them 'community cards?' The other players at the table also may play off them.

Texas Hold ‘Em

Played in the World Series of Poker, Texas Hold ‘Em is easily the most popular poker game in America today. In Texas Hold ‘Em, players are dealt two 'pocket' or 'hole cards' then wait for 5 community cards to be revealed.

Betting takes place in four rounds: once after the hole cards are dealt, once after the first three community cards are revealed (referred to as 'the flop'), once after the fourth community card is revealed ('the turn') and lastly after the fifth community card is flipped ('the river'). Players must make their best hands with any combination of 5 cards (their hole cards and the communal).

Checking gives one the option to raise, call, fold or even check again later on in the betting round. When one checks, they do not have to put anything into the pot unless they are playing in a. Poker rules check call raise.

Omaha

Omaha is another type of Hold ‘Em that can be played by 2-10 players at a time. Like Texas Hold ‘Em, there are four rounds of betting, but unlike that version, each player is dealt four hole cards and the five community cards are immediately revealed. Players must make their best 5-card hands from two of their hole cards and three of the common.

7-Card Stud

In 7-Card Stud, each player is dealt 7 cards, three down and four up. Players must make best possible 5-card hand from their 7.

5-Card Draw

Each player is dealt 5 cards, but on the initial go around, the player may choose to trade in up to 3 of them.

High / Low Chicago

This stud game can be played for the highest hand or the lowest. In High Chicago, the player with the highest spade face-down wins half the pot. In Low Chicago, the player with the lowest spade face-down wins half the pot.

The other half of the pot is won by the player with the best hand. If someone, however, has the best hand and the winning spade (high or low, depending on version), that player will win the entire pot.

This game can be added to, and played simultaneously with, many other poker variations.

Follow the Queen

This is a 7-card stud poker game in which the wild card is designated to be the next exposed card after a queen is flipped. If no queens are flipped, there are no wild cards that hand.

And keep in mind there are almost infinite ways to win at poker, and many rules are malleable. It is important to know the specific guidelines of the game you're in…

For example, be sure to know:

• If a high hand or low hand wins in your game (some games offer hi/low, in which the high hand and the low hand split the pot).
• If an Ace is high or low.
• If there are wild cards.
• If there is a pot limit (how much money can be wagered on any single hand).
• If the deck is a typical 52 or some other amalgamation (for example, a 'royal deck' uses two decks but only cards 9-A, which results in a deck of 48).

At Clearwater Casino Resort, one of the top Seattle casino resorts, we offer 3-card poker on the floor as well as regular poker games and tournaments in our Poker Room where we pay out more than $50,000 in tournament cash every month!

This post works with 5-card Poker hands drawn from a standard deck of 52 cards. The discussion is mostly mathematical, using the Poker hands to illustrate counting techniques and calculation of probabilities

Working with poker hands is an excellent way to illustrate the counting techniques covered previously in this blog – multiplication principle, permutation and combination (also covered here). There are 2,598,960 many possible 5-card Poker hands. Thus the probability of obtaining any one specific hand is 1 in 2,598,960 (roughly 1 in 2.6 million). The probability of obtaining a given type of hands (e.g. three of a kind) is the number of possible hands for that type over 2,598,960. Thus this is primarily a counting exercise.

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Preliminary Calculation

Usually the order in which the cards are dealt is not important (except in the case of stud poker). Thus the following three examples point to the same poker hand. The only difference is the order in which the cards are dealt.

These are the same hand. Order is not important.

The number of possible 5-card poker hands would then be the same as the number of 5-element subsets of 52 objects. The following is the total number of 5-card poker hands drawn from a standard deck of 52 cards.

The notation is called the binomial coefficient and is pronounced 'n choose r', which is identical to the number of -element subsets of a set with objects. Other notations for are , and . Many calculators have a function for . Of course the calculation can also be done by definition by first calculating factorials.

Thus the probability of obtaining a specific hand (say, 2, 6, 10, K, A, all diamond) would be 1 in 2,598,960. If 5 cards are randomly drawn, what is the probability of getting a 5-card hand consisting of all diamond cards? It is

This is definitely a very rare event (less than 0.05% chance of happening). The numerator 1,287 is the number of hands consisting of all diamond cards, which is obtained by the following calculation.

The reasoning for the above calculation is that to draw a 5-card hand consisting of all diamond, we are drawing 5 cards from the 13 diamond cards and drawing zero cards from the other 39 cards. Since (there is only one way to draw nothing), is the number of hands with all diamonds.

If 5 cards are randomly drawn, what is the probability of getting a 5-card hand consisting of cards in one suit? The probability of getting all 5 cards in another suit (say heart) would also be 1287/2598960. So we have the following derivation.

Thus getting a hand with all cards in one suit is 4 times more likely than getting one with all diamond, but is still a rare event (with about a 0.2% chance of happening). Some of the higher ranked poker hands are in one suit but with additional strict requirements. They will be further discussed below.

Another example. What is the probability of obtaining a hand that has 3 diamonds and 2 hearts? The answer is 22308/2598960 = 0.008583433. The number of '3 diamond, 2 heart' hands is calculated as follows:

One theme that emerges is that the multiplication principle is behind the numerator of a poker hand probability. For example, we can think of the process to get a 5-card hand with 3 diamonds and 2 hearts in three steps. The first is to draw 3 cards from the 13 diamond cards, the second is to draw 2 cards from the 13 heart cards, and the third is to draw zero from the remaining 26 cards. The third step can be omitted since the number of ways of choosing zero is 1. In any case, the number of possible ways to carry out that 2-step (or 3-step) process is to multiply all the possibilities together.

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The Poker Hands

Here's a ranking chart of the Poker hands.

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The chart lists the rankings with an example for each ranking. The examples are a good reminder of the definitions. The highest ranking of them all is the royal flush, which consists of 5 consecutive cards in one suit with the highest card being Ace. There is only one such hand in each suit. Thus the chance for getting a royal flush is 4 in 2,598,960.

Royal flush is a specific example of a straight flush, which consists of 5 consecutive cards in one suit. There are 10 such hands in one suit. So there are 40 hands for straight flush in total. A flush is a hand with 5 cards in the same suit but not in consecutive order (or not in sequence). Thus the requirement for flush is considerably more relaxed than a straight flush. A straight is like a straight flush in that the 5 cards are in sequence but the 5 cards in a straight are not of the same suit. For a more in depth discussion on Poker hands, see the Wikipedia entry on Poker hands.

The counting for some of these hands is done in the next section. The definition of the hands can be inferred from the above chart. For the sake of completeness, the following table lists out the definition.

Definitions of Poker Hands

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Counting Poker Hands

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Straight Flush
Counting from A-K-Q-J-10, K-Q-J-10-9, Q-J-10-9-8, …, 6-5-4-3-2 to 5-4-3-2-A, there are 10 hands that are in sequence in a given suit. So there are 40 straight flush hands all together.

Four of a Kind
There is only one way to have a four of a kind for a given rank. The fifth card can be any one of the remaining 48 cards. Thus there are 48 possibilities of a four of a kind in one rank. Thus there are 13 x 48 = 624 many four of a kind in total.

Full House
Let's fix two ranks, say 2 and 8. How many ways can we have three of 2 and two of 8? We are choosing 3 cards out of the four 2's and choosing 2 cards out of the four 8's. That would be = 4 x 6 = 24. But the two ranks can be other ranks too. How many ways can we pick two ranks out of 13? That would be 13 x 12 = 156. So the total number of possibilities for Full House is

Texas holdem poker 2 download full version free. Note that the multiplication principle is at work here. When we pick two ranks, the number of ways is 13 x 12 = 156. Why did we not use = 78?

Flush
There are = 1,287 possible hands with all cards in the same suit. Recall that there are only 10 straight flush on a given suit. Thus of all the 5-card hands with all cards in a given suit, there are 1,287-10 = 1,277 hands that are not straight flush. Thus the total number of flush hands is 4 x 1277 = 5,108.

Straight
There are 10 five-consecutive sequences in 13 cards (as shown in the explanation for straight flush in this section). In each such sequence, there are 4 choices for each card (one for each suit). Thus the number of 5-card hands with 5 cards in sequence is . Then we need to subtract the number of straight flushes (40) from this number. Thus the number of straight is 10240 – 10 = 10,200.

Three of a Kind
There are 13 ranks (from A, K, …, to 2). We choose one of them to have 3 cards in that rank and two other ranks to have one card in each of those ranks. The following derivation reflects all the choosing in this process.

Two Pair and One Pair
These two are left as exercises.

High Card
The count is the complement that makes up 2,598,960.

The following table gives the counts of all the poker hands. The probability is the fraction of the 2,598,960 hands that meet the requirement of the type of hands in question. Note that royal flush is not listed. This is because it is included in the count for straight flush. Royal flush is omitted so that he counts add up to 2,598,960.

Probabilities of Poker Hands

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2017 – Dan Ma