1. Meilleure Main Possible Poker Tournaments
2. Poker Meilleure Main Possible
3. Meilleure Main Possible Poker Games
4. Meilleure Main Possible Poker Game

• General principles
  • Betting limits
• Principal forms
  • Stud poker
  • Community-card poker
  • House-banked games

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. 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.” But there are many versions and variations of poker, the main types being stud, draw and community card games. Then take on the challenge of the PCC Poker Tour, an immersive online career mode that takes players on a journey from backroom card shark to bringing in the big bucks at the PCC main events. From Single-Table and Multi-Table tournaments, to Freezeouts, Shootouts, Turbos, Super Turbos, Bounties and more, we’re bringing more ways to play than. Although it is only possible to play Texas hold’ em in this title, players can switch between shootouts, bounties, freezeouts, and cash buy-ins. Poker Club also has a tour that users can progress through, although it's not a career mode and simply involves trying to meet certain objectives in a match to get stars. As users play more matches.

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Poker, card game, played in various forms throughout the world, in which a player must call (i.e., match) the bet, raise (i.e., increase) the bet, or concede (i.e., fold). Its popularity is greatest in North America, where it originated. It is played in private homes, in poker clubs, in casinos, and over the Internet. Poker has been called the national card game of the United States, and its play and jargon permeate American culture.

Although countless variants of poker are described in the literature of the game, they all share certain essential features. A poker hand comprises five cards. The value of the hand is in inverse proportion to its mathematical frequency; that is, the more unusual the combination of cards, the higher the hand ranks. Players may bet that they have the best hand, and other players must either call (i.e., match) the bet or concede. Players may bluff by betting that they have the best hand when in fact they do not, and they may win by bluffing if players holding superior hands do not call the bet.

General principles

There are forms of poker suitable to any number of players from 2 to 14, but in most forms the ideal number is 6, 7, or 8 players. The object is to win the “pot,” which is the aggregate of all bets made by all players in any one deal. The pot may be won either by having the highest-ranking poker hand or by making a bet that no other player calls. The following principles apply to nearly all forms of poker.

Cards

Poker is almost always played with the standard 52-card deck, the playing cards in each of the four suits (spades, hearts, diamonds, clubs) ranking A (high), K, Q, J, 10, 9, 8, 7, 6, 5, 4, 3, 2, A (low only in the straight [a series of five cards numbered consecutively] or straight flush [a series of five cards numbered consecutively within the same suit] 5-4-3-2-A and in certain variants described below).

In social play, especially in “dealer’s choice” (i.e., a card-playing session in which each player takes a turn at dealing the cards and selecting the game), certain cards may be designated wild cards. A wild card stands for any other card its holder wishes to name. There are many methods of introducing wild cards into the game. The most popular are:

1. Joker. A 53-card pack is used, including the joker as a wild card.
2. Bug. The same 53-card pack including the joker is used, but the joker—here called the bug—counts only as a fifth ace or to fill a flush [a series of five cards of the same suit], a straight, or certain special hands.
3. Deuces wild. All four deuces (2s) are wild cards.
4. One-eyes. In the standard pack the king of diamonds, jack of spades, and jack of hearts are the only cards shown in profile. They are often designated as wild cards.

Rank of poker hands

The rank of standard poker hands is determined by their odds (probability). Two or more identical hands tie and divide any winning equally. The suits have no relative rank in poker. When there is any wild card in the game, the highest possible hand is five of a kind, which beats any straight flush. When there are several wild cards, there may be identical fours of a kind or threes of a kind, in which case ties are broken by the highest unmatched cards or secondary pairs (in a full house [a five-card hand made up of three of a kind and a pair]).

Deal

At the start of the game, any player takes a pack of cards and deals them in rotation to the left, one at a time faceup, until a jack appears. The player receiving that card becomes the first dealer. The turn to deal and the turn to bet always pass to the left from player to player. For each deal, any player may shuffle the cards, the dealer having the last right to shuffle. The dealer must offer the shuffled pack to the opponent to the right for a cut. If that player declines to cut, any other player may cut.

A professional dealer is used in poker clubs, casinos, and tournament play, where a round disc (known as a dealer button) is passed clockwise each hand to indicate the nominal dealer for betting purposes. Also, such environments almost invariably charge the players either by setting an hourly rental fee for their seats or by “raking” a small percentage (say, 5 percent) from each pot.

Betting procedure

In each deal there are one or more betting intervals according to the specific poker variant. In each betting interval, one player, as designated by the rules of the variant being played, has the privilege or obligation of making the first bet. This player and each player in turn after him must place in the pot the number of chips (representing money, for which poker is almost invariably played) to make his total contribution to the pot at least equal to the total contribution of the player before him. When a player does this, he is said to be in the pot, or an active player. If a player declines to do this, he discards his hand and is said to drop or fold, and he may no longer compete for the pot.

Before the deal, each player may be required to make a contribution to the pot, called an ante. In each betting interval, the first player to make a bet is said to bet, a player who exactly meets the previous bet is said to call, and a player who bets more than the previous bettor is said to raise. In some variants, a player is permitted to check, which is to stay in without betting, provided no other player has made a bet in that betting interval. Since a player cannot raise his own bet, each betting interval ends when the betting turn has returned to the person who made the last raise or when all players have checked.

At the end of each betting interval except the last, dealing is resumed. At the end of the last betting interval, there is the “showdown,” in which each active player shows his full hand, and the highest-ranking hand wins the pot.

Betting limits

There are “no-limit” or “sky’s-the-limit” games, but in practice most poker games place some limit on what one may bet in any game. There are three popular methods.

Fixed limit

In fixed-limit games, no one may bet or raise by more than the established limit. In draw poker the limit is usually twice as much after the draw as before—for example, two chips before the draw, four chips after. In stud poker the limit is usually twice as much in the final betting interval as in previous betting intervals. (The higher limit applies also when any player’s exposed cards include a pair.) These respective forms of the game are described below. In a fixed-limit game a limit is usually placed on the number of raises that may be made in any betting interval.

Pot limit

In pot-limit contests, a player may bet or raise by no more than the amount in the pot at the time the bet or raise is made. When raising, the player may first put in the pot the number of chips required to call the previous bet and then raise by the number of chips in the pot. When pot limit is played, it is customary also to place a maximum limit on any bet or raise, regardless of the size of the pot.

Table stakes

This method most closely approximates the no-limit game. Each player’s limit is the number of chips he has on the table at the beginning of the deal. He may not bet more, but for this amount he may call any higher bet (go “all in”) and compete for the pot in the showdown. Other players having more chips may continue to bet, but their further bets go into one or more side pots in the manner decided among the players who contributed fully to the side pot. When a player drops out of any side pot, he drops out of the original pot as well, in effect surrendering his rights in the original pot to the player whose later bet he did not call. Thus, there may be different winners of the main pot and various side pots.

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.

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

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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.

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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