Four Card Poker Table

Ezugi live dealer studios call this side bet '3+3,' using pay table 4 below, in their Teen Patti game, which is the same thing as Three Card Poker. All together, I've seen or heard of the four pay tables listed below. Pay Table 1 is the only one I know of to be actually used. Another bet is available (similar to the Pairplus in Three Card Poker), based only on the player's four card hand, called the Aces Up. Seven pay tables are available as indicated below. The only one I know of to be actually used is pay table 5. 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.

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

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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.

Introduction

Four Poker is a new poker variation invented by Roger Snow and marketed by Shufflemaster. The game is similar to Three Card Poker but as the title suggests, four cards are used instead of three. Also, there is no dealer qualifying hand and the player can raise up to three times his ante. However, the dealer gets one extra card to form his best hand.

Rules

1. Two initial bets are available: The Ante and the Aces Up.
2. All players get five cards each and the dealer gets six cards. One of the dealer cards is placed face up, and five face down.
3. Players making the Ante bet must decide to fold or raise.
4. If the player folds he forfeits his Ante bet. He may or may not forfeit his Aces Up bet, depending on casino rules. It shouldn't matter because if the player has a paying Aces Up bet, he shouldn't be folding anyway.
5. If player raises, then he must raise at least the amount of the Ante and at most, three times the Ante.
6. The player keeps his best four cards and discards one.
7. Following is the ranking of hands from lowest to highest: high card, pair, two pair, straight, flush, three of a kind, straight flush, four of a kind.
8. After all decisions have been made, the dealer will turn over his cards and select the best four out of six.
9. The player's hand shall be compared to the dealer's hand, the higher hand winning.
10. If the dealer's hand is higher, then the player shall lose the Ante and Raise.
11. If the player's hand is higher or equal then the Ante and Raise shall pay one to one.
12. If the player has at least a three of a kind, then he shall also be paid a Bonus, regardless of the value of the dealer's hand. Two different pay tables are available for the Bonus, as displayed below, and are based on the ante bet. Pay Table 1 is the only one I know of to be actually used.
13. Another bet is available (similar to the Pairplus in Three Card Poker), based only on the player's four card hand, called the Aces Up. Seven pay tables are available as indicated below. The only one I know of to be actually used is pay table 5.

4 Card Poker Table Game

Four Card Poker Table

Bonus Pay Table

Aces Up Pay Table

Of these pay tables for the Aces Up side bet, number five is the most popular. The only exceptions that I'm aware of are an unconfirmed report that that Tulalip in Washington uses pay table 4 and the Grand Casino Hinckley in Minnesota uses pay table 1.

Analysis

The following return table is based on optimal player strategy under the 2-20-25 Ante Bonus pay table. The lower right cell shows a house edge of 2.79%.

Return Table Based on Optimal Strategy

The average final bet under optimal strategy is 2.142342 units, making the element of risk, -0.027879/2.142342 = 1.30%. The standard deviation, relative to the original bet, is 2.71.

Beginner Strategy

A simple strategy to this game, first proposed by Stanley Ko, is as follows.

• Raise 3X with a pair of tens or higher.
• Raise 1X with a pair of twos to nines.
• Fold all other.

According to the second edition of 'Beyond Counting' by James Grosjean, this 'simple strategy' results in a house edge of 3.396%.

Intermediate Strategy

The following intermediate strategy was created to balance power and simplicity by our own JB.

• Pair of Aces or better: Bet 3X
• Pair of Js, Qs, Ks: Bet 3X if dealer's upcard is lower than your pair or matches a rank in your hand, otherwise bet 1X
• Pair of 9s, 10s: Bet 1X if dealer's upcard outranks your pair, otherwise bet 3X
• Pair of 8s: Bet 3X if dealer's upcard is a 2, otherwise bet 1X
• Pair of 3s, 4s, 5s, 6s, 7s: Bet 1X
• Pair of 2s or AKQ: Bet 1X if dealer's upcard matches a rank in your hand, otherwise fold
• All other: Fold

Against the 2-20-25 Ante Bonus pay table, the house edge is 2.8526% and the element of risk is 1.3233%.

Advanced Strategy

I'm proud to present the following advanced strategy, also created by my sidekick JB.

• Pair of Aces or better: Bet 3X
• Pair of Ks: Bet 3X, except bet 1X against an Ace and you don't have an Ace nor 4.
• Pair of Js or Qs: Bet 3X, except bet 1X if the dealer's card outranks pair your pair rank and does not match a singleton in your hand.
• Pair of 9s or 10s: Bet 3X, except bet 1X if dealer card outranks your pair rank.
• Pair of 8s: Bet 1X, except bet 3X against a 2
• Pair of 4s thru 7s: Bet 1X
• Pair of 3s: Bet 1X, except fold against a Jack if your highest kicker is a 10 or lower
• Pair of 2s or AKQ: Fold, except bet 1X if dealer card matches a rank in your hand
• AKJT: Fold, except bet 1X against a Jack
• AKJ9 or lower: Fold

Against the 2-20-25 Ante Bonus pay table, the house edge is 2.8498% and the element of risk is 1.3216%. Here is a house edge comparison of various known strategies.

• Simple: 3.396%
• Intermediate: 2.853%
• Advanced: 2.850%
• Optimal: 2.788%

To put it another way, here are the cost of errors:

• Simple: 0.606%
• Intermediate: 0.065%
• Advanced: 0.062%
• Optimal: 0.000%

Aces Up Analysis

The next table shows the probability of each hand and the return under pay table five of the Aces Up side bet. The lower right cell shows a house edge of 3.89%.

Return for Aces Up Pay Table 5

The next table shows the house edge according to all four Aces Up pay tables.

Aces Up House Edge

Note: There is also a similar game called Crazy Four Poker.

Acknowledgments

I would like to recognize:

• JB for the analysis of the optimal strategy.
• Stanley Ko for the simplified strategy.
• James Grosjean for the unpublished advanced strategy.