A wild card is specified by the holder to be a card of any rank or suit, such as a fifth queen, or the card needed to combine with the other four in a player's hand to form a straight or a flush. Wild cards in a Poker game add variety, and of course, they greatly increase the chances of getting a rare combination such as a full house or a.
Three Card Poker is a casino table game based on poker.
Four of a kind, also known as quads, is a hand that contains four cards of one rank and one card of another rank (the kicker), such as 9 ♣ 9 ♠ 9 ♦ 9 ♥ J ♥ ('four of a kind, nines'). It ranks below a straight flush and above a full house. Each four of a kind is ranked first by the rank of its quadruplet, and then by the rank of its kicker. This is a list of traditional card and tile games that are designed for or work well with four players. Each game is listed just once - for alternative names see the general alphabetical index. For each game the configuration of players and the type and number of cards or tiles is listed. There is an explanation of the symbols below the 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.
History[edit]
The casino variant of Three Card Poker was first created by Derek Webb in 1994 and patented in 1997.[1] Webb's goal was to create a version of poker that played with the speed of other table games. It was important to Webb that he got the correct mix of three important factors for any casino game: the game rules were easy to understand, the payouts were large enough to attract players, and the house edge was enough that casino owners would be interested in adopting the game.
Webb established a business called Prime Table Games to market the game in both the United States and United Kingdom.[2] The British Casino Association, now known as the National Casino Industry Forum (NCiF) suggested that Webb gain some experience in the US first, since the UK had regulations against such a table game and his application was not strong enough to convince regulators to make significant changes to their rules and regulations for a new game.
The first to adopt the game was Barry Morris, Vice President of Grand Casino Gulfport in Mississippi, after Webb had unsuccessful sales pitches with casino owners in Reno, Las Vegas, and Atlantic City. A key aspect of Webb's offer to Morris was to stand on the floor to train the dealers himself, as well as watch to make sure the game was being played correctly.[3] United Kingdom gambling regulations were changed to allow the introduction of Three Card Poker in 2002.
Prime Table Games continued marketing Three Card Poker until 1999, when Shuffle Master acquired the rights to the game outside the British Isles. The sale was prompted by a lawsuit filed that year in US federal court by Progressive Gaming International Corporation (PGIC), the then-owners of Caribbean stud poker, alleging patent infringement; Shuffle Master agreed to defend that litigation as part of the purchase. Subsequently in 2007, Prime Table Games showed in a countersuit that the 1999 PGIC litigation was based on invalid patent claims; PGIC settled for $20 million.[4] Further, Prime Table Games filed suit against Shuffle Master in 2008 alleging in part that Shuffle Master had undisclosed knowledge that the PGIC claims were invalid prior to the 1999 purchase; it was later settled for over $2 million.[5]
Rules[edit]
Three Card Poker is played as heads-up between the player's hand and the dealer's hand. After all ante wagers are placed, three cards are dealt to each player and the dealer. Players have a choice to either fold or continue in the game by placing a 'play' wager equal to their ante. Hands are then exposed and wagers resolved.[6]
The dealer's hand must be Queen high or better for the dealer hand to play. If the dealer does not play, then there is no action on play wagers and ante wagers are paid 1 to 1. If the dealer does play, the dealer and player hands are compared. If the player hand loses, both the ante and play wagers are lost. If the player hand wins both the ante and play wagers are paid 1 to 1. If the hands are tied, then there is no action on either wager.[6]
Additional optional bets are offered. The Pair Plus wager is a bet that the player's hand will be a pair or better. The Pair Plus wager wins if the player has at least a pair of twos. The payoff applies regardless of the dealer's hand, as the Pair Plus wager is not in competition against the dealer's hand. Some casinos also offer an Ante Bonus, which is paid on the ante wager for a straight or better. The typical Ante Bonus paytable pays 5 to 1 for a straight flush, 4 to 1 for a three of a kind, and 1 to 1 for a straight. Like the Pair Plus wager, the Ante Bonus pays regardless of whether that hand beats the dealer's hand.[6]
Hand ranks[edit]
Straight flush
Three of a kind
Straight
Flush
Pair
High card
| Hand Ranks of Three Card Poker[7] | |||
|---|---|---|---|
| Rank | Description | Frequency | Probability |
| Straight flush | Three suited cards in sequence | 48 | 0.22% |
| Three of a kind | Three cards of same rank | 52 | 0.24% |
| Straight | Three cards in sequence | 720 | 3.26% |
| Flush | Three suited cards | 1,096 | 4.96% |
| Pair | Two cards of same rank | 3,744 | 16.94% |
| High card | None of the above | 16,440 | 74.39% |
| Total hands | - | 22,100 | - |
Probability of Queen high or better is 69.59%[citation needed]
Variations[edit]
Some venues have added a wager called Prime in United Kingdom casinos and the game is known as Prime Three Card Poker. The Prime wager is optionally placed before cards are dealt and pays on the color of the player cards. If all three cards are the same color the payoff is 3 to 1. However, when included with the dealer hand if all six cards are the same color then the payoff is increased to 4 to 1.
Another variation is 'six card bonus', in which the players are given a payout based on the best five-card poker hand that can be made using any combination of the player's three cards and the dealer's three cards. Payoff ranges from 5 to 1 for three of a kind to 1000 to 1 for royal flush. Payoffs are paid regardless of whether any other bets pay.
See also[edit]
References[edit]
- ^'Three Card Poker'. Retrieved August 29, 2017.
- ^'Intellectual Property Office patent entry'. Retrieved May 27, 2011.
- ^'3CardPoker.com'. Retrieved November 5, 2013.
- ^Stutz, Howard (November 7, 2007). 'Progressive agrees to pay $20 million to end lawsuit'. Las Vegas Review-Journal. Retrieved August 13, 2018.
- ^Stutz, Howard (January 14, 2011). 'Charge hurts Shuffle Master earnings'. Las Vegas Review-Journal. Retrieved August 13, 2018.
- ^ abcMatt Villano (August 27, 2014). 'Winning a 3-card poker can be tough'. SfGate.
- ^'Three Card Poker - Wizard of Odds'. wizardofodds.com. Retrieved 2020-02-01.
On This Page
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
- Two initial bets are available: The Ante and the Aces Up.
- 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.
- Players making the Ante bet must decide to fold or raise.
- 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.
- If player raises, then he must raise at least the amount of the Ante and at most, three times the Ante.
- The player keeps his best four cards and discards one.
- 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.
- After all decisions have been made, the dealer will turn over his cards and select the best four out of six.
- The player's hand shall be compared to the dealer's hand, the higher hand winning.
- If the dealer's hand is higher, then the player shall lose the Ante and Raise.
- If the player's hand is higher or equal then the Ante and Raise shall pay one to one.
- 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.
- 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.
Bonus Pay Table
| Hand | Table 1 | Table 2 |
|---|---|---|
| Four of a kind | 25 | 30 |
| Straight flush | 20 | 15 |
| Three of a kind | 2 | 2 |
Aces Up Pay Table
| Hand | Table 1 | Table 2 | Table 3 | Table 4 | Table 5 | Table 6 | Table 7 |
|---|---|---|---|---|---|---|---|
| Four of a kind | 50 to 1 | 50 to 1 | 50 to 1 | 50 to 1 | 50 to 1 | 50 to 1 | 50 to 1 |
| Straight flush | 40 to 1 | 40 to 1 | 30 to 1 | 30 to 1 | 40 to 1 | 40 to 1 | 40 to 1 |
| Three of a kind | 9 to 1 | 7 to 1 | 9 to 1 | 7 to 1 | 8 to 1 | 8 to 1 | 7 to 1 |
| Flush | 6 to 1 | 6 to 1 | 6 to 1 | 6 to 1 | 5 to 1 | 6 to 1 | 5 to 1 |
| Straight | 4 to 1 | 5 to 1 | 4 to 1 | 5 to 1 | 4 to 1 | 4 to 1 | 4 to 1 |
| Two pair | 2 to 1 | 2 to 1 | 2 to 1 | 2 to 1 | 3 to 1 | 2 to 1 | 3 to 1 |
| Pair of aces or better | 1 to 1 | 1 to 1 | 1 to 1 | 1 to 1 | 1 to 1 | 1 to 1 | 1 to 1 |
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
| Player Hand | Raise/Fold | Win/Loss | Combinations | Probability | Pays | Return |
|---|---|---|---|---|---|---|
| Four of a Kind | 3 | Win | 40,182,878,736 | 0.000240 | +29 | 0.006960 |
| Four of a Kind | 3 | Lose | 18,594,576 | 0.000000 | +21 | 0.000002 |
| Straight Flush | 3 | Win | 133,224,330,456 | 0.000796 | +24 | 0.019096 |
| Straight Flush | 3 | Lose | 265,177,080 | 0.000002 | +16 | 0.000025 |
| Three of a Kind | 3 | Win | 3,675,379,352,400 | 0.021951 | +6 | 0.131703 |
| Three of a Kind | 3 | Lose | 103,559,138,928 | 0.000618 | -2 | -0.001237 |
| Flush | 3 | Win | 6,599,621,152,728 | 0.039415 | +4 | 0.157660 |
| Flush | 3 | Lose | 784,564,849,080 | 0.004686 | -4 | -0.018743 |
| Straight | 3 | Win | 5,257,469,039,688 | 0.031399 | +4 | 0.125597 |
| Straight | 3 | Lose | 1,301,555,952,216 | 0.007773 | -4 | -0.031093 |
| Two Pair | 3 | Win | 5,539,444,298,496 | 0.033083 | +4 | 0.132333 |
| Two Pair | 3 | Lose | 2,420,447,417,280 | 0.014456 | -4 | -0.057823 |
| One Pair | 3 | Win | 14,764,551,298,548 | 0.088179 | +4 | 0.352714 |
| One Pair | 3 | Lose | 10,806,299,820,804 | 0.064539 | -4 | -0.258155 |
| One Pair | 1 | Win | 13,535,004,289,296 | 0.080835 | +2 | 0.161671 |
| One Pair | 1 | Lose | 22,887,448,286,136 | 0.136691 | -2 | -0.273382 |
| One Pair | Fold | Fold | 5,495,692,732,992 | 0.032822 | -1 | -0.032822 |
| High Card | 1 | Win | 148,058,445,132 | 0.000884 | +2 | 0.001769 |
| High Card | 1 | Lose | 422,493,233,796 | 0.002523 | -2 | -0.005047 |
| High Card | Fold | Fold | 73,523,856,056,112 | 0.439108 | -1 | -0.439108 |
| Totals | 167,439,136,344,480 | 1.000000 | -0.027879 |
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
| Hand | Combinations | Probability | Pays | Return |
|---|---|---|---|---|
| Four of a kind | 624 | 0.00024 | 50 | 0.012005 |
| Straight flush | 2072 | 0.000797 | 40 | 0.03189 |
| Three of a kind | 58656 | 0.022569 | 8 | 0.180552 |
| Flush | 114616 | 0.044101 | 5 | 0.220504 |
| Straight | 101808 | 0.039173 | 4 | 0.15669 |
| Two pair | 123552 | 0.047539 | 3 | 0.142617 |
| Pair of aces | 81096 | 0.031203 | 1 | 0.031203 |
| Nothing | 2116536 | 0.814378 | -1 | -0.814378 |
| Total | 2598960 | 1 | -0.038917 |
The next table shows the house edge according to all four Aces Up pay tables.
Aces Up House Edge
| Pay Table | House Edge |
|---|---|
| 1 | 1.98% |
| 2 | 2.58% |
| 3 | 2.78% |
| 4 | 3.37% |
| 5 | 3.89% |
| 6 | 4.24% |
| 7 | 6.15% |
Note: There is also a similar game called Crazy Four Poker.
4 Card Poker Table
Acknowledgments
I would like to recognize:
Four Card Poker Table Layout Template
- JB for the analysis of the optimal strategy.
- Stanley Ko for the simplified strategy.
- James Grosjean for the unpublished advanced strategy.