Odds Of Winning Three Card Poker
- The Wizard of Odds teaches Three Card Poker. For more about Three Card Poker, please visit Mike mentions ho.
- The player will win the Ante bet 44.91 per cent of the time. There are 22,100 possible three-card hands. The Ante bonus pays on 824 of those, for a total of just 3.73 per cent of the time. If you play on a table with six players, someone gets paid on the Ante bonus about every four rounds.
- For example, the probability of drawing three of a kind is approximately 2.11%, while the.
- Poker Card Winning Hands
- Three Card Poker Odds Of Winning
- 3 Card Poker Odds Calculator
- What Are The Odds Of Winning 3 Card Poker
- Odds Of Winning Three Card Poker
- Poker Outs Odds
On This Page
Introduction
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.
This page details what I call the Florida variant of Three Card Poker. It is played at some player-banked card rooms in Florida where conventional Three Card Poker would not conform to Florida law. Seminole tribal casinos are exempt from these laws and thus may and do offer conventional Three Card Poker.
It is my understanding that the pertinent law in the Florida card clubs is that every bet must be based on beating an opponent. Thus, to conform to the law, it is a requirement of the Pairplus bet that the player beat the 'dealer.' The Ante bonus is completely eliminated. The rest of this page details the rules and odds of Three Card Poker under the Florida rules.
Rules
There are two bets, the Ante and Pairplus. The player may bet one or both.
Poker Card Winning Hands
Ante Bet rules
- A single 52-card deck is used.
- The player makes an Ante bet.
- The dealer gives each player three cards and himself three cards. The player may examine his own cards. The dealer's cards are dealt face down.
- If the player made the Ante bet, then he has must either fold or raise.
- If the player folds, then he forfeits his Ante wager.
- If the player raises, then he must make an additional Play bet, equal exactly to his Ante bet.
- The dealer will turn over his cards.
- The dealer needs a queen high or better to qualify.
- If the dealer does not qualify, then the player will win even money on the Ante bet and the Play bet will push.
- If the dealer qualifies, then the player's hand will be compared to the dealer's hand, the higher hand wins. The order of poker hands is indicated below.
- If the player has the higher poker hand, then the Ante and Play will both pay even money.
- If the dealer has the higher poker hand, then the Ante and Play will both lose.
- If the player and dealer tie, then the Ante and Play bets will push.
Pairplus rules
- As with the Ante bet, the player and dealer each receive three cards from a 52-card deck.
- The poker value of each hand will be compared, the higher hand wins. The ranking of poker hands is shown below.
- If the player has at least a pair and the higher hand, then the Pairplus bet will pay according to the pay table below.
- If the player has less than a pair or the lower hand, then the Pairplus bet shall lose.
- If the player and dealer have exactly equal poker hands of a pair or greater, then the Pairplus bet shall push.
- I'm getting conflicting reports on what happens if the player and dealer tie with less than a a pair. Some say it is a push and others say it is a loss. It seems to me that losing would be the more logical rule.
Ranking of poker hands
- Straight flush.
- Three of a kind.
- Straight.
- Flush.
- Pair.
- Trash (all other).
The following is the pay table for winning Pairplus wagers. All pays are on a 'to one' basis.
Three Card Poker Odds Of Winning
Pairplus Pay Table
3 Card Poker Odds Calculator
Event | Pays |
---|---|
Mini Royal | 200 |
Straight flush | 40 |
Three of a kind | 30 |
Straight | 4 |
Flush | 3 |
Pair | 2 |
Trash | Loss |
For those familiar with conventional Three Card Poker rules, here are the differences:
- Ante: There is no Ante bonus.
- Pairplus: The player must beat the dealer to win. A conventional pay table is used, except pays 2 to 1 on a pair. Opinions vary on what happens on a tie.
Analysis
The following table shows my analysis of the Ante bet. The lower right cell shows a house edge of 8.68% (ouch!). The player will make the raise bet 67.42% of the time, for an average final wager of 1.6742 units. That makes the Element of Risk 5.17%.
Ante Analysis
Event | Pays | Combinations | Probability | Return |
---|---|---|---|---|
Player wins | 2 | 97,354,684 | 0.239101 | 0.478201 |
Dealer doesn't qualify | 1 | 85,493,652 | 0.209970 | 0.209970 |
Push | 0 | 267,648 | 0.000657 | 0.000000 |
Player folds | -1 | 132,652,800 | 0.325792 | -0.325792 |
Dealer wins | -2 | 91,401,616 | 0.224480 | -0.448960 |
Total | 407,170,400 | 1.000000 | -0.086580 |
The next table shows my analysis of the Pairplus bet if all ties result in a push. The lower right cell shows a house edge of 4.23%.
Pairplus Analysis — All Ties Push
Event | Pays | Combinations | Probability | Return |
---|---|---|---|---|
Player wins with Mini Royal | 200 | 73,684 | 0.000181 | 0.036193 |
Player wins with straight flush | 40 | 809,556 | 0.001988 | 0.079530 |
Player wins with three of a kind | 30 | 954,736 | 0.002345 | 0.070344 |
Player wins with straight | 4 | 12,976,488 | 0.031870 | 0.127480 |
Player wins with flush | 3 | 18,928,820 | 0.046489 | 0.139466 |
Player wins with pair | 2 | 57,094,704 | 0.140223 | 0.280446 |
Tie | 0 | 450,528 | 0.001106 | 0.000000 |
Player wins with trash | -1 | 315,881,884 | 0.775798 | -0.775798 |
Total | 407,170,400 | 1.000000 | -0.042338 |
The next table shows my analysis of the Pairplus bet if ties with a non-paying hand (like K-9-5) lose. The lower right cell shows a house edge of 4.34%.
Pairplus Analysis — Tie with Trash Loses
Event | Pays | Combinations | Probability | Return |
---|---|---|---|---|
Player wins with Mini Royal | 200 | 73,684 | 0.000181 | 0.036193 |
Player wins with straight flush | 40 | 809,556 | 0.001988 | 0.079530 |
Player wins with three of a kind | 30 | 954,736 | 0.002345 | 0.070344 |
Player wins with straight | 4 | 12,976,488 | 0.031870 | 0.127480 |
Player wins with flush | 3 | 18,928,820 | 0.046489 | 0.139466 |
Player wins with pair | 2 | 57,094,704 | 0.140223 | 0.280446 |
Tie | 0 | 32,952 | 0.000081 | 0.000000 |
Loss | -1 | 316,299,460 | 0.776823 | -0.776823 |
Total | 407,170,400 | 1.000000 | -0.043364 |
Strategy
Between the two bets, the Pairplus offers the better odds, regardless of the tie rule. If you must play, I would recommend playing that only. However, if you must play the Ante, the strategy is the same as for conventional Three Card Poker — raise with Q-6-4 or higher.
External Links
- Wizard of Vegas — Discussion about this game.
Written by:Michael Shackleford
Three Card Poker is a casino table game based on poker.
History[edit]
What Are The Odds Of Winning 3 Card Poker
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.
Odds Of Winning Three Card Poker
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]
Poker Outs Odds
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.