Three Card Poker
Three Card Poker is a betting game played in casinos throughout the world. Unlike most forms of poker, the player wins when they can manage to beat the house, as in Blackjack and Mini Baccarat. Accordingly, Three Card Poker tables are usually located in the blackjack pit, not in the poker room.
Unlike most games played with traditional cards, Three Card Poker is a proprietary game. It was originally marketed by ShuffleMaster, a company which made and supplied automatic card shufflers to casinos. Due to a chain of acquisitions, the game is now owned by Scientific Games. Scientific Games still licenses the rights to the Three Card Poker name, as well as selling layouts and specialized shufflers that can also be programmed to deal three-card hands for each player.
Object of Three Card Poker
The object of Three Card Poker is to hold a hand higher than that of the dealer, or walk away when they feel they are unlikely to do so.
Setup
Unlike many casino table games, Three Card Poker is played with only one standard, 52-card deck of playing cards. Happily, that means if you’re wanting to play a home game, you can use your favorite deck of Denexa 100% Plastic Playing Cards. You’ll also need chips to bet with.
Casinos spread the game on a felt table with a printed layout that facilitates the placing and payout of bets. Each player position has three betting boxes, typically laid out as shown at right. Because Three Card Poker is a proprietary game, pre-printed felt layouts are not as readily available as those found in games such as Blackjack. If you’re playing at home, you will most likely have to get creative, making a betting layout for yourself.
All players place a bet (which must be between the posted table minimums and maximums) in the Ante box on the layout. If they wish, they may also place an additional bet in the Pair Plus circle. Shuffle and deal three cards face down to each player, including the dealer.
Game play
Rank of Three Card Poker hands
Because there are only three cards involved, the hands available in Three Card Poker and their ranking differ from traditional poker. The hands are, from highest to lowest:
- Straight flush: Three cards of the same suit, in sequence.
- Three of a kind: Three cards of the same rank.
- Straight: Three cards in sequence.
- Flush: Three cards of the same suit.
- Pair: Two cards of the same rank, plus one unmatched card.
- High card: Three unmatched cards.
Competing pairs are evaluated by the rank of the pair, with the kicker (unmatched card) breaking ties. All other hands are evaluated by comparing the top-ranked card, then the second-highest, then the lowest. Cards rank in their usual order, with aces high (although A-2-3 is a valid straight).
Play of the hand
Each player picks up their cards (touching the cards is allowed in Three Card Poker) and examines their hand. They now make the only decision in the game—whether to raise (play) or fold. If the player folds, they surrender their cards to the dealer, who collects their money from the Ante and Pair Plus circles. If they raise, they place another bet, exactly the same amount as their Ante wager, on top of their cards (which are placed in the box overlapping the Play box, such that a bet placed on top of the cards ends up being in the Play box).
When all players have acted, the dealer reveals their hand. If the dealer’s hand is queen high or better, they are said to qualify. Should the dealer fail to qualify, the hand ends immediately, with each player being paid even money on their Ante bet and the Play bet pushing. (It should be noted that, so long as the player hasn’t folded, the Ante bet always pays when the dealer fails to qualify, even if the player’s hand is lower than the dealer’s.)
If the dealer qualifies, each player’s hand is compared with the dealer’s. Starting with the player to their right, and proceeding counter-clockwise around the table, the dealer reveals each player’s hand. If the player’s hand is higher than the dealer’s, they are paid even money on both the Ante and Play bets. When the dealer’s hand is higher, both bets are lost. If the dealer and player tie exactly, both bets push.
Pair Plus and Ante bonus payouts
If the player holds a high enough hand, they may get paid no matter what the dealer holds. Usually, this will happen because they made the Pair Plus bet, which operates entirely independently of the other two bets. If the player has a pair or higher, they are paid according to the hand they hold; otherwise, the bet is lost. A player holding a straight or better also receives a bonus on their Ante bet (regardless of if they played the Pair Plus bet).
Pair Plus bet and Ante bonuses are paid according to the following paytable. Note that these are typical values; some casinos may pay different rates.
| Hand | Pair Plus | Ante bonus |
|---|---|---|
| Straight flush | 40 to 1 | 5 to 1 |
| Three of a kind | 30 to 1 | 4 to 1 |
| Straight | 6 to 1 | even money |
| Flush: | 3 to 1 | – |
| Pair | even money | – |
Three Card Poker strategy
According to Michael Shackelford of the popular Wizard of Odds gambling probabilities site, the mathematically ideal strategy for Three Card Poker is to play hands of Q-6-4 and higher and to fold hands of Q-6-3 and lower.
It should be noted that the house edge on the Pairs Plus bet is 7.28%. This is not much better than betting on a slot machine. However, to many players, the chance to catch a straight flush and win $200 on a $5 bet is too great a temptation to resist…
As a mathematician, I have the formulas for three-card Poker by using regular monomino playing cards. Here are the formulas; whole straight flush without terminals = z • u; whole basic flush without terminals = [C (z, 3) – z] • u; whole basic straight without terminals = z • (u^3 – u); trio = C (u, 3) • z; pair = z • C (u, 2) • (z • u – u); Whammy (A.K.A. high card) = C [(z • u), 3] – Σ. If you want a two-in-one terminal (Usually, an ace is the two-in-one terminal.), first, move the number (3 – 2) • u from whole straight flush to whole basic flush, and second, move the number (c – 2) • (u^3 – u) from whole basic straight to Whammy. If you want two terminals (Usually, aces are the lowest, and usually, kings are the highest.), first, move the number (3 – 1) • u from whole straight flush to whole basic flush, second, move the number (c – 1) • (u^3 – u) from whole basic straight to Whammy. Here are the following meaning of variables to each formula; z = number of possible ranks; u = number of possible sub-suits; Σ = sum of the non-Whammy hands. The ranking from best to worst in three-card poker by playing with 13 ranks of four sub-suits without terminal ranks is [whole straight flush (52)/trio (52)], whole basic straight (780), whole basic flush (1,092), pair (3,744), and Whammy (16,380); please note that whole straight flush and trio are tied, and as an alternative rule, you determine the ranking of the tied hands to break the tie. The ranking from best to worst in three-card poker by playing with 13 ranks of four sub-suits with a two-in-one terminal rank (Usually, an ace is the two-in-one terminal.) is whole straight flush (48), trio (52), whole basic straight (720), whole basic flush (1,088), pair (3,744), and Whammy (16,448). The ranking from best to worst in three-card poker by playing with 13 ranks of four sub-suits with two terminal ranks (Usually, aces are the lowest, and usually, kings are the highest.) is whole straight flush (44), trio (52), whole basic straight (660), whole basic flush (1,084), pair (3,744), and Whammy (16,516). The less the combinations, the better the Poker hand, and you can do the math to correct the mistakes.
I need to talk about why intellectual-property laws are a negative influence in society. The truth is that there is no such thing as trademark/patent/copyright protection, but there is such thing as trademark/patent/copyright selfishness truly. The truly subliminal side to intellectual-property barriers is that intellectual-property barriers destroy community development and that pro-intellectual-property people are continuing their greed of “selfish rights” and of “royalty money” to put other people into nonexistence (caring about money more than people). Using pro-intellectual-property actions and not giving permission frequently are selfish, and selfishness counts as murder, and pro-intellectual property actions are dishonorable acts, and pro-intellectual-property acts must be outlawed. If we do not repeal intellectual-property laws soon, there will be hopelessness for potential people from using the resources to the public audience freely of any purpose. If one serious prohibition exists, there will be a multitude of serious prohibitions thus beginning civil madness. Material hope and material honor will eradicate soon. One of these days, there will be no more original ideas for everyone (present/future generations) in this world due to the laws of trademark/patent/copyright; in a simile, a specific type of species will become extinct if hunters keep killing that specific species; in another simile, there will be a time that we will be out of fresh permutations of phone numbers, of usernames, and of Internet domain names if we keep adding more accounts of these. As a mathematician and as a libertarian, the more trademarks/patents/copyrights filed, the less the chances of a fresh idea for a newcomer, the less the chances of honor for a newcomer, the more the nonsensical prohibitions. The truth about me is that I am against intellectual-property laws; I am not with the status quo (Respecting intellectual-property laws is one example) like you; most of my creativity is not Adam Branca original; I am the type of person who modifies and resurrects regardless of respecting intellectual-property laws. We need to be sharers more instead of being non-sharers because we, all, are on the same team (God’s team) to be more productive; if I was you, I would declare every single piece of work to be public domain thus being generous, and if I was you, I would tell Congress to repeal intellectual-property laws. With prayer, I hope that you understand this lecture against intellectual-property laws for the sake of a brighter future and for the sake of libertarianism. My ideas are public domain because I am a sharer, and because I hate intellectual-property laws, and because intellectual-property laws contain selfish murder; we need to be sharers more instead of being non-sharers (A non-sharer cares about money, about power, and/or about credit instead of people.) because we, all, are on the same team (God’s team) for productive communities.
My comment is not related to this question but it is the only place I have found where I CAN post something. In Three Card Poker there is the Pair Plus bonus you can play and/or the Ante Bonus. With the Pair Plus, there is 5 ways the player can win & in the Ante Bonus only 3 ways the player can win but the house edge is approximately twice as high in the Pair Plus vs. the Ante Bonus. This flies in the face of statistical reasoning. Do you know why this is?
Hey Rodney,
In most casino games, the house edge comes from a discrepancy between the true odds of a result occurring and its payout. To use a simpler example, betting on red in roulette pays even money (1 to 1, a winning $5 bet is paid out $5). This would be the correct payout if there is a 50% chance of the ball landing on red. However, only 18 of the 38 spaces of the wheel are red (there are also 18 black spaces and 2 green spaces), so there is only roughly a 47% chance of landing on red. This 3% difference is the house edge.
It’s important to note that while there’s five different categories of win on the Pair Plus bet, there are actually 22,100 possible Three Card Poker hands, 16,440 of which are Pair Plus losers, and 5,660 of which are Pair Plus winners. These figures are what goes into the odds calculations. The Wizard of Odds has all of the gory mathematical details if you want to see them.