Three Card Poker
Last Update: June 13, 2013
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|Hand Order and Probabilities in Three Card Poker|
|Three of a kind||52||0.002353|
|Ace High or Less||16440||0.743891|
Ante and Play Analysis
Various pay tables are known to exist for the Ante Bonuses. The table below shows the various pay tables known, the contribution to the return for each and, and the overall house edge and element of risk for each pay table. The vast majority of tables follow pay table #1.
|Ante Bet Bonus|
|Hand||Probability||Table 1||Table 2||Table 3||Table 4|
|Straight flush||0.002172||5 to 1||4 to 1||3 to 1||5 to 1|
|Three of a kind||0.002353||4 to 1||3 to 1||2 to 1||3 to 1|
|Straight||0.032579||1 to 1||1 to 1||1 to 1||1 to 1|
|Element of Risk||2.01%||2.28%||2.56%||2.16%|
The next table shows the probability and return for each net win under the table 1 ante bonuses.
|Ante Return Table|
Overall on the ante the probability of a win is 44.91%, push 0.06%, and loss 55.03%.
Mini Royal rules
Some casinos now offer a line item for a Mini Royal in the Ante Bonus pay table. A Mini Royal is a suited AKQ. Following are pay tables I have seen or heard to exist. The bottom row shows the overall house edge on the Ante bet for the given pay table.
|Mini Royal Summary Table|
|Hand||Table 1||Table 2||Table 3|
|Mini Royal in Spades||50||50||10|
|Three of a kind||3||6||4|
|Element of Risk||4.06%||2.84%||1.96%|
Mini Royal Ante Bonus locations:
Pay Table 1: Wynn, Las Vegas
Pay Table 2: Casino Arizona
Pay Table 3: Borgata, Atlantic City; Galewind Internet casinos
The following table shows the probability and return for the most common pay table of the Pairplus bet. The lower right cell shows a house edge of 7.28%.
|Pairplus Return Table|
|Three of a Kind||30||52||0.002353||0.070588|
The following two tables show various pay tables for Pairplus. It used to be that the only table was pay table 1. Now, pay table 7 is the norm. The only casino in southern Nevada that I know of to still offer table 1 is the Pioneer in Laughlin. Bovada offers pay table 1 in its online casino. The Borgota in Atlantic City offers pay table 11 as the "Three Card Bonus Bet" in Let it Ride.
In 2007 some casinos added a "Mini Royal" to the pay table. A Mini Royal is a suited ace/king/queen.
The following two pay tables show the house edge of various Pairplus pay tables, both with and without the Mini Royal.
|Pairplus Pay Tables — Without Mini Royal|
|Hand||Probability||Table 1||Table 2||Table 3||Table 4||Table 5||Table 6||Table 7|
|Three of a kind||0.24%||30||33||25||25||30||30||30|
|Pairplus Pay Tables — With Mini Royal|
|Hand||Probability||Table 8||Table 9||Table 10||Table 11||Table 12||Table 13|
|Three of a kind||0.24%||25||30||30||30||30||30|
The next table shows the probability and return for net win assuming the player bets equally on the Ante and Pairplus, assuming the most common pay tables of 1/4/5 on the Ante Bonus and 1/3/6/30/40 on the Pairplus. The lower left cell shows an expected loss of -.10649 units on a two unit initial bet. So the house edge of the combined bet would be -.10649/2 = -0.053245, or a house edge of 5.32%
|Combined Return Table|
Overall betting equally on the Ante and Pairplus on the pay tables stated above the probability of a win is 32.06%, push 13.23%, and a loss 54.71%.
Three Card Poker Progressive
Three Card Poker Progressive is a side bet I noticed at the Fitzgerald's in Las Vegas on February 4, 2009. It is a $1 wager that pays according to the pay table below. All wins are on a "for one" basis, in other words the player does not get back his original wager, even if he wins. The "envy bonus" pays if the player made the bet, but another player gets a mini royal.
|Three Card Poker Progressive — Pay Table|
|Mini Royal in spades||Jackpot||$100|
|Three of a Kind||$90||$0|
The return depends on the jackpot amount and number of other players. To be specific, it is 47.87%, plus 4.52% for each $1000 in the jackpot, and 0.79% per number of other players. To break even the meter needs to be $11,520, less $175 for each other player.
The "Prime" is a side bet I noticed at the Wynn on July 2, 2010. If the player's three cards are all the same color it pays 3 to 1. If all six player and dealer cards are the same color, then it pays 4 to 1. The following return table shows a house edge of 3.62%, which for a side bet isn't bad.
|6 Same Color||4||9,209,200||0.022618||0.090470|
|3 Same Color||3||86,595,600||0.212677||0.638030|
Red Hawk Bonus
I have an unconfirmed report that the Red Hawk casino, near Sacramento, offers the following $1 side bet. All wins are on a "for one"basis, meaning the players never get the original bet back, even if they win. The player can win based on his own hand, plus "envy bonus" wins based on the hands of other players. The following return table shows the pay table for player's own cards. The lower right cell shows a return of 57.47%.
|Red Hawk Bonus — Player's Hand|
|Mini Royal in spades||4000||1||0.000045||0.180995|
|Three of a Kind||25||52||0.002353||0.058824|
|Red Hawk Bonus — Envy Bonus|
|Mini Royal in spades||100||1||0.000045||0.004525|
|Three of a Kind||0||52||0.002353||0.000000|
|Red Hawk Bonus — House Edge|
6 Card Bonus
The "6 Card Bonus" is a side bet based on the highest five-card poker hand that can be composed out of the player's and dealer's three cards. It is most likely to be found at Caesars Entertainment casinos. I've seen two different pay tables, as follows.
Pay table 1 I noticed at Harrah's in Las Vegas on September 18, 2009. The lower right cell shows a house edge of 15.28%.
|6 Card Bonus — Pay Table 1|
|Four of a kind||50||14664||0.000720||0.036014|
|Three of a kind||5||732160||0.035963||0.179817|
Pay table 2 is allegedly found at the Matrix casino in San Jose, California. The lower right cell shows a house edge of 8.56%.
|6 Card Bonus — Pay Table 2|
|Four of a kind||100||14,664||0.000720||0.072029|
|Three of a kind||7||732,160||0.035963||0.251743|
Pay table 3 I have seen at lots of casinos owned by Caesars Entertainment, beginning about 2012. The minimum bet is $5. The top two prizes are capped at $1,000,000 and $100,000 respectively. The table below is based on a $5 bet. Betting more would increase the house edge, because the player is not rewarded on the top two prizes for betting more than $5.
|6 Card Bonus — Pay Table 3 — $5 Bet|
|6-Card Super Royal - Diamonds||200,000||1||0.00000005||0.00982390|
|6-Card Super Royal||20,000||3||0.00000015||0.00294717|
|5-Card Royal Flush||1,000||184||0.00000904||0.00903799|
|5-Card Straight Flush||200||1,656||0.00008134||0.01626837|
|Four of a Kind||50||14,664||0.00072029||0.03601441|
|Three of a Kind||5||732,160||0.03596332||0.17981661|
The lower right cell shows a house edge of 18.10% for a $5 bet. For every additional $5 bet above $5 the house edge increases by 0.64%. My advice, if you must make this bet at all, is to bet the minimum $5. Signage may tempt you with the possibility of winning $1,000,000 with a $5 bet. The probability of winning the million is 1 in 20,358,520.
Optimal strategy in ante and play is to raise if you have a queen/6/4 (that is a queen, 6, and 4 all in the same hand) or greater, regardless of the bonus pay table. Overall the player stands to lose 8.66% of the Ante but win5.29% on the Raise.
Many people have asked me what I mean by queen/6/4, wondering for example whether queen/7/3 is greater than queen/6/4. In any poker based game hands are scored first according to the highest card, then the second, and then the third, and so on if there are more. So a queen/7/3 would beat queen/6/4. The queens tie so the second highest cards are used to break the tie, and a 7 beats a 6. The third card does not matter in this case because the hand was resolved by the second card.
If you want to know why queen/6/4 is the borderline hand it is because if you raise on queen/6/3 you can expect to lose 1.00255 units, more than the 1 unit by folding. However if you raise on queen/6/4 the expected loss is .993378, less than the 1 unit by folding.
I have been asked several times about the strategy of raising on any queen or better, in other words mimicking the dealer. This is not a bad strategy but you will lose more with it than the optimal strategy above. The house edge playing the mimic the dealer strategy is 3.45%. Raising on everything, or playing blind, results in a house edge of7.65%.
Player Wins Ties
I have been asked a few times about the probability of tying the dealer in Three Card Poker. This is a valid question because some casinos let ties go to the player. The effect of this rule lowers the house edge in the "full pay" bonus table 1 above from 3.37% to 3.24%.
There is a small strategy change to make if the ties go to the player. Under this rule the player should still raise on Q/6/4 or better, plus raise on Q/6/3, only when all three suits are different (this lowers the probability of a dealer flush).
If the player follows the proper raising strategy under the ties win rules then the probability of a tie is 268272/407170400 = 1 in 1517.75 hands. For academic purposes only, if the player always raises then the probability of a tie is 450528/407170400 = 1 in 903.76.
In the poker casinos of Los Angeles county Three Card Poker has a few rule changes. For more information see my section on California Three Card Poker.
Ultimate Three Card Poker
The Silver Legacy in Reno has a variation, in which the player may raise up to 3X his bet. For all the details, visit my page on Ultimate Three Card Poker.
In 2007 the Sands had a game titled "3 Card Poker." However, this game is a simple showdown between the player and dealer, higher hand wins. A player win paid 19 to 20, or even money less a 5% commission. Below is a return table for this game. The lower right cell shows a house edge of 2.50%.
|3 Card Poker — Sands Macau Rules|
In 2007 there was also a game in Macau called Q Poker, which is very similar to Three Card Poker.
In August, 2009, many casinos had traditional Three Card Poker, only they call it Fortune Three Card Poker in Macau. For more information, please see the page on Fortune Three Card Poker at WizardOfMacau.com.
At many casinos if the player makes a tip for the dealer then the player has the option to call on the tip portion of the bet. For example, if the player bets $5 for himself, and $1 for the dealer, the player may raise his own wager but not the tip. The correct strategy based on the tip alone is to call any hand of king high or less. So on hands of Q/6/4 to K/Q/10 the player should raise his own bet but not the tip. However, with less than Q/6/4 there is a conflict of interest. To maximize the total expected value of the player's bet and the tip, the player should raise on hands just under Q/6/4. The greater the ratio of tip to bet the more hands under Q/6/4 the player should raise on.
A fantastic advantage play, in collusion with the dealers, would be to bet the table minimum on the bet and the table maximum on the tip. Then raise on ace high or better, otherwise call. This would result in a player advantage on the tip of 26.09%.
- To see how to calculate the probabilities in Three Card Poker yourself visit my Three Card Poker Appendix.
- My Hole Carding in Three Card Poker page shows the proper strategy and player advantage if you can catch a peek at one of the dealer's cards.
Play for Fun
Practice playing Three Card Poker for free on myJava applet.
- German translation of this article.
- For a simplified explanation of Three Card Poker, please visit my companion site Wizard of Vegas .