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# Three Card Poker

## Rules

1. Player makes an Ante and/or Pairplus bet
2. 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.
3. If the player made the Ante bet, then he has must either fold or raise.
4. If the player folds, then he forfeits his Ante wager.
5. If the player raises, then he must make an additional Play bet, equal exactly to his Ante bet.
6. The dealer will turn over his cards.
7. The dealer needs a queen high or better to qualify.
8. If the dealer does not qualify then the player will win even money on the Ante bet and the Play bet will push.
9. 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.
10. If the player has the higher poker hand then the Ante and Play will both pay even money.
11. If the dealer has the higher poker hand then the Ante and Play will both lose.
12. If the player and dealer tie then the Ante and Play bets will push.
13. If the player made the Ante bet and has a straight or higher then the player will receive an Ante Bonus, regardless of the value of the dealer's hand.
14. The Pairplus bet will pay entirely based on the poker value of the player's hand, as shown in the Pairplus section below.

### Hand Order and Probabilities in Three Card Poker

Hand Combinations Probability
Straight flush 48 0.002172
Three of a kind 52 0.002353
Straight 720 0.032579
Flush 1096 0.049593
Pair 3744 0.169412
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 Table 1 Table 2 Table 3 Table 4 Table 5 Table 6
Straight flush 5 4 3 5 9 12.5
Three of a kind 4 3 2 3 8 10
Straight 1 1 1 1 1 1
House Edge 3.37% 3.83% 4.28% 3.61% 1.56% 0.33%
Element of Risk 2.01% 2.28% 2.56% 2.16% 0.93% 0.20%

In case you're wondering, tables 5 and 6 can be found at Internet casinos using Gamesys N.V. software. With table 6 the player must pay a 10% commission on any net win per gambling session.

The next table shows the probability and return for each net win under the table 1 Ante bonuses.

### Ante Return Table

Win Combinations Probability Return
7 617044 0.001515 0.010608
6 931972 0.002289 0.013733
5 289104 0.000710 0.003550
3 8976452 0.022046 0.066138
2 91100696 0.223741 0.447482
1 80955780 0.198825 0.198825
0 249216 0.000612 0.000000
-1 132923304 0.326456 -0.326456
-2 91126832 0.223805 -0.447610
Total 407170400 1.000000 -0.033730

Here is another way of presenting the same information, broken down by the outcomes between player and dealer and Ante bonus.

### Ante Return TableExpand

Event Pays Combinations Probability Return
Player wins with straight flush 7 617,044 0.001515 0.010608
Player has straight flush, dealer doesn't qualify 6 266,196 0.000654 0.003923
Player wins with three of a kind 6 665,776 0.001635 0.009811
Player ties with straight flush 5 144 0.000000 0.000002
Player has three of a kind, dealer doesn't qualify 5 288,960 0.000710 0.003548
Player ties with three of a kind 4 - 0.000000 0.000000
Player loses with straight flush 3 968 0.000002 0.000007
Player wins with straight 3 8,975,484 0.022044 0.066131
Player loses with three of a kind 2 3,312 0.000008 0.000016
Player has straight, dealer doesn't qualify 2 4,001,004 0.009826 0.019653
Player wins with flush or less 2 87,096,380 0.213906 0.427813
Player ties with straight 1 18,288 0.000045 0.000045
Player has flush or less, dealer doesn't qualify 1 80,937,492 0.198780 0.198780
Player ties with flush or less 0 249,216 0.000612 0.000000
Player loses with straight -1 270,504 0.000664 -0.000664
Player folds -1 132,652,800 0.325792 -0.325792
Player loses with flush or less -2 91,126,832 0.223805 -0.447610
Total 407,170,400 1.000000 -0.033730

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
Mini Royal 10 50 10
Straight flush 4 8 5
Three of a kind 3 6 4
Straight 0 0 1
House Edge 6.79% 4.75% 3.28%
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

## Pairplus

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

Hand Pays Combinations Probability Return
Straight Flush 40 48 0.002172 0.086878
Three of a Kind 30 52 0.002353 0.070588
Straight 6 720 0.032579 0.195475
Flush 3 1096 0.049593 0.148778
Pair 1 3744 0.169412 0.169412
All Other -1 16440 0.743891 -0.743891
Total 22100 1 -0.07276

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 RoyalExpand

Hand Pay Table
1 2 3 4 5 6 7 8 9 10
Straight flush 40 35 40 35 50 40 40 40 40 42
Three of a kind 30 33 25 25 30 30 25 30 32 38
Straight 6 6 6 6 6 5 5 6 6 6
Flush 4 4 4 4 3 4 4 3 4 4
Pair 1 1 1 1 1 1 1 1 1 1
Nothing -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
House edge 2.32% 2.70% 3.49% 4.58% 5.10% 5.57% 6.75% 7.28% 1.85% 0.00%

In case you're wondering, tables 9 and 10 can be found at Internet casinos using Gamesys N.V. software. With table 10 the player must pay a 10% commission on any net win per gambling session.

### Pairplus Pay Tables — With Mini Royal

Hand Pay Table
1 2 3 4 5 6
Mini Royal 80 50 50 200 100 50
Straight flush 40 40 40 40 50 40
Three of a kind 25 30 30 30 30 30
Straight 6 6 5 6 6 6
Flush 3 3 4 3 3 4
Pair 1 1 1 1 1 1
Nothing -1 -1 -1 -1 -1 -1
House edge 7.73% 7.10% 5.39% 4.38% 4.20% 2.14%

## Combined

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

Win Combinations Probability Return
-3 77992716 0.191548 -0.574644
-2 132652800 0.325792 -0.651584
-1 12108216 0.029737 -0.029737
0 53876136 0.132318 0.000000
1 39406040 0.096780 0.09678
2 20926080 0.051394 0.102788
3 36171912 0.088837 0.266512
4 6135276 0.015068 0.060272
5 13064048 0.032085 0.160425
7 18288 0.000045 0.000314
8 4001004 0.009826 0.078611
9 8975484 0.022044 0.198392
32 3312 0.000008 0.000260
35 288960 0.000710 0.024839
36 665776 0.001635 0.058865
43 968 0.000002 0.000102
45 144 0.000000 0.000016
46 266196 0.000654 0.030073
47 617044 0.001515 0.071226
Total 407170400 1 -0.106490

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

I have seen two versions of the progressive side bet in Three Card Poker. Both cost \$1 to play and pay a progressive jackpot for a royal flush in spades. Both versions also feature an envy bonus if another player gets a royal flush.

### Version 1

What I will call version 1 I first 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.

### Three Card Poker Progressive — Version 1

Hand Pays Envy Bonus
Mini Royal in spades Jackpot \$100
Mini Royal \$500 \$25
Straight Flush \$100 \$0
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.

### Version 2

What I will call version 2 I saw that Casino Caribbean in Yakima Washington in June 2014. The most notable difference compared to version 1 is that version 2 pays for a straight as well.

### Three Card Poker Progressive — Version 2

Hand Pays Envy Bonus
Mini Royal in spades Jackpot \$100
Mini Royal \$500 \$25
Straight Flush \$70 \$0
Three of a Kind \$60 \$0
Straight \$6 \$0

The return depends on the jackpot amount and number of other players. To be specific, it is 54.39%, plus 4.52% for each \$1,000 in the jackpot, and 0.79% per number of other players. To break even the meter needs to be \$10,800, less \$175 for each other player.

## Prime

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.

### Prime

Hand Pays Combinations Probability Return
6 Same Color 4 9,209,200 0.022618 0.090470
3 Same Color 3 86,595,600 0.212677 0.638030
Loser -1 311,365,600 0.764706 -0.764706
Total 407,170,400 1.000000 -0.036206

## 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

Hand Pays Combinations Probability Return
Mini Royal in spades 4000 1 0.000045 0.180995
Mini Royal 1000 3 0.000136 0.135747
Straight Flush 100 44 0.001991 0.199095
Three of a Kind 25 52 0.002353 0.058824
Loser 0 22000 0.995475 0
Total 22100 1 0.574661
The next table shows the value of the Envy Bonus per additional player. The lower right cell shows that the return increases by 0.79% per additional player at the table.

### Red Hawk Bonus — Envy Bonus

Hand Pays Combinations Probability Return
Mini Royal in spades 100 1 0.000045 0.004525
Mini Royal 25 3 0.000136 0.003394
Straight Flush 0 44 0.001991 0.000000
Three of a Kind 0 52 0.002353 0.000000
Loser 0 22000 0.995475 0.000000
Total 22100 1 0.007919
The next table shows the house edge according to the total number of players.

### Red Hawk Bonus — House Edge

Players House Edge
6 38.57%
5 39.37%
4 40.16%
3 40.95%
2 41.74%
1 42.53%

## 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 or heard of three possible pay tables.

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

Hand Pays Combinations Probability Return
Royal flush 1000 188 0.000009 0.009234
Straight flush 200 1656 0.000081 0.016268
Four of a kind 50 14664 0.000720 0.036014
Full house 25 165984 0.008153 0.203826
Flush 15 205792 0.010108 0.151626
Straight 10 361620 0.017763 0.177626
Three of a kind 5 732160 0.035963 0.179817
Loser -1 18876456 0.927202 -0.927202
Total 20358520 1 -0.152790

The next table shows all three known pay tables and the house edge.

### 6 Card Bonus — Pay Table Summary

Hand Version 1 Version 2 Version 3
Royal flush 1000 2000 1000
Straight flush 200 200 200
Four of a kind 100 50 50
Full house 20 25 25
Flush 15 15 15
Straight 10 10 10
Three of a kind 7 5 5
House edge 8.56% 14.36% 15.28%

## Millionaire Maker

Millionaire Maker is a six-card side bet that 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

Hand Pays Combinations Probability Return
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
Full House 20 165,984 0.00815305 0.16306097
5-Card Flush 15 205,792 0.01010840 0.15162595
5-Card Straight 10 361,620 0.01776259 0.17762588
Three of a Kind 5 732,160 0.03596332 0.17981661
All other -1 18,876,456 0.92720178 -0.92720178
Total 20,358,520 1.00000000 -0.18098054

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. However, the probability of winning the million is 1 in 20,358,520.

## Strategy

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.

## California Rules

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.

## Florida Rules

In the poker casinos of Florida, Three Card Poker has a few rule changes. For more information see my section on Three Card Poker -- Florida Variant.

## 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.

## Macau Rules

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

Event Pays Probability Return
Win 0.95 0.499434 0.474462
Lose -1 0.499434 -0.499434
Tie 0 0.001132 0
total 1.000000 -0.024972

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.

## Tipping Strategy

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%.