Three Card Poker House Edge
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In full play Three Card Poker the house edge on Pairplus is 2.32% and on Ante & Play is 3.37%.
Introduction
- There are three betting circles in front of each seat. The top betting circle is labeled Pair.
- The higher the odds allowed, the lower the house edge. That is because there is no house edge on an odds bet at a craps game. It theoretically returns 100% to the player. The best bet on the craps table to start a roll is the Don’t Pass. Don’t Come is the identical bet and has the same edge, but is only available after the come out roll.
- The house edge of Three Card Poker using the standard paytable and across the full round of wagering (both Ante and Play bet) and assuming that the player plays using the optimal strategy listed above is 2.01%. If the player does not play optimally this figure will rise. The house edge of the Pair Plus bet using the standard paytable is 2.32%.
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
Three Card Poker Strategy
| 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.
Acknowledgments
I would like to recognize:
- JB for the analysis of the optimal strategy.
- Stanley Ko for the simplified strategy.
- James Grosjean for the unpublished advanced strategy.
Written by:Michael Shackleford
Playing Three Card Poker is Easy and Fun. You are dealt three cards and the dealer is dealt three cards. The object is to have your three card poker hand to beat the dealer’s three card poker hand. You first make an Ante bet. After receiving your three card hand, you can surrender your hand and Ante wager or make a Play bet equal to your Ante bet before the dealer’s hand is revealed. If you win, you win both of your bets. The Ante and Play wagers pay even money (1:1). This is how the game is played nearly everywhere, including Las Vegas.
However at the California Grand Casino, because we show you one of the dealer’s cards before you make your Play bet, you are Playing With Better Odds Than Vegas and other casinos. Seeing one of the dealer card’s also changes the correct strategy for deciding when to make your Play bet. You will want to adjust your strategy so you can maximize your opportunity to win.
You are also playing against other players, not the casino. So at the California Grand Casino you have the opportunity to wager on the dealer hand if you want to do so.
3 CARD POKER – THE BASICS
Let’s start with a few basics. If you bet and the dealer does not have Queen or better, the dealer does not play; you win your Ante bet and your Play bet pushes (neither wins nor loses), even if the dealer’s hand beats your hand. If the dealer has Queen high or higher then you must beat the dealer to win. If you win, you’re paid on both your Ante bet and Play bet. If you lose, the dealer takes both bets.
The ranking of most hands is the same as in Poker except you are using only three cards and a straight is higher than a flush. So a mini-royal flush (AKQ) and straight flush are at the top of the hand rankings, followed by three of a kind, straight, flush, pair, and high card. If your highest card and the dealer’s highest card are the same, the tie is broken by the second-highest card, then the third highest card. If your hand and the dealer’s hand are exactly the same, you tie and the bets push.
BASIC 3 CARD POKER STRATEGY
The usual strategy for when to make the Play wager is to bet whenever you have Queen-6-4 or better, including any time your high card is an Ace or a King, no matter how high your other two cards are, and also anytime your hand is Q-7 or better, regardless of your third card. Fold if your hand is not at least that high. If your high card is a Jack or lower, fold, no matter how high your other two cards are.
MODIFIED THREE-CARD POKER STRATEGY WHEN YOU KNOW ONE OF THE DEALER’S CARDS
When you have the advantage of seeing one of the dealer’s cards, you should change your basic strategy. If the dealer card is:
- A Jack or Lower = Always Make a Play Bet. The odds that the dealer hand won’t qualify or will be lower than yours are increased.
- Queen = Only Play with Q, 9, 2 or better. If the dealer is showing a queen, your second card now needs to be stronger.
- King = Only Play with a K, 9, 2 or better. The same logic applies here. You need at least the same high card as the dealer and a stronger second card better than the average card value.
- Ace = Only Play with an A, 9, 2.
You also have the option of playing the hand house-way. This takes all the guess work out deciding when you should play. To play your hand house way, you put up your Ante and your Play bet, and the hand will be played according to the strategy outlined above.
OPTIONAL BONUS WAGERS
One of the exciting aspects of Three Card Poker is the opportunity to win large amounts through optional bonus wagers. You can win up to 1,000 times your wager on a bonus bet. There are two bonus bets: the Pair Plus bonus and the 6 Card bonus.
The Pair Plus bonus is based on the three cards in your hand. If you’re dealt a pair or better in your three cards, you win the Pair Plus bonus wager. The amount you win depends on what type of hand you are dealt.
Three Card Poker House Edge Water
The 6 Card bonus looks at the three cards in your hand and the three cards in the dealer’s hand. If, after combining the 6 cards, you can make a poker hand of three of a kind or better, you win the 6 Card bonus wager. The amount you win depends on what type of poker hand you can make with the six cards.
Three Card Poker House Edge Ultimate
MONEY MANAGEMENT IN THREE CARD POKER
Three Card Poker House Edge
We want you to have a good time when you are here. When playing you should always think about money management. Your bet sizes should be relative to your bankroll. For example if you are playing win a $300 bankroll you should probably only make bets of $10-$20 per hand to make your play opportunities last longer. You should also think about win and loss limits. This means if you win you leave with your winnings and if you lose you do not lose more than you can afford.
3 Card Poker Pair Plus House Edge
If you want more information about how to play Three Card Poker, don’t hesitate to come to the California Grand Casino in Pacheco and ask a staff member. We are more than happy to explain any of our action-packed games.