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Four Card Poker
Introduction
Four Poker, a fresh twist on the classic poker game, was created by Roger Snow and is promoted by Shufflemaster. In this variation, players are dealt four cards instead of the usual three seen in Three Card Poker. Moreover, there are no requirements for the dealer's hand to qualify, and players have the option to double their ante up to three times. The dealer, however, is provided with an additional card to enhance their hand.
Rules
- Players have two initial betting options: the Ante bet and the Aces Up bet.
- Each player is dealt five cards, while the dealer receives six cards. Out of these, one dealer card is displayed face up, and the remaining five cards are kept hidden.
- Those who place an Ante bet must then choose between folding or raising their stakes.
- If a player chooses to fold, they will lose their Ante bet. Depending on the rules of the casino, they may also lose their Aces Up bet, although if they have a strong Aces Up bet, folding is usually not advisable.
- When a player decides to raise, they need to increase their bet by at least the amount of their Ante, but they can't exceed three times that amount.
- Players must select their best four cards and can discard one card from their hand.
- The ranking of hands, from the weakest to the strongest, is as follows: high card, pair, two pair, straight, flush, three of a kind, straight flush, and four of a kind.
- Once all players have made their decisions, the dealer will reveal their cards and choose the best four from their six.
- The winning hand will be determined by comparing the player's hand with that of the dealer, with the higher hand declared the winner.
- In the event that the dealer's hand surpasses the player's, the player loses both their Ante and Raise bets.
- If the player's hand is greater than or equal to the dealer's hand, both the Ante and Raise will return at a one-to-one payout.
- In cases where the player holds at least three of a kind, they will receive a Bonus, irrespective of the dealer's hand. There are two pay tables for this Bonus, detailed below, although the first pay table is the only one that seems to be actively used.
- Additionally, players can place a bet known as Aces Up, akin to the Pairplus bet in Three Card Poker, which solely considers the player's four-card hand. There are seven available pay tables for this bet, with pay table 5 being the most commonly implemented.
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 |
Among the available Aces Up pay tables, option five is the preferred choice for many players, though there are unverified claims of other tables being used as well. Tulalip in Washington uses pay table 4 and the Grand Casino Hinckley in Minnesota uses pay table 1.
Analysis
The following return table is derived from optimal player strategy based on the 2-20-25 Ante Bonus pay table, with a house edge noted at 2.79%.
Optimal Strategy Return Table
| 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 |
On average, the final bet under ideal strategy amounts to 2.142342 units, indicating a calculation of -0.027879/2.142342 = 1.30% for the edge. The standard deviation compared to the initial bet is 2.71. element of risk A straightforward strategy for this game, originally introduced by Stanley Ko, can be summarized as follows.
Beginner Strategy
As noted in the second edition of 'Beyond Counting' by James Grosjean, this 'straightforward strategy' results in a house edge of 3.396%.
- Raise 3X with a pair of tens or higher.
- Raise 1X with a pair of twos to nines.
- Fold all other.
The intermediate strategy outlined here was developed to strike a balance between effectiveness and simplicity, courtesy of our collaborator JB.
Intermediate Strategy
If you hold a pair of Jacks, Queens, or Kings, place a bet of 3X if the dealer's upcard is lower than yours or matches a rank from your hand; otherwise, wager 1X.
- Pair of Aces or better: Bet 3X
- For a pair of Nines or Tens, bet 1X if the dealer's upcard is higher than your pair; if not, go with a 3X bet.
- In the case of Eights, place a bet of 3X if the dealer's upcard is a 2, otherwise opt for a 1X bet.
- If you are dealt a pair of Twos or a hand including Ace, King, and Queen, bet 1X if the dealer's upcard matches any of your ranks; if it does not, it's best to fold.
- Pair of 3s, 4s, 5s, 6s, 7s: Bet 1X
- When playing with the 2-20-25 Ante Bonus pay table, the house edge is at 2.8526%, with the risk element calculated at 1.3233%.
- All other: Fold
I'm excited to share this advanced strategy crafted by my companion JB.
Advanced Strategy
For a pair of Kings, a 3X bet is advised; however, if the dealer shows an Ace and you have neither an Ace nor a four, reduce your bet to 1X.
- Pair of Aces or better: Bet 3X
- With a pair of Jacks or Queens, bet 3X unless the dealer's card outranks your pair without matching a singleton in your hand.
- Holding a pair of Nines or Tens suggests a 3X bet, unless the dealer's card is higher than your pair.
- For a pair of Threes, stick with a 1X bet; if your highest kicker is 10 or lower, fold against a Jack.
- Pair of 8s: Bet 1X, except bet 3X against a 2
- Pair of 4s thru 7s: Bet 1X
- For a pair of Twos or holding the Ace, King, Queen, it's best to fold, except if the dealer's card corresponds to a rank in your hand, in which case bet 1X.
- Utilizing the 2-20-25 Ante Bonus pay table, the house edge stands at 2.8498% with a risk factor of 1.3216%. A comparison of various strategies reveals differences in house edges.
- AKJT: Fold, except bet 1X against a Jack
- AKJ9 or lower: Fold
In other words, let's break down the costs associated with errors:
- Simple: 3.396%
- Intermediate: 2.853%
- Advanced: 2.850%
- Optimal: 2.788%
The subsequent table outlines the probabilities of each hand and the potential return under pay table five for the Aces Up side bet. The house edge here is recorded at 3.89%.
- Simple: 0.606%
- Intermediate: 0.065%
- Advanced: 0.062%
- Optimal: 0.000%
Aces Up Analysis
The following table presents the house edges as they correspond to all four Aces Up pay tables.
Return for Aces Up Pay Table 5
| 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 |
Note: There is also a comparable game known as
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% |
JB provided a study on optimal strategy analysis. Crazy Four Poker .
Acknowledgments
I would like to recognize:
- Stanley Ko contributed insights for the simplified strategy.
- James Grosjean is credited with the advanced strategy that remains unpublished.
- Accurate mathematical strategies and insights for a variety of casino games, including blackjack, craps, and roulette, among many others, are readily available.