4 Card Poker Layout

Posted : admin On 4/9/2022

Roger Snow invented Four Card Poker, which is a trademark of Shuffle Master, a company known for manufacturing automatic shuffling machines. You get to play an ante bet, an “aces up” bet, or a combination of both. You and the dealer each get 5 cards and get to make your best four-card hand from those cards. There’s also a sixth face-up card. Play one times your Ante with a K,Q,8,4 or better as your four best cards. Anything less than K,Q,8,4 should be folded. The Queens Up side bet with the above pay table has a house advantage of 4.52%, which is pretty fair for a side bet. Available pay tables can go as high as 6.77% if the Three of a Kind only pays 7-1 instead of 8-1.

Introduction

Four Card Prime is a poker variant that follows the raise or fold structure of many other poker-based games, like Three Card Poker. In this case there is no dealer qualifying hand, but the dealer gets an extra card. The game is very similar to Four Card Poker. The main difference is a Bad Beat Bonus that pays a premium when the player loses with a three of a kind or higher.

Galaxy Gaming is the distributor behind Four Card Prime. The game made its Nevada debut on field trial at the Boulder Station on March 14, 2018.

Rules

Following are the rules of the base game.

The object of the game is to form a higher-ranking four-card poker hand than the dealer.
Following is the ranking of hands from highest to lowest:
- Four of a kind
- Straight flush
- Three of a kind
- Flush
- Straight
- Two pair
- Pair
- High card
The player makes a required Ante bet. The optional Prime and Aces Baby Bonus side bets may be made at this time as well, which are explained below.
The player gets five cards and the dealer gets six cards. One dealer card is exposed and the other five are dealt face down.
The player may fold or raise.
If the player folds, then he forfeits his Ante bet.
If the player raises, then he must raise at least the amount of the Ante and, at most, three times the Ante.
After all decisions have been made, the dealer will turn over his cards and determine the best four-card poker hands for both the player and dealer.
The player's hand shall be compared to the dealer's hand, the higher hand winning.
If the dealer's hand is higher, and the player has a flush or less, then the player shall lose the Ante and Raise.
If the dealer's hand is higher, and the player has a three of a kind or greater, then the player shall push the Ante and lose the Raise. In addition, the player will win a Bad Beat Bonus. Four available pay tables for the Bad Beat Bonus are shown in the following table.
Bad Beat Bonus Pay Table
Event Table 1 Table 2 Table 3 Table 4
Four of a kind 25 50 100 100
Straight flush 20 40 50 50
Three of a kind 2 5 5 10
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 and beats the dealer, then he shall win a Win/Copy Bonus, as follows:
- Four of a kind: 25 to 1
- Straight flush: 20 to 1
- Three of a kind: 2 to 1

Event	Table 1	Table 2	Table 3	Table 4
Four of a kind	25	50	100	100
Straight flush	20	40	50	50
Three of a kind	2	5	5	10

The Prime bet pays if at least four of the player's cards are the same color. There are two known pay tables, as follows. All wins are on a 'to one' basis.

Prime Pay Table

Event	Table 1	Table 2
Five cards same color	5	6
Four cards same color	1	1

The Aces Baby Bonus bet pays based on the poker value of the player's best four-card poker hand. There are eight known pay tables, as follows. All wins are on a 'to one' basis.

Aces Baby Bonus Pay Table

Hand	Table 1	Table 2	Table 3	Table 4	Table 5	Table 6	Table 7	Table 8
Four aces	500	500	500	500	500	50	50	50
Four 2's-K's	100	100	100	100	100	50	50	50
Royal flush	50	40	50	50	50	30	30	40
Straight flush	30	30	40	30	20	30	30	40
Three aces	20	15	25	20	15	7	9	8
Three 2's-K's	10	10	10	10	10	7	9	8
Flush	5	5	5	5	5	6	6	5
Straight	4	4	3	3	3	5	4	4
Two pair	2	2	2	2	2	2	2	3
Pair of aces	1	1	1	1	1	1	1	1

Strategy

The strategy is the same as that for Four Card Poker. My page on that game has three levels of strategy.

Ante Analysis

The following return table, for the base game, is based on optimal player strategy under pay table 3 of the Bad Beat Bonus (that goes 5-50-100). The lower right cell shows a house edge of 2.53%, defined as the ratio of the expected player loss to the Ante wager.

Return Table Based on Optimal Strategy

Player Hand	Outcome	Raise	Net Win	Combinations	Probability	Pays
Four of a Kind	Win/push	3	29	40,182,878,736	0.000240	0.006960
Four of a Kind	Lose	3	97	18,594,576	0.000000	0.000011
Straight Flush	Win/push	3	24	133,224,330,456	0.000796	0.019096
Straight Flush	Lose	3	47	265,177,080	0.000002	0.000074
Three of a Kind	Win/push	3	6	3,675,379,352,400	0.021951	0.131703
Three of a Kind	Lose	3	2	103,559,138,928	0.000618	0.001237
Flush	Win/push	3	4	6,599,621,152,728	0.039415	0.157660
Flush	Lose	3	-4	784,564,849,080	0.004686	-0.018743
Straight	Win/push	3	4	5,257,469,039,688	0.031399	0.125597
Straight	Lose	3	-4	1,301,555,952,216	0.007773	-0.031093
Two Pair	Win/push	3	4	5,539,444,298,496	0.033083	0.132333
Two Pair	Lose	3	-4	2,420,447,417,280	0.014456	-0.057823
One Pair	Win/push	3	4	14,764,551,298,548	0.088179	0.352714
One Pair	Lose	3	-4	10,806,299,820,804	0.064539	-0.258155
One Pair	Win/push	1	2	13,535,004,289,296	0.080835	0.161671
One Pair	Lose	1	-2	22,887,448,286,136	0.136691	-0.273382
One Pair	Fold	Fold	-1	5,495,692,732,992	0.032822	-0.032822
High Card	Win/push	1	2	148,058,445,132	0.000884	0.001769
High Card	Lose	1	-2	422,493,233,796	0.002523	-0.005047
High Card	Fold	Fold	-1	73,523,856,056,112	0.439108	-0.439108
Totals	167,439,136,344,480	1.000000	-0.025347

The average final bet under optimal strategy is 2.142342 units, making the element of risk, 2.5347%/2.142342 = 1.18%.

Prime Analysis

The next table shows the probability of each hand and the return under pay table 1 of the Prime bet. The lower right cell shows a house edge of 9.80%.

Prime Side Bet — Pay Table 1

Event	Pays	Combinations	Probability	Return
Five cards same color	5	131,560	0.050620	0.253101
Four cards same color	1	777,400	0.299120	0.299120
Three cards same color	-1	1,690,000	0.650260	-0.650260
Total	2,598,960	1.000000	-0.098039

The next table shows the probability of each hand and the return under pay table 2 of the Prime bet. The lower right cell shows a house edge of 4.74%.

Prime Side Bet — Pay Table 2

Event	Pays	Combinations	Probability	Return
Five cards same color	6	131,560	0.050620	0.303721
Four cards same color	1	777,400	0.299120	0.299120
Three cards same color	-1	1,690,000	0.650260	-0.650260
Total	2,598,960	1.000000	-0.047419

Aces Baby Bonus Analysis

The next table shows the probability of each hand and the return under pay table 5 of the Aces Baby Bonus bet. The lower right cell shows a house edge of 6.61%.

Aces Baby Bonus — Pay Table 5

Hand	Combinations	Probability	Pays	Return
Four aces	500	48	0.000018	0.009234
Four 2's-K's	100	576	0.000222	0.022163
Royal flush	50	192	0.000074	0.003694
Straight flush	20	1,880	0.000723	0.014467
Three aces	15	4,512	0.001736	0.026041
Three 2's-K's	10	54,144	0.020833	0.208329
Flush	5	114,616	0.044101	0.220504
Straight	3	101,808	0.039173	0.117518
Two pair	2	123,552	0.047539	0.095078
Pair of aces	1	81,096	0.031203	0.031203
All other	-1	2,116,536	0.814378	-0.814378
Total	2,598,960	1.000000	-0.066146

The next table shows the house edge for all eight pay tables available for the Aces Baby Bonus.

Aces Baby Bonus — House Edge Summary

Number	Pay Table	House Edge
1	500,100,50,30,20,10,5,4,2,1	1.11%
2	500,100,40,30,15,10,5,4,2,1	2.05%
3	500,100,50,40,25,10,5,3,2,1	3.43%
4	500,100,50,30,20,10,5,3,2,1	5.02%
5	500,100,50,20,15,10,5,3,2,1	6.61%
6	50,50,30,30,7,7,6,5,2,1	3.37%
7	50,50,30,30,9,9,6,4,2,1	2.78%
8	50,50,40,40,8,8,5,4,3,1	3.89%

Methodology

The analysis of the base game was taken from my page on Four Card Poker. My analysis of that game was based on a combinatorial analysis by JB. The side bets were analyzed by my own combinatorial analysis.

Acknowledgments

I would like to recognize:

Galaxy Gaming for providing the math reports by Charles Mousseau and GLI for Four Card Prime.
JB for the analysis of Four Card Poker, which applied to Four Card Prime as well.

External Links

Demo game by Galaxy Gaming.

Written by:Michael Shackleford

Introduction

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.

4 Card Poker Online

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