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Four Card Prime

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.

  1. The object of the game is to form a higher-ranking four-card poker hand than the dealer.
  2. 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
  3. 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.
  4. The player gets five cards and the dealer gets six cards. One dealer card is exposed and the other five are dealt face down.
  5. The player may fold or raise.
  6. If the player folds, then he forfeits his Ante bet.
  7. If the player raises, then he must raise at least the amount of the Ante and, at most, three times the Ante.
  8. 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.
  9. The player's hand shall be compared to the dealer's hand, the higher hand winning.
  10. If the dealer's hand is higher, and the player has a flush or less, then the player shall lose the Ante and Raise.
  11. 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
  12. If the player's hand is higher or equal, then the Ante and Raise shall pay one to one.
  13. 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

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 Return
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