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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.
- 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
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.