Four Card Prime

Introduction

Four Card Prime is an exciting variation of poker that follows the familiar raise or fold approach found in numerous other poker games, such as: Three Card Poker In this variant, there is no need for the dealer to have a qualifying hand, although the dealer is dealt an extra card. This game closely resembles: Four Card Poker One notable distinction is the inclusion of a Bad Beat Bonus, rewarding players with a premium payout if they lose with three of a kind or better.

Galaxy Gaming serves as the developer behind Four Card Prime, which was first introduced to Nevada audiences on: field trial at the Boulder Station on March 14, 2018.

Rules

Here are the foundational rules governing the base game.

1. The primary goal is to construct a four-card poker hand that ranks higher than that of the dealer.
2. Below, you'll find the hierarchy of hands ranked from highest to lowest:
   • Four of a kind
   • Straight flush
   • Three of a kind
   • Flush
   • Straight
   • Two pair
   • Pair
   • High card
3. Players are required to place an Ante bet. It's also possible to make optional side bets, such as the Prime and Aces Baby Bonus, which are detailed further below.
4. Each player is dealt five cards while the dealer receives six. One card from the dealer is shown, and the other five remain face down.
5. The player may fold or raise.
6. If the player opts to fold, they will lose their Ante bet.
7. In case the player chooses to raise, they must increase their bet by at least the Ante amount, but they can increase it up to three times that amount.
8. Once all players have made their decisions, the dealer reveals their cards to determine the best four-card poker hand for both the player and the dealer.
9. The player's hand is then compared against the dealer's hand, with the higher hand securing victory.
10. If the dealer's hand surpasses the player's and the player has a flush or lower hand, they will lose both their Ante and Raise bets.
11. If the dealer’s hand is stronger, but the player holds a three of a kind or a higher hand, the player will only lose their Raise bet while pushing the Ante. Moreover, they will qualify for a Bad Beat Bonus payout. The following table outlines the four potential pay tables for the Bad Beat Bonus.

    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. When the player's hand is either higher or matches the dealer's, both the Ante and Raise will return a one-to-one payout.
13. For players with at least a three of a kind who beat the dealer, they will receive a Win/Copy Bonus as detailed below:
    • Four of a kind: 25 to 1
    • Straight flush: 20 to 1
    • Three of a kind: 2 to 1

The Prime bet rewards players if four of their cards are of the same color. There are two recognized pay tables available, presented as follows. Payouts are calculated on a 'to one' basis.

The Aces Baby Bonus offers payouts based on the value of the player's strongest four-card poker hand. There are eight acknowledged pay tables detailed below, also calculated on a 'to one' basis.

Strategy

The strategy is the same as that for Four Card Poker I have developed a page dedicated to strategies for that game, offering three different strategic approaches.

Ante Analysis

The return table for the base game is drawn from optimal player strategy corresponding to pay table 3 of the Bad Beat Bonus, which consists of payouts of 5-50-100. This analysis reveals a house edge of 2.53%, representing the ratio of the anticipated player loss in relation to the Ante wager.

Under the most effective strategy, the average bet made is 2.142342 units, which results in the: element of risk , 2.5347%/2.142342 = 1.18%.

Prime Analysis

The next table illustrates the probabilities of obtaining each hand and the respective returns according to pay table 1 for the Prime bet. The last cell in the lower right corner indicates a house edge of 9.80%.

In the following table, you can see the hand probabilities and returns under pay table 2 of the Prime bet, with the lower right cell showcasing a house edge of 4.74%.

Lose

Another table presents the hand probabilities and returns for pay table 5 of the Aces Baby Bonus, featuring a house edge of 6.61% in the lower right cell.

This upcoming table summarizes the house edge for all eight available pay tables concerning the Aces Baby Bonus.

Pays

The evaluation of the base game information has been referenced from my analysis on Four Card Poker. My insights are influenced by a combinatorial study conducted by JB. The side bets were evaluated using my original combinatorial approach.

Combinations

Probability

• Acknowledgments to Galaxy Gaming for supplying the mathematical reports prepared by Charles Mousseau and GLI regarding Four Card Prime.
• Thanks to JB for the insight on Four Card Poker, which is applicable to Four Card Prime as well.

Return

Five cards same color Four cards same color

Three cards same color -1