Four Card Poker

Last update: June 20, 2004

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.

Normally I do all the game analysis on this site but this game is an exception. The math was done by Stanley Ko of Gambology and provided to me with permission to publish on this site by Shufflemaster, the owners of the game.

Rules

1. Two initial bets are available: The Ante and the Aces Up.
2. All players get five cards each and the dealer gets six cards.
3. Players making the Ante bet must decide to fold or raise.
4. If the player folds he forfeits all bets.
5. If player raises he must raise at least the amount of the Ante and at most, three times the Ante.
6. Players then keep their best four cards and discard one.
7. 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.
8. After all decisions have been made the dealer will turn over his cards and select the best four out of six.
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 the player shall lose the Ante and Raise.
11. If the player's hand is higher or equal then the Ante and Raise shall pay one to one.
12. If the player has at least a three of a kind 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.
13. 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.

Strategy

Stanley Ko's "simplified strategy" is as follows.

1. Fold with a pair of twos or less.
2. Raise 1x your ante with a pair of threes to a pair of nines.
3. Raise 3x your ante with a pair of tens or greater.

The cost of using the simplified strategy compared to optimal strategy is only 0.0416% of the Ante bet.

Analysis

The next table shows the probability of each hand and the return under pay table 5 of the Aces Up side bet. I chose table 5 because that is the only one I knew to be in play at the time of this writing. The lower right cell shows a house edge of 3.89%.

The next table shows the house edge according to all four Aces Up pay tables.

Although I do not implicitly know the probabilities for winning and losing the Ante bet, I do know the frequency of the total amount bet. It is as follows.

• Player folds: 47.3719%
• Player raises one unit: 22.4305%
• Player raies three units: 30.1976%

Under bonus table 1, the only one I know to be in use at the time of this writing, the expected return on the Ante bet is -0.100640 but the player gains 0.067083 on the Bonus, for a net return of -0.033555, or a house edge of 3.36%. The average wager is 2.1457 units for an element of risk (ratio of expected loss to total amount bet) equal to 1.58%.

Under bonus table 2 the overall house edge is 3.63% and the element of risk is 1.69%.

Note: There is also a similar game called Crazy Four Poker.