Four Card Poker
Last update: July 7, 2009
Update
This page was updated on July 7, 2009. Previously, I incorrectly indicated that the dealer did not expose one of his cards. He does, the the same manner as Caribbean Stud Poker. So my analysis of the Ante bet was incorrect.
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 all bets.
- If player raises, then he must raise at least the amount of the Ante and at most, three times the Ante.
- Players then keep their best four cards and discard 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 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 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 |
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.
According to the second edition of ‘Beyond Counting’ by James Grosjean, this “simple strategy” results in a house edge of 3.396%.
In the same book, Grosjean presents a ten-step strategy, which also takes into consideration the dealer’s up card, and the player’s singletons. Out of respect of copyright, I will not re-publish his strategy. According to Grosjean, his ten-step stategy has a house edge of 2.840% under Bonus pay table 1, and 3.199% under pay table 2.
Aces Up 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%.
|
Return for Aces Up Pay Table 5
|
|
Hand
|
Combinations |
Probability |
Pays |
Return |
| Four of a kind | 624 | 0.00024 | 50 | 0.012005 |
| Straight flush | 2072 | 0.000797 | 40 | 0.03189 |
| Three of a kind | 58656 | 0.022569 | 8 | 0.180552 |
| Flush | 114616 | 0.044101 | 5 | 0.220504 |
| Straight | 101808 | 0.039173 | 4 | 0.15669 |
| Two pair | 123552 | 0.047539 | 3 | 0.142617 |
| Pair of aces | 81096 | 0.031203 | 1 | 0.031203 |
| Nothing | 2116536 | 0.814378 | -1 | -0.814378 |
| Total | 2598960 | 1 | | -0.038917 |
The next table shows the house edge according to all four Aces Up pay tables.
|
Aces Up House Edge
|
|
Pay Table
|
House Edge
|
| 1 | 1.98% |
| 2 | 2.58% |
| 3 | 2.78% |
| 4 | 3.37% |
| 5 | 3.89% |
| 6 | 4.24% |
| 7 | 6.15% |
Note: There is also a similar game called Crazy Four Poker.
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