Four Card Poker
Last Update: June 5, 2013
|Bonus Pay Table|
|Hand||Table 1||Table 2|
|Four of a kind||25||30|
|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|
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 strategy 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|
|Four of a kind||624||0.00024||50||0.012005|
|Three of a kind||58656||0.022569||8||0.180552|
|Pair of aces||81096||0.031203||1||0.031203|
The next table shows the house edge according to all four Aces Up pay tables.
|Aces Up House Edge|
|Pay Table||House Edge|
Note: There is also a similar game called Crazy Four Poker.