225% up to $12250
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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.
|Hand||Table 1||Table 2|
|Four of a kind||25||30|
|Three of a kind||2||2|
|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|
Of these pay tables for the Aces Up side bet, number five is the most popular. The only exceptions that I'm aware of are an unconfirmed report that that Tulalip in Washington uses pay table 4 and the Grand Casino Hinckley in Minnesota uses pay table 1.
The following return table is based on optimal player strategy under the 2-20-25 Ante Bonus pay table. The lower right cell shows a house edge of 2.79%.
|Four of a Kind||3||Win||40,182,878,736||0.000240||+29||0.006960|
|Four of a Kind||3||Lose||18,594,576||0.000000||+21||0.000002|
|Three of a Kind||3||Win||3,675,379,352,400||0.021951||+6||0.131703|
|Three of a Kind||3||Lose||103,559,138,928||0.000618||-2||-0.001237|
The average final bet under optimal strategy is 2.142342 units, making the element of risk, -0.027879/2.142342 = 1.30%. The standard deviation, relative to the original bet, is 2.71.
A simple strategy to this game, first proposed by Stanley Ko, is as follows.
According to the second edition of "Beyond Counting" by James Grosjean, this "simple strategy" results in a house edge of 3.396%.
The following intermediate strategy was created to balance power and simplicity by our own JB.
Against the 2-20-25 Ante Bonus pay table, the house edge is 2.8526% and the element of risk is 1.3233%.
I'm proud to present the following advanced strategy, also created by my sidekick JB.
Against the 2-20-25 Ante Bonus pay table, the house edge is 2.8498% and the element of risk is 1.3216%. Here is a house edge comparison of various known strategies.
To put it another way, here are the cost of errors:
The next table shows the probability of each hand and the return under pay table five of the Aces Up side bet. The lower right cell shows a house edge of 3.89%.
|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.
|Pay Table||House Edge|
Note: There is also a similar game called Crazy Four Poker.
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