Crazy 4 Poker
Last Update: June 24, 2004
Super Bonus Pay Table
|Four aces||200 to 1|
|Four 2-K||30 to 1|
|Straight flush||15 to 1|
|Three of a kind||2 to 1|
|Flush||1.5 to 1|
|Straight||1 to 1|
Queens Up Pay Table
|Table 1||Table 2||Table 3||Table 4|
|Four of a kind||50 to 1||50 to 1||50 to 1||50 to 1|
|Straight flush||30 to 1||40 to 1||30 to 1||40 to 1|
|Three of a kind||9 to 1||8 to 1||8 to 1||7 to 1|
|Flush||4 to 1||4 to 1||4 to 1||4 to 1|
|Straight||3 to 1||3 to 1||3 to 1||3 to 1|
|Two pair||2 to 1||2 to 1||2 to 1||2 to 1|
|Pair of queens or better||1 to 1||1 to 1||1 to 1||1 to 1|
Stanley Ko's "simplified strategy" is as follows.
- Fold if the highest 4-card hand is less than K-Q-8-4.
- Raise 1 unit if the highest 4-card hand is K-Q-8-4 to a pair of kings.
- Raise 3 units with pair of aces or higher.
The cost of using the simplified strategy compared to optimal strategy is only 0.0002% of the total wager.
The next table shows the probability of each hand and the return under pay table 3 of the Queens Up side bet. I chose table 3 because that is the one I noticed at a casino here in Las Vegas. The lower right cell shows a house edge of 5.32%.
Return for Queens Up Pay Table 3
|Four of a kind||624||0.00024||50||0.012005|
|Three of a kind||58656||0.022569||8||0.180552|
|Pair of queens or better||242916||0.093467||1||0.093467|
The next table shows the house edge according to all four Queens Up pay tables.
Queens Up House Edge
The next table shows the return of the Ante bet under optimal player strategy.
Return for Ante bet
|Player raises 1 unit and wins||0.215511||2||0.431022|
|Player raises 1 unit and ties||0.000206||0||0|
|Player raises 1 unit and loses||0.274169||-2||-0.548338|
|Player raises 1 unit and dealer doesn't qualify||0.08942||1||0.08942|
|Player raises 3 units and wins||0.139517||4||0.558067|
|Player raises 3 units and ties||0.000073||0||0|
|Player raises 3 units and loses||0.017084||-4||-0.068335|
|Player raises 3 units and dealer doesn't qualify||0.028948||3||0.086844|
The next table shows the return of the Super Bonus bet under optimal player strategy.
Return for Super Bonus bet
|Three of a kind||0.022569||2||0.045138|
|Player loses with less than straight or folds||0.520558||-1||-0.520558|
So, the player has an expected return of 0.313607 on the Ante bet and -0.347795 on the Super Bonus. The net player expected return on these two bets is 0.313607-0.347795 = -0.034189. If we were to define the house edge as the expected player loss to either one of the Ante or Super Bonus bets then the answer would be 3.42%. For example if the player bet $1 on the Ante and $1 on the Super Bonus then he could expect to lose 3.42 cents overall. If we were to define the house edge as the expected loss of the sum of both wagers then we would divide by 3.42% by 2 to get 1.71%. The overall average wager is 3.136171 units, thus the element of risk (expected loss divided by total wager) is 1.09%.
Note: There is also a similar game called Four Card Poker.
Shufflemaster's official web site for Crazy 4 Poker .