Crazy 4 Poker

Last Update: June 24, 2004

Introduction

Crazy 4 Poker is a new poker variation invented by Roger Snow and is marketed by Shufflemaster. The game bears some similarities to Three Card Poker but as the name says, is based on four cards. With proper strategy the element of risk is only 1.09%, which is comparitively good for the new generation of casino games.

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

Rules

1. Three initial bets are available: The Ante, Super Bonus, and the Queens Up. The player must bet equal amounts on the Ante and Super Bonus. The Queens Up may be any amount.
2. All players and dealer get five cards each.
3. Players making the Ante and Super Bonus bets 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. With a pair of aces or better the player may raise up to three times the Ante amount. With less than a pair of aces the player must raise exactly the amount of 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 five.
9. The player's hand shall be compared to the dealer's hand, the higher hand winning.
10. The dealer must have a king high or better to qualify. If the dealer does not qualify the player shall win even money on the Raise and the Ante shall push.
11. If the dealer's hand is higher the player shall lose the Ante and Raise.
12. If the two hands are equal the Ante and Raise shall push.
13. If the player's hand is higher the Ante and Raise shall pay one to one.
14. The Super Bonus bet shall pay if the player has a straight or higher, regardless of the value of the dealer's hand. The Super Bonus Pay Table below shows what each hand pays.
15. If the player (1) folds or (2) has less than a straight and loses to the dealer then the Super Bonus shall lose.
16. If (1) the player has less than a straight and (2) the dealer doesn't qualify or the player beats the dealer then the Super Bonus shall push.
17. Another bet is available (similar to the Pairplus in Three Card Poker) based only on the player's four card hand called the Queens Up. Four pay tables are available as indicated below.
 Super Bonus Pay Table Hand Pays 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 Hand 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

Strategy

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

1. Fold if the highest 4-card hand is less than K-Q-8-4.
2. Raise 1 unit if the highest 4-card hand is K-Q-8-4 to a pair of kings.
3. 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.

Analysis

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 Hand Combinations Probability Pays Return Four of a kind 624 0.00024 50 0.012005 Straight flush 2072 0.000797 30 0.023917 Three of a kind 58656 0.022569 8 0.180552 Flush 114616 0.044101 4 0.176403 Straight 101808 0.039173 3 0.117518 Two pair 123552 0.047539 2 0.095078 Pair of queens or better 242916 0.093467 1 0.093467 Nothing 1954716 0.752115 -1 -0.752115 Total 2598960 1 -0.053175

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

 Queens Up House Edge Pay Table House Edge 1 3.06% 2 4.52% 3 5.32% 4 6.78%

The next table shows the return of the Ante bet under optimal player strategy.

 Return for Ante bet Event Probability Pays Return Player folds 0.235073 -1 -0.235073 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 Total 1 0.313607

The next table shows the return of the Super Bonus bet under optimal player strategy.

 Return for Super Bonus bet Event Probability Pays Return Four aces 0.000018 200 0.003694 Four 2-K 0.000222 30 0.006649 Straight flush 0.000797 15 0.011959 Three of a kind 0.022569 2 0.045138 Flush 0.044101 1.5 0.066151 Straight 0.039173 1 0.039173 Player loses with less than straight or folds 0.520558 -1 -0.520558 Other 0.372562 0 0 Total 1 -0.347795

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 .

Reason #3 why the Wizard likes Bovada:

Excellent Odds

In my opinion many online casinos are too stingy when setting the odds on their games. They think they will make more money that way but I believe they are misguided, because when players lose too quickly it’s not fun, and those players might not come back.

Bovada is one of the few casinos that understands this. They offer generous odds to let you play longer and get you a better chance of winning. Among their generous offerings are Full-Pay Jacks or Better returning 99.54%, five other video poker games paying over 99%, single-zero roulette, and my favorite, Double Jackpot Poker, returning 99.63%!

Kudos to Bovada for not being afraid to give their players a good gamble.

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