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Crazy 4 Poker

Last Update: Jun 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

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.
All players and dealer get five cards each.
Players making the Ante and Super Bonus bets must decide to fold or raise.
If the player folds he forfeits all bets.
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.
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 five.
The player's hand shall be compared to the dealer's hand, the higher hand winning.
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.
If the dealer's hand is higher the player shall lose the Ante and Raise.
If the two hands are equal the Ante and Raise shall push.
If the player's hand is higher the Ante and Raise shall pay one to one.
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.
If the player (1) folds or (2) has less than a straight and loses to the dealer then the Super Bonus shall lose.
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.
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.

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.

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.

Links

Shufflemaster's official web site for Crazy 4 Poker.