Last Updated: December 26, 2012

Crazy 4 Poker

Wizard Recommends

  • $777 Welcome Bonus
  • $3000 Welcome Bonus
  • $5000 Welcome Bonus
  • $3000 Welcome Bonus
Wizard of Odds Approved

Introduction

Crazy 4 Poker is a poker variation invented by Roger Snow and is marketed by Shufflemaster. It has been around since about 2004 and one of the more successful poker-based casino games.

Rules

  1. Play starts with the player making equal bets on the Ante and Super Bonus. The player may also bet on the Queens Up side bet at this time.
  2. All player and dealer get five cards each.
  3. The player decides to fold or raise.
  4. If the player folds he forfeits all bets.
  5. The Raise bet may be up to three times the Ante bet if the player has at least a pair of aces. Otherwise, the Raise bet must be exactly equal to the Ante bet.
  6. Players make their best four-card poker hand, and discard the fifth card.
  7. Following is the ranking of hands from highest to lowest:
    • Four of a kind.
    • Straight flush
    • Three of a kind
    • Flush
    • Straight
    • Two pair
    • Pair
    • Four singletons
  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. For purposes of the Ante bet only, the dealer needs at least a king high to open.
  11. The Ante bet pays as follows:
    • Dealer does not open: Ante pushes.
    • Dealer opens and player wins: Ante wins.
    • Dealer opens and ties: Ante pushes.
    • Dealer opens and wins: Ante loses.
  12. The Raise bet pays as follows:
    • Player wins: Raise wins.
    • Tie: Raise pushes.
    • Dealer wins: Raise loses.
  13. The Super Bonus bet pays as follows:
    • Player has straight or higher (beating dealer not required): Super Bonus wins according to pay table below.
    • Player has less than straight and wins or pushes: Super Bonus pushes.
    • Player has less than straight and loses: Super Bonus loses.

Super Bonus Pay Table

Player Hand Pays
Four aces 200
Four 2-K 30
Straight flush 15
Three of a kind 2
Flush 1.5
Straight 1

Strategy

Optimal strategy would be tedious and complicated memorize. However, the player can get extremely close to it with this simple strategy. Follow the first rule to apply.

  1. Make large raise when allowed (with pair of aces or higher).
  2. Make small raise with K-Q-8-4 or higher.
  3. Fold all other.

The increase in house edge with the KQ84 strategy, compared to optimal, is 0.000089%.

Analysis

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

Ante Bet

Event Pays Combinations Probability Return
Win 1 1,415,369,375,148 0.355028 0.355028
Push 0 473,003,972,892 0.118647 0.000000
Loss -1 2,098,272,755,400 0.526325 -0.526325
Total 3,986,646,103,440 1.000000 -0.171298

The next table shows the return of the Raise bet under optimal player strategy. A win of 0 also includes folding, in which case a raise bet was never made.

Raise Bet

Win Combinations Probability Return
3 671,609,661,948 0.168465 0.505394
1 1,215,649,215,684 0.304930 0.304930
0 938,265,298,824 0.235352 0.000000
-1 1,093,014,959,196 0.274169 -0.274169
-3 68,106,967,788 0.017084 -0.051251
Total 3,986,646,103,440 1.000000 0.484904

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

Super Bonus Bet

Event Pays Combinations Probability Return
Four aces 200 73,629,072 0.000018 0.003694
Four 2-K 30 883,548,864 0.000222 0.006649
Straight flush 15 3,178,321,608 0.000797 0.011959
Three of a kind 2 89,974,725,984 0.022569 0.045138
Flush 1.5 175,813,952,424 0.044101 0.066151
Straight 1 156,167,261,712 0.039173 0.039173
Push 0 1,485,273,310,140 0.372562 0.000000
Loss -1 2,075,281,353,636 0.520558 -0.520558
Total 3,986,646,103,440 1.000000 -0.347795

The next table summarizes the Ante, Raise, and Super Bonus bets. The sum shows the player can expect to lose 3.48% for every hand played, compared to the size of his Ante (or Super Bonus) bet. For example, if the player started with $10 on both the Ante and Super Bonus, then he could expect to lose 34.8¢, assuming optimal strategy.

Summary

Bet Return
Ante -0.171298
Raise 0.484904
Super Bonus -0.347795
Total -0.034189

The next table shows the net overall win between the Ante, Raise, and Super Bonus under optimal player strategy.

Net Win

Win Combinations Probability Return
204 56,580,432 0.000014 0.002895
203 17,048,640 0.000004 0.000868
34 764,060,808 0.000192 0.006516
33 119,340,480 0.000030 0.000988
26 147,576 0.000000 0.000001
19 2,708,500,216 0.000679 0.012908
18 467,451,204 0.000117 0.002111
15 239,544 0.000000 0.000001
11 2,130,644 0.000001 0.000006
6 75,428,689,424 0.018920 0.113522
5.5 140,729,630,976 0.035300 0.194151
5 132,528,726,036 0.033243 0.166216
4.5 26,782,817,436 0.006718 0.030232
4 240,544,812,516 0.060338 0.241351
3 51,462,003,780 0.012909 0.038726
2 859,165,302,444 0.215511 0.431022
1.5 11,157,384 0.000003 0.000004
1 356,744,817,336 0.089485 0.089485
0 842,169,384 0.000211 0.000000
-2 938,364,828,496 0.235377 -0.470754
-2.5 8,290,346,628 0.002080 -0.005199
-3 1,106,499,736,032 0.277552 -0.832655
-5 45,115,566,024 0.011317 -0.056583
Total 3,986,646,103,440 1.000000 -0.034189

The bottom right cell of the table above shows a house edge of 3.42%. This is the ratio of the expected player loss to the Ante bet. One might argue that since the Super Bonus bet is required I define the house edge as the expected loss to the sum of the required starting bets. However, in the interests of consistency with how the term is defined in other games, I choose to base the house edge on the Ante only. So, for every $100 you bet on the Ante you can expect to lose $3.42 between the Ante, Raise, and Super Bonus combined.

The standard deviation is 3.13, based on the Ante bet.

Overall the player has a 18.56% chance of making a big raise, 57.93% for a small raise, and 23.51% for folding, for an average final wager of 3.14 units. Thus, the element of risk of the game (ratio of expected loss to average total bet) is 3.42%/3.14 = 1.09%.

Queens Up

As far as I know, there are four pay tables available for the Queens Up, according to the choice of casino management. Most Las Vegas casinos use pay table 4.

Queens Up Pay Tables

Player Hand Pay Table 1 Pay Table 2 Pay Table 3 Pay 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

Queens Up — Pay Table 1

Event Pays Combinations Probability Return
Four of a kind 50 624 0.000240 0.012005
Straight flush 30 2,072 0.000797 0.023917
Three of a kind 9 58,656 0.022569 0.203121
Flush 4 114,616 0.044101 0.176403
Straight 3 101,808 0.039173 0.117518
Two pair 2 123,552 0.047539 0.095078
Pair of Qs to As 1 242,916 0.093467 0.093467
Loser -1 1,954,716 0.752115 -0.752115
Total 2,598,960 1.000000 -0.030606

Queens Up — Pay Table 2

Event Pays Combinations Probability Return
Four of a kind 50 624 0.000240 0.012005
Straight flush 40 2,072 0.000797 0.031890
Three of a kind 8 58,656 0.022569 0.180552
Flush 4 114,616 0.044101 0.176403
Straight 3 101,808 0.039173 0.117518
Two pair 2 123,552 0.047539 0.095078
Pair of Qs to As 1 242,916 0.093467 0.093467
Loser -1 1,954,716 0.752115 -0.752115
Total 2,598,960 1.000000 -0.045203

Queens Up — Pay Table 3

Event Pays Combinations Probability Return
Four of a kind 50 624 0.000240 0.012005
Straight flush 30 2,072 0.000797 0.023917
Three of a kind 8 58,656 0.022569 0.180552
Flush 4 114,616 0.044101 0.176403
Straight 3 101,808 0.039173 0.117518
Two pair 2 123,552 0.047539 0.095078
Pair of Qs to As 1 242,916 0.093467 0.093467
Loser -1 1,954,716 0.752115 -0.752115
Total 2,598,960 1.000000 -0.053175

Queens Up — Pay Table 4

Event Pays Combinations Probability Return
Four of a kind 50 624 0.000240 0.012005
Straight flush 40 2,072 0.000797 0.031890
Three of a kind 7 58,656 0.022569 0.157983
Flush 4 114,616 0.044101 0.176403
Straight 3 101,808 0.039173 0.117518
Two pair 2 123,552 0.047539 0.095078
Pair of Qs to As 1 242,916 0.093467 0.093467
Loser -1 1,954,716 0.752115 -0.752115
Total 2,598,960 1.000000 -0.067772

Practice Game

Before you play for real money, practice your Crazy 4 Poker game right here.

There is also a similar game called Four Card Poker.

Shufflemaster's official web site for Crazy 4 Poker.

Wizard Recommends

  • $777 Welcome Bonus
  • $3000 Welcome Bonus
  • $5000 Welcome Bonus
  • $3000 Welcome Bonus
Wizard of Odds Approved
View Full Site View Mobile Site

Copyright © 1998-2014 Wizard of Odds Consulting, Inc. All rights reserved. Privacy & Terms.