Probability Baccarat
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Live dealer blackjack is nowadays one of the most popular online casino games. It has the same feel and look of the real blackjack found in land-based casinos, but it’s played through a live stream with a professional dealer sitting in front of the camera. Crazy 4 Poker 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.
- Baccarat is a betting game best played using a strategy. There’re many Baccarat strategies to choose from. But if you were to ask me for my top three, I would have to choose Baccarat strategies that are logical, easy & have the best possible chances of reducing the casinos house edge.
- Criss Cross Poker Introduction Photo taken at 2014 Global Gaming Expo. Criss Cross Poker is poker variation by In Bet Gaming.In 2014, I started to hear reports of the game in several casinos in the eastern United States.
Introduction
Photo taken at 2014 Global Gaming Expo.
Criss Cross Poker is poker variation by In Bet Gaming. In 2014, I started to hear reports of the game in several casinos in the eastern United States. The thrust of the game is the player bets on two hands, in part using five community cards placed in a cross pattern.
Rules
- Play begins with the player making Ante Across and Ante Down bets of equal size. The player may also make an optional Five Card Bonus Bet.
- The dealer gives the player two hole cards and places five community cards face down in a cross pattern.
- The player may make an Across Bet, based on the Across Hand, equal to 1x to 3x the Ante Across bet, or fold.
- The dealer will reveal the two outside cards on the horizontal row of the cross.
- The player may make a Down bet, based on the Down Hand, equal to 1x to 3x the Ante Down bet, or fold.
- The dealer will reveal the two outside cards on the vertical column of the cross.
- The player may make a Middle Bet of 1x to 3x either Ante bet or fold.
- The dealer will reveal the middle card.
- The player uses his two hole cards and the three cards on the horizontal row of the cross to form the Across Hand.
- Likewise, the player uses his two hole cards and the three cards on the vertical column of the cross to form the Down Hand.
- The Middle Bet pays according to the higher ranking of the Across and Down hands.
- All bets pay according to the pay table below. Wins are expressed on a 'to one' basis.
Criss Cross Poker Pay Table
Hand Ante
Bets PayAcross, Down &
Middle Bets PayRoyal flush 1 500 Straight flush 1 100 Four of a kind 1 40 Full house 1 12 Flush 1 8 Straight 1 5 Three of a kind 1 3 Two pair 1 2 High pair (J-A) 1 1 Low pair (6-10) 0 0 All other -1 -1 - The Five Card Bonus bet pays according to the five community cards in the cross pattern and following pay table.
Five Card Bonus Bet Pay Table
Hand Pays Royal flush 250 Straight flush 100 Four of a kind 40 Full house 15 Flush 10 Straight 6 Three of a kind 4 Two pair 3 Sixes or better 1 Loser -1
Analysis
Between two sets of possible hands, four combinations of raise bets, and folding at various stages of the game, there are 975 possible outcomes. I indicate the probability of all of them in my Criss Cross Poker Full Expected Value Table. However, I don't want to scare you off with that gigantic table here. Instead, I summarize the outcome of each hand below.
The following table shows the possible outcome of both the Ante Across and Across bets. The 'pays' column shows the combined win between the two bets. The lower right cell shows that the player can expect to lose 0.600581 units between the two bets.
Ante Across and Across Bets
| Hand | Across Bet | Pays | Combinations | Probability | Return |
|---|---|---|---|---|---|
| Royal flush | 3 | 1501 | 12,972 | 0.000000 | 0.000231 |
| Royal flush | 1 | 501 | 116,748 | 0.000001 | 0.000694 |
| Straight flush | 3 | 301 | 25,944 | 0.000000 | 0.000093 |
| Straight flush | 1 | 101 | 1,141,536 | 0.000014 | 0.001368 |
| Four of a kind | 3 | 121 | 12,167,736 | 0.000144 | 0.017468 |
| Four of a kind | 1 | 41 | 7,601,592 | 0.000090 | 0.003698 |
| Full house | 3 | 37 | 48,800,664 | 0.000579 | 0.021423 |
| Full house | 1 | 13 | 68,414,328 | 0.000812 | 0.010552 |
| Flush | 3 | 25 | 2,101,464 | 0.000025 | 0.000623 |
| Flush | 1 | 9 | 163,550,976 | 0.001940 | 0.017464 |
| Straight | 3 | 16 | 2,451,708 | 0.000029 | 0.000465 |
| Straight | 1 | 6 | 288,484,308 | 0.003423 | 0.020537 |
| Three of a kind | 3 | 10 | 538,234,224 | 0.006386 | 0.063859 |
| Three of a kind | 1 | 4 | 1,170,645,168 | 0.013889 | 0.055557 |
| Two pair | 3 | 7 | 811,632,096 | 0.009630 | 0.067408 |
| Two pair | 1 | 3 | 3,010,230,432 | 0.035715 | 0.107146 |
| High pair | 3 | 4 | 1,170,593,280 | 0.013889 | 0.055555 |
| High pair | 1 | 2 | 9,458,722,620 | 0.112224 | 0.224448 |
| Medium pair | 3 | 0 | 1,385,409,600 | 0.016437 | 0.000000 |
| Medium pair | 1 | 0 | 11,610,887,160 | 0.137759 | 0.000000 |
| Loser | 3 | -4 | 1,240,719,912 | 0.014721 | -0.058883 |
| Loser | 1 | -2 | 44,512,795,932 | 0.528127 | -1.056254 |
| Fold one unit | 0 | -1 | 4,576,521,600 | 0.054299 | -0.054299 |
| Fold two units | 0 | -2 | 4,203,010,800 | 0.049867 | -0.099734 |
| Fold four units | 0 | -4 | 0 | 0.000000 | 0.000000 |
| Total | 84,284,272,800 | 1.000000 | -0.600581 |
The following table shows the possible outcome of both the Ante Down and Down bets. The 'pays' column shows the combined win between the two bets. The lower right cell shows that the player can expect to lose 0.597666 units on the two bets combined.
Ante Down and Down Bets
| Hand | Down Bet | Pays | Combinations | Probability | Return |
|---|---|---|---|---|---|
| Royal flush | 3 | 1501 | 45,792 | 0.000001 | 0.000815 |
| Royal flush | 1 | 501 | 83,928 | 0.000001 | 0.000499 |
| Straight flush | 3 | 301 | 37,116 | 0.000000 | 0.000133 |
| Straight flush | 1 | 101 | 1,118,700 | 0.000013 | 0.001341 |
| Four of a kind | 3 | 121 | 12,233,808 | 0.000145 | 0.017563 |
| Four of a kind | 1 | 41 | 7,485,048 | 0.000089 | 0.003641 |
| Full house | 3 | 37 | 48,603,888 | 0.000577 | 0.021337 |
| Full house | 1 | 13 | 68,156,856 | 0.000809 | 0.010513 |
| Flush | 3 | 25 | 6,951,456 | 0.000082 | 0.002062 |
| Flush | 1 | 9 | 157,641,288 | 0.001870 | 0.016833 |
| Straight | 3 | 16 | 4,780,980 | 0.000057 | 0.000908 |
| Straight | 1 | 6 | 285,297,516 | 0.003385 | 0.020310 |
| Three of a kind | 3 | 10 | 540,593,136 | 0.006414 | 0.064139 |
| Three of a kind | 1 | 4 | 1,160,967,816 | 0.013774 | 0.055098 |
| Two pair | 3 | 7 | 814,576,176 | 0.009665 | 0.067652 |
| Two pair | 1 | 3 | 2,988,662,184 | 0.035459 | 0.106378 |
| High pair | 3 | 4 | 1,336,724,496 | 0.015860 | 0.063439 |
| High pair | 1 | 2 | 9,281,584,656 | 0.110122 | 0.220245 |
| Medium pair | 3 | 0 | 1,417,841,568 | 0.016822 | 0.000000 |
| Medium pair | 1 | 0 | 11,550,329,616 | 0.137040 | 0.000000 |
| Loser | 3 | -4 | 1,450,469,088 | 0.017209 | -0.068837 |
| Loser | 1 | -2 | 44,370,555,288 | 0.526439 | -1.052879 |
| Fold one unit | 0 | -1 | 5,013,003,456 | 0.059477 | -0.059477 |
| Fold two units | 0 | -2 | 3,766,528,944 | 0.044688 | -0.089377 |
| Fold four units | 0 | -4 | 0 | 0.000000 | 0.000000 |
| Total | 84,284,272,800 | 1.000000 | -0.597666 |
The following table shows the possible outcome of Middle bet. The lower right cell shows that the player can expect to win 1.111675 units on this bet.
Middle Bet
| Hand | Middle Bet | Pays | Combinations | Probability | Return |
|---|---|---|---|---|---|
| Royal flush | 3 | 1500 | 259,440 | 0.000003 | 0.004617 |
| Royal flush | 1 | 500 | 0 | 0.000000 | 0.000000 |
| Straight flush | 3 | 300 | 2,323,104 | 0.000028 | 0.008269 |
| Straight flush | 1 | 100 | 0 | 0.000000 | 0.000000 |
| Four of a kind | 3 | 120 | 39,488,184 | 0.000469 | 0.056221 |
| Four of a kind | 1 | 40 | 0 | 0.000000 | 0.000000 |
| Full house | 3 | 36 | 231,865,848 | 0.002751 | 0.099036 |
| Full house | 1 | 12 | 0 | 0.000000 | 0.000000 |
| Flush | 3 | 24 | 325,921,056 | 0.003867 | 0.092806 |
| Flush | 1 | 8 | 0 | 0.000000 | 0.000000 |
| Straight | 3 | 15 | 375,011,412 | 0.004449 | 0.066740 |
| Straight | 1 | 5 | 199,154,268 | 0.002363 | 0.011814 |
| Three of a kind | 3 | 9 | 2,751,292,188 | 0.032643 | 0.293787 |
| Three of a kind | 1 | 3 | 399,927,564 | 0.004745 | 0.014235 |
| Two pair | 3 | 6 | 5,494,091,328 | 0.065185 | 0.391111 |
| Two pair | 1 | 2 | 1,329,787,368 | 0.015777 | 0.031555 |
| High pair | 3 | 3 | 11,485,872,240 | 0.136275 | 0.408826 |
| High pair | 1 | 1 | 4,170,202,716 | 0.049478 | 0.049478 |
| Medium pair | 3 | 0 | 12,309,204,636 | 0.146044 | 0.000000 |
| Medium pair | 1 | 0 | 4,837,617,228 | 0.057396 | 0.000000 |
| Loser | 3 | -3 | 1,789,381,740 | 0.021230 | -0.063691 |
| Loser | 1 | -1 | 29,763,340,080 | 0.353130 | -0.353130 |
| Fold | 0 | 0 | 8,779,532,400 | 0.104166 | 0.000000 |
| Total | 84,284,272,800 | 1.000000 | 1.111675 |
The next table summarizes the expected win of all three groups of bets.
Summary
| Bet(s) | Expected Win |
|---|---|
| Ante Across & Across | -0.600581 |
| Ante Down & Down | -0.597666 |
| Middle | 1.111675 |
| Total | -0.086571 |
The lower right cell shows an expected loss of 0.086571 units. Since the player must wager two units at least, I divided that by two to get a house edge of 4.33%.
Considering the raise bets, the average total bet by the end of the hand is 5.86529 units. Thus the element of risk, which is the ratio of expected loss to the total amount wagered, is 8.6571/5.8629 = 1.48%, which isn't bad for a poker variant game.
The standard deviation, relative to the combined initial wager, is 4.802.
Strategy
With all decision points, the only viable options are fold, minimum 1x raise, or maximum 3x raise. Never raise anything between 1x and 3x.
Across Strategy
- If the hole cards are unsuited, unpaired, and the largest one is five or less, then fold.
- If the hole cards are suited J/Q or any pair, then make the large raise.
- With all other hole cards, make the small raise.
Down Strategy
This is a very similar decision to raising on the Across hand. However, the player has the benefit of seeing two extra cards. This can help in borderline situations. I have not implicitly identified these deviations from the Across strategy. However, I can say that knowing them, whatever they are, will increase the expected return by 0.29% the amount of the Ante Down bet, or lower the house edge by 0.15%.
Middle Strategy
With four cards seen, there are thousands of possible situations in terms of a Middle bet strategy. However, a perfect decision can be made by averaging the win over all possible 46 cards left in the deck under both a small and large Middle bet. I can say that if the player made either 3x bet, then he shouldn't fold. I can also say that 4.5% of the time the player will make both a small Across and Down bet and then fold the Middle bet.
Five Card Bonus Bet
The following table presents the possible outcomes of the Five Card Bonus Bet. The lower right cell shows a house edge of 3.53%, which for a side bet isn't bad.
Five Card Bonus Bet
| Hand | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Royal flush | 250 | 4 | 0.000002 | 0.000385 |
| Straight flush | 100 | 36 | 0.000014 | 0.001385 |
| Four of a kind | 40 | 624 | 0.000240 | 0.009604 |
| Full house | 15 | 3,744 | 0.001441 | 0.021609 |
| Flush | 10 | 5,108 | 0.001965 | 0.019654 |
| Straight | 6 | 10,200 | 0.003925 | 0.023548 |
| Three of a kind | 4 | 54,912 | 0.021128 | 0.084514 |
| Two pair | 3 | 123,552 | 0.047539 | 0.142617 |
| Sixes or better | 1 | 760,320 | 0.292548 | 0.292548 |
| Loser | -1 | 1,640,460 | 0.631199 | -0.631199 |
| Total | 2,598,960 | 1.000000 | -0.035336 |
Methodology
The game was analyzed by me in C++ by looping through all combin(52,2)*combin(50,2)*combin(48,2)*46 = 84,284,272,800 possible combinations. The program is about 600 lines of code and takes about six hours to run.
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Full expected value table. This page shows the probability and return from all 974 possible outcomes.
Written by:Michael Shackleford
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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.
Video Tutorial
Video uses our practice Crazy 4 Poker game.
Rules
- 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.
- 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
- All player and dealer get five cards each.
- The player decides to fold or raise by making a Play wager.
- If the player folds he forfeits all bets.
- The Play bet may be up to three times the Ante bet if the player has at least a pair of aces. Otherwise, the Play bet must be exactly equal to the Ante bet.
- Players make their best four-card poker hand, and discard the fifth card.
- 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.
- For purposes of the Ante bet only, the dealer needs at least a king high to open.
- 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.
- The Play bet pays as follows:
- Dealer does not open: Play wins.
- Dealer opens and player wins: Play wins.
- Dealer opens and ties player: Play pushes.
- Dealer opens and wins: Play loses.
- The Super Bonus bet pays as follows. It is not pertinent whether or not the dealer opens.
- 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.
- Make large raise when allowed (with pair of aces or higher).
- Make small raise with K-Q-8-4 or higher.
- 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 Play 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, Play, 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, Play, 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 |
6-Card Bonus
Some casinos add on a side bet known as the 6-Card Bonus. This side bet is found on multiple poker-derivative games, so I created a special page for it. For more information, please see my page on the 6-Card Bonus.
Millionaire Progressive
This is a $5 'red light' progressive side bet that pays $1,000,000 for a royal flush in spades, using the player's five cards. For all the rules and analysis, please see my page on the Millionaire Progressive.
Practice Game
Before you play for real money, practice your Crazy 4 Poker game right here.
Internal Links
Probability Of Baccarat
There is also a similar game called Four Card Poker.
Probability Baccarat Pdf
External Links
Shufflemaster's official web site for Crazy 4 Poker.