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Criss Cross Poker
Photo taken at 2014 Global Gaming Expo.
Criss Cross Poker is poker variation by . 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.
- 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
Across, Down &
Middle Bets Pay
Royal 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
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
|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|
|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|
|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|
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
|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|
|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|
|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|
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.
|Four of a kind||3||120||39,488,184||0.000469||0.056221|
|Four of a kind||1||40||0||0.000000||0.000000|
|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|
The next table summarizes the expected win of all three groups of bets.
|Ante Across & Across||-0.600581|
|Ante Down & Down||-0.597666|
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.
With all decision points, the only viable options are fold, minimum 1x raise, or maximum 3x raise. Never raise anything between 1x and 3x.
- 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.
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%.
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
|Four of a kind||40||624||0.000240||0.009604|
|Three of a kind||4||54,912||0.021128||0.084514|
|Sixes or better||1||760,320||0.292548||0.292548|
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.
Full expected value table. This page shows the probability and return from all 974 possible outcomes.