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Criss Cross Poker
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Introduction
Photo taken at 2014 Global Gaming Expo.
Criss Cross Poker is a unique variant of poker brought to you by In Bet Gaming Back in 2014, I began hearing about this game being played in various casinos across the eastern United States. The essence of this game revolves around the player betting on two distinct hands, utilizing five community cards arranged in a cross formation.
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Rules
- The gameplay begins with the player placing equal Ante Across and Ante Down bets. Additionally, there’s an option to place a Five Card Bonus Bet.
- The dealer deals two hole cards for the player and places five community cards face down in a cross layout.
- The player has the option to execute an Across Bet, linked to the Across Hand, which can range from 1x to 3x the Ante Across bet, or decide to fold.
- The dealer will then unveil the two outer cards in the horizontal row of the cross.
- Subsequently, the player can opt to place a Down bet linked to the Down Hand, which can also be between 1x to 3x the Ante Down bet, or choose to fold.
- The dealer will unveil the two outer cards on the vertical column of the cross.
- The player can make a Middle Bet ranging from 1x to 3x either Ante bet or fold.
- The dealer will then disclose the middle card.
- Using their two hole cards and the three cards in the horizontal row, the player creates the Across Hand.
- Similarly, the player means to utilize their hole cards along with three vertical cards to form the Down Hand.
- The payout on the Middle Bet is determined based on which of the Across and Down hands is of higher rank.
- All wagering outcomes will adhere to the payout table listed below. Payouts 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's payout is determined by the five community card arrangement in the cross format, following the payout 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
With the various hand possibilities, multiple combinations of bets, and opportunities to fold at different stages, there are a total of 975 potential outcomes. I have outlined the probabilities of all these outcomes in my Criss Cross Poker Full Expected Value Table. However, I don't wish to overwhelm you by presenting that extensive table here. Allow me to provide a summary of each hand's potential results below.
The subsequent table depicts potential outcomes for both the Ante Across and Across bets. The \"pays\" column indicates the total winnings derived from both bets. The bottom right cell reveals that players can anticipate a loss of 0.600581 units across 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 | -1 | 1,240,719,912 | 0.014721 | -1 |
Three of a kind | 1 | Two pair | 44,512,795,932 | 0.528127 | High pair (J-A) |
Low pair (6-10) | 0 | All other | 4,576,521,600 | 0.054299 | -1 |
-1 | 0 | Five Card Bonus Bet Pay Table | 4,203,010,800 | 0.049867 | Hand |
Pays | 0 | Royal flush | 0 | 0.000000 | 0.000000 |
Straight flush | 84,284,272,800 | 1.000000 | Four of a kind |
The next table illustrates the possible outcomes associated with both Ante Down and Down bets. The \"pays\" column here indicates the aggregate winnings from these two bets, showing an expected loss of 0.597666 units when considered together.
Full house
Flush | Straight | Three of a kind | Two pair | Sixes or better | Loser |
---|---|---|---|---|---|
-1 | 3 | 1501 | 45,792 | 0.000001 | 0.000815 |
Analysis | 1 | 501 | 83,928 | 0.000001 | 0.000499 |
Ante Across and Across Bets | 3 | 301 | 37,116 | 0.000000 | 0.000133 |
Hand | 1 | 101 | 1,118,700 | 0.000013 | 0.001341 |
Across Bet | 3 | 121 | 12,233,808 | 0.000145 | 0.017563 |
Pays | 1 | 41 | 7,485,048 | 0.000089 | 0.003641 |
Combinations | 3 | 37 | 48,603,888 | 0.000577 | 0.021337 |
Probability | 1 | 13 | 68,156,856 | 0.000809 | 0.010513 |
Return | 3 | 25 | 6,951,456 | 0.000082 | 0.002062 |
Royal flush | 1 | 9 | 157,641,288 | 0.001870 | 0.016833 |
Royal flush | 3 | 16 | 4,780,980 | 0.000057 | 0.000908 |
Straight flush | 1 | 6 | 285,297,516 | 0.003385 | 0.020310 |
Straight flush | 3 | 10 | 540,593,136 | 0.006414 | 0.064139 |
Four of a kind | 1 | 4 | 1,160,967,816 | 0.013774 | 0.055098 |
Four of a kind | 3 | 7 | 814,576,176 | 0.009665 | 0.067652 |
Full house | 1 | 3 | 2,988,662,184 | 0.035459 | 0.106378 |
Full house | 3 | 4 | 1,336,724,496 | 0.015860 | 0.063439 |
Flush | 1 | 2 | 9,281,584,656 | 0.110122 | 0.220245 |
Flush | 3 | 0 | 1,417,841,568 | 0.016822 | 0.000000 |
Straight | 1 | 0 | 11,550,329,616 | 0.137040 | 0.000000 |
Straight | 3 | Three of a kind | 1,450,469,088 | 0.017209 | Three of a kind |
Two pair | 1 | Two pair | 44,370,555,288 | 0.526439 | High pair |
High pair | 0 | Medium pair | 5,013,003,456 | 0.059477 | Medium pair |
Loser | 0 | -1 | 3,766,528,944 | 0.044688 | -1 |
Three of a kind | 0 | Two pair | 0 | 0.000000 | 0.000000 |
High pair (J-A) | 84,284,272,800 | 1.000000 | Low pair (6-10) |
The table below details the potential outcome of placing a Middle bet. The last cell in this table indicates an expected win of 1.111675 units from this particular bet.
All other
-1 | -1 | Five Card Bonus Bet Pay Table | Hand | Pays | Royal flush |
---|---|---|---|---|---|
Straight flush | 3 | 1500 | 259,440 | 0.000003 | 0.004617 |
Four of a kind | 1 | 500 | 0 | 0.000000 | 0.000000 |
Full house | 3 | 300 | 2,323,104 | 0.000028 | 0.008269 |
Flush | 1 | 100 | 0 | 0.000000 | 0.000000 |
Straight | 3 | 120 | 39,488,184 | 0.000469 | 0.056221 |
Three of a kind | 1 | 40 | 0 | 0.000000 | 0.000000 |
Two pair | 3 | 36 | 231,865,848 | 0.002751 | 0.099036 |
Sixes or better | 1 | 12 | 0 | 0.000000 | 0.000000 |
Loser | 3 | 24 | 325,921,056 | 0.003867 | 0.092806 |
-1 | 1 | 8 | 0 | 0.000000 | 0.000000 |
Analysis | 3 | 15 | 375,011,412 | 0.004449 | 0.066740 |
Ante Across and Across Bets | 1 | 5 | 199,154,268 | 0.002363 | 0.011814 |
Hand | 3 | 9 | 2,751,292,188 | 0.032643 | 0.293787 |
Across Bet | 1 | 3 | 399,927,564 | 0.004745 | 0.014235 |
Pays | 3 | 6 | 5,494,091,328 | 0.065185 | 0.391111 |
Combinations | 1 | 2 | 1,329,787,368 | 0.015777 | 0.031555 |
Probability | 3 | 3 | 11,485,872,240 | 0.136275 | 0.408826 |
Return | 1 | 1 | 4,170,202,716 | 0.049478 | 0.049478 |
Royal flush | 3 | 0 | 12,309,204,636 | 0.146044 | 0.000000 |
Royal flush | 1 | 0 | 4,837,617,228 | 0.057396 | 0.000000 |
Straight flush | 3 | Straight flush | 1,789,381,740 | 0.021230 | Four of a kind |
Four of a kind | 1 | Full house | 29,763,340,080 | 0.353130 | Full house |
Flush | 0 | 0 | 8,779,532,400 | 0.104166 | 0.000000 |
Flush | 84,284,272,800 | 1.000000 | 1.111675 |
The following table consolidates the anticipated winnings from all three categories of bets.
Straight
Straight | Three of a kind |
---|---|
Three of a kind | Two pair |
Two pair | High pair |
High pair | 1.111675 |
Medium pair | Medium pair |
The bottom right cell reports an estimated loss of 0.086571 units. Since players are obliged to wager a minimum of two units, I have divided this number by two, resulting in a house edge of 4.33%.
Taking into account the raise options, the average total wager by the conclusion of the hand is 5.86529 units. Therefore, the Loser ratio of anticipated loss to total wagering amounts to 8.6571/5.8629 = 1.48%, which is relatively favorable for a poker variant.
The standard deviation in relation to the total initial wager stands at 4.802.
-1
In terms of decision-making, players only have three valid choices: fold, raise by a minimum of 1x, or raise by a maximum of 3x. There should never be any raises falling in between these two figures.
-1
- If the hole cards are not suited, do not match, and the highest card is five or lower, then it is advisable to fold.
- If the hole cards are suited J/Q or form any type of pair, then a larger raise should be made.
- For any other combinations of hole cards, a small raise is recommended.
-4
This decision-making process is quite akin to raising on the Across hand. Nonetheless, players do gain the advantage of viewing two additional cards, which can assist in making decisions in uncertain scenarios. I have not explicitly outlined these differences in strategy from the Across hand. However, understanding those deviations can boost expected returns by 0.29% of the Ante Down bet or effectively decrease the house edge by 0.15%.
-0.058883
Once four cards are revealed, there are countless potential situations for strategizing a Middle bet. Yet, an optimal decision can be made by evaluating winnings across all remaining 46 cards in the deck for both small and large Middle bets. I can assert that should a player place a 3x bet, folding would not be a wise choice; additionally, there are instances, approximately 4.5% of the time, when a player will opt for both small bets on Across and Down but then choose to fold the Middle bet.
Loser
The table that follows outlines potential outcomes linked to the Five Card Bonus Bet. The last cell indicates a house edge of 3.53%, which is reasonable for a side bet.
-2
-1.056254 | Fold one unit | -1 | -0.054299 | Fold two units |
---|---|---|---|---|
-2 | 250 | 4 | 0.000002 | 0.000385 |
-0.099734 | 100 | 36 | 0.000014 | 0.001385 |
Fold four units | 40 | 624 | 0.000240 | 0.009604 |
-4 | 15 | 3,744 | 0.001441 | 0.021609 |
Total | 10 | 5,108 | 0.001965 | 0.019654 |
-0.600581 | 6 | 10,200 | 0.003925 | 0.023548 |
Ante Down and Down Bets | 4 | 54,912 | 0.021128 | 0.084514 |
Hand | 3 | 123,552 | 0.047539 | 0.142617 |
Down Bet | 1 | 760,320 | 0.292548 | 0.292548 |
Pays | Combinations | 1,640,460 | 0.631199 | Probability |
Return | 2,598,960 | 1.000000 | Royal flush |
Royal flush
I utilized C++ to analyze the game by processing an exhaustive loop covering all Straight flush (52,2)*combin(50,2)*combin(48,2)*46 = 84,284,272,800 potential combinations. The code comprises approximately 600 lines and requires about six hours to execute.
Straight flush
Four of a kind This page will provide the probability and expected returns from all 974 possible outcomes.