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Criss Cross Poker

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Introduction

Criss Cross Poker
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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rule card

Rules

  1. 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.
  2. The dealer deals two hole cards for the player and places five community cards face down in a cross layout.
  3. 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.
  4. The dealer will then unveil the two outer cards in the horizontal row of the cross.
  5. 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.
  6. The dealer will unveil the two outer cards on the vertical column of the cross.
  7. The player can make a Middle Bet ranging from 1x to 3x either Ante bet or fold.
  8. The dealer will then disclose the middle card.
  9. Using their two hole cards and the three cards in the horizontal row, the player creates the Across Hand.
  10. Similarly, the player means to utilize their hole cards along with three vertical cards to form the Down Hand.
  11. The payout on the Middle Bet is determined based on which of the Across and Down hands is of higher rank.
  12. 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 Pay
    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
  13. 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.