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How Criss Cross Poker is Played. What's unique about Criss Cross Poker is that there are two ways to win with one hand. The objective of this poker table game is to have a winning five card poker hand which pays according to a poker ranking pay table. The dealer does not play. A standard 52 card deck is used. Awesome session of 3 Card Poker at The El Cortez in Las Vegas! Please LIKE and SUBSCRIBE! Follow me on Twitch: Follow. Developed by the creators of World Series of Poker: Full House Pro, Prominence Poker delivers an underground poker experience where your rep is all you've got and one hand can make all the difference. Build the rep, prestige, and bankroll needed to be, and beat, the best of the best.
Introduction
Just play it like you would any single-hand video poker machine, except you don't need to put in money. If you want to improve your game, select 'Warn on strategy errors.' The advice given is optimal, based on all the possible combinations of cards on the draw.
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
Cross Hand Poker Card Game
- 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.
Cross Hand Poker Game
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.
Internal Links
Full expected value table. This page shows the probability and return from all 974 possible outcomes.
Written by:Michael Shackleford
The card game of poker has many variations, most of which were created in the United States in the mid-1900s. The standard order of play applies to most of these games, but to fully specify a poker game requires details about which hand values are used, the number of betting rounds, and exactly what cards are dealt and what other actions are taken between rounds.
Popular poker variants[edit]
The three most popular poker variants are spread in casinos and poker rooms worldwide and can be divided into the following groups:
- Draw poker: Games in which players are dealt a complete hand, hidden, and then improve it by replacing cards. The most common of these is five-card draw.
- Stud poker: Games in which each player receives a combination of face-up cards and face-down cards in multiple betting rounds. The most common of these are five-card stud and seven-card stud. These two variants are further played in other different formats.
- Community card poker: Games in which each player's incomplete hidden hand is combined with shared face-up cards. The most common of these are Texas hold 'em and Omaha hold 'em.
Here are more common rule variations:
- Lowball: The lowest hand wins the pot. There are different rules about whether or not aces count as low, and the effects of straights and flushes. The most common variants are Razz and 2-7 Triple Draw
- High-low split: the highest and lowest hands split the pot. Generally there is a qualifier for the low hand. For example, the low hand must have 5 cards with ranks of 8 or less. In most high-low games the usual rank of poker hands is observed, so that an unsuited broken straight (7-5-4-3-2) wins low (see Morehead, Official Rules of Card Games). In a variant, based on Lowball, where only the low hand wins, a straight or a flush does not matter for a low hand. So the best low hand is 5-4-3-2-A, suited or not.
- Players can pass cards to each other. An example of this would be Anaconda.
- Kill game: When a fixed limit game is played and a player wins two pots in a row, the stakes are doubled. In some split-pot games, a player winning both halves of the pot may also cause a kill. In some variants of Lowball, a player may choose to kill by placing a double bet after seeing his first two cards.
- Wild cards are added. This can range from simply making deuces wild to the 7-card stud variant named baseball.
- A twist round in which players can buy another card from the deck. If a player does not like the purchased card, the player can purchase another one by adding money to the pot. This is sometimes called a 'tittle.'
- A stripped deck may be used. Poker was first played with only 20 cards. In the spirit of poker history, players will sometimes only play with a stripped deck. A popular poker game in Spain is played with cards 8-A. It is played similar to hold'em, except that one card is dealt at a time and a player must use both hole cards.
- Roll your own is played in stud games, and allows the player to determine which of his or her cards are turned up and visible to the other players. In a game like Seven-card Stud, the 'roll' action only applies to the first 3 cards, all of which are dealt face down. Each player then determines which card to expose. Play then continues as with regular Seven-card Stud. But a game like Mexican stud applies the roll option throughout the game. Two cards are dealt face down, and the players roll one card up. The game continues just as in Five-card Stud, except the cards are dealt face down, and each player then decides which of the two down cards is exposed.[1]
Mixed poker games[edit]
Poker can be played in a mixed game format, for example one half-hour of Texas hold 'em followed by one half-hour of Seven-card stud. There are many types of mixed poker games. The most notable mixed poker variation is H.O.R.S.E. poker. H.O.R.S.E. is a mix of Texas hold 'em, Omaha high-low, Razz, Seven-card stud and Seven-card stud Eight-or-better. Each game will usually be played for a fixed number of hands or time and then the players will move on to the next game.
Other mixed games include:
- H.O.S.E. – same as H.O.R.S.E., except without Razz.
- H.O.E. – same as H.O.R.S.E, except no Razz or Seven-card stud.
- H.O. – Texas hold 'em and Omaha high-low
- O.E. – Omaha high-low and Seven-card Stud Eight or better.
- H.A. – Pot limit Texas hold 'em and pot limit Omaha.
- Omaha High-low Mixed – Fixed limit Omaha and pot limit Omaha high-low
- Holdem Mixed – Fixed limit and no limit Texas hold 'em.
- Eight Game Mix – Fixed limit 2-7 Triple Draw, fixed limit Texas hold 'em, fixed limit Omaha Hi-Low Eight or better, Razz, fixed limit Seven-card stud, fixed limit Seven-card stud Hi-Low eight or better, no limit Texas hold 'em and pot limit Omaha.
- Ten Game Mix (introduced at 2011 World Series of Poker) – No limit Hold'em, fixed limit Seven-card Razz, fixed limit Hold'em, fixed limit Badugi, fixed limit Seven-card Stud, no limit 2-7 Single Draw, fixed limit Omaha Hi-Low eight or better, pot limit Omaha, fixed limit 2-7 Triple Draw and fixed limit Seven-card stud Hi-Low eight or better (played with 6 players on a table).
Specific poker variant games[edit]
On This Page
How Criss Cross Poker is Played. What's unique about Criss Cross Poker is that there are two ways to win with one hand. The objective of this poker table game is to have a winning five card poker hand which pays according to a poker ranking pay table. The dealer does not play. A standard 52 card deck is used. Awesome session of 3 Card Poker at The El Cortez in Las Vegas! Please LIKE and SUBSCRIBE! Follow me on Twitch: Follow. Developed by the creators of World Series of Poker: Full House Pro, Prominence Poker delivers an underground poker experience where your rep is all you've got and one hand can make all the difference. Build the rep, prestige, and bankroll needed to be, and beat, the best of the best.
Introduction
Just play it like you would any single-hand video poker machine, except you don't need to put in money. If you want to improve your game, select 'Warn on strategy errors.' The advice given is optimal, based on all the possible combinations of cards on the draw.
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
Cross Hand Poker Card Game
- 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.
Cross Hand Poker Game
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.
Internal Links
Full expected value table. This page shows the probability and return from all 974 possible outcomes.
Written by:Michael Shackleford
The card game of poker has many variations, most of which were created in the United States in the mid-1900s. The standard order of play applies to most of these games, but to fully specify a poker game requires details about which hand values are used, the number of betting rounds, and exactly what cards are dealt and what other actions are taken between rounds.
Popular poker variants[edit]
The three most popular poker variants are spread in casinos and poker rooms worldwide and can be divided into the following groups:
- Draw poker: Games in which players are dealt a complete hand, hidden, and then improve it by replacing cards. The most common of these is five-card draw.
- Stud poker: Games in which each player receives a combination of face-up cards and face-down cards in multiple betting rounds. The most common of these are five-card stud and seven-card stud. These two variants are further played in other different formats.
- Community card poker: Games in which each player's incomplete hidden hand is combined with shared face-up cards. The most common of these are Texas hold 'em and Omaha hold 'em.
Here are more common rule variations:
- Lowball: The lowest hand wins the pot. There are different rules about whether or not aces count as low, and the effects of straights and flushes. The most common variants are Razz and 2-7 Triple Draw
- High-low split: the highest and lowest hands split the pot. Generally there is a qualifier for the low hand. For example, the low hand must have 5 cards with ranks of 8 or less. In most high-low games the usual rank of poker hands is observed, so that an unsuited broken straight (7-5-4-3-2) wins low (see Morehead, Official Rules of Card Games). In a variant, based on Lowball, where only the low hand wins, a straight or a flush does not matter for a low hand. So the best low hand is 5-4-3-2-A, suited or not.
- Players can pass cards to each other. An example of this would be Anaconda.
- Kill game: When a fixed limit game is played and a player wins two pots in a row, the stakes are doubled. In some split-pot games, a player winning both halves of the pot may also cause a kill. In some variants of Lowball, a player may choose to kill by placing a double bet after seeing his first two cards.
- Wild cards are added. This can range from simply making deuces wild to the 7-card stud variant named baseball.
- A twist round in which players can buy another card from the deck. If a player does not like the purchased card, the player can purchase another one by adding money to the pot. This is sometimes called a 'tittle.'
- A stripped deck may be used. Poker was first played with only 20 cards. In the spirit of poker history, players will sometimes only play with a stripped deck. A popular poker game in Spain is played with cards 8-A. It is played similar to hold'em, except that one card is dealt at a time and a player must use both hole cards.
- Roll your own is played in stud games, and allows the player to determine which of his or her cards are turned up and visible to the other players. In a game like Seven-card Stud, the 'roll' action only applies to the first 3 cards, all of which are dealt face down. Each player then determines which card to expose. Play then continues as with regular Seven-card Stud. But a game like Mexican stud applies the roll option throughout the game. Two cards are dealt face down, and the players roll one card up. The game continues just as in Five-card Stud, except the cards are dealt face down, and each player then decides which of the two down cards is exposed.[1]
Mixed poker games[edit]
Poker can be played in a mixed game format, for example one half-hour of Texas hold 'em followed by one half-hour of Seven-card stud. There are many types of mixed poker games. The most notable mixed poker variation is H.O.R.S.E. poker. H.O.R.S.E. is a mix of Texas hold 'em, Omaha high-low, Razz, Seven-card stud and Seven-card stud Eight-or-better. Each game will usually be played for a fixed number of hands or time and then the players will move on to the next game.
Other mixed games include:
- H.O.S.E. – same as H.O.R.S.E., except without Razz.
- H.O.E. – same as H.O.R.S.E, except no Razz or Seven-card stud.
- H.O. – Texas hold 'em and Omaha high-low
- O.E. – Omaha high-low and Seven-card Stud Eight or better.
- H.A. – Pot limit Texas hold 'em and pot limit Omaha.
- Omaha High-low Mixed – Fixed limit Omaha and pot limit Omaha high-low
- Holdem Mixed – Fixed limit and no limit Texas hold 'em.
- Eight Game Mix – Fixed limit 2-7 Triple Draw, fixed limit Texas hold 'em, fixed limit Omaha Hi-Low Eight or better, Razz, fixed limit Seven-card stud, fixed limit Seven-card stud Hi-Low eight or better, no limit Texas hold 'em and pot limit Omaha.
- Ten Game Mix (introduced at 2011 World Series of Poker) – No limit Hold'em, fixed limit Seven-card Razz, fixed limit Hold'em, fixed limit Badugi, fixed limit Seven-card Stud, no limit 2-7 Single Draw, fixed limit Omaha Hi-Low eight or better, pot limit Omaha, fixed limit 2-7 Triple Draw and fixed limit Seven-card stud Hi-Low eight or better (played with 6 players on a table).
Specific poker variant games[edit]
Some poker games don't fit neatly into the above categories, and some have features of more than one of these categories. These variants are most often played in home games, usually as part of a dealer's choice format.
High Chicago or Low Chicago[edit]
Either of these two versions can be played in any stud high game. In High Chicago, or sometimes simply called Chicago, the player with the highest spade face down (referred to as in the hole) receives half the pot. In Low Chicago, the player with the lowest spade in the hole receives half of the pot, with the A♠ being the lowest. If the player with the highest hand also has the highest/lowest spade in the hole, then that player receives the entire pot - having won both sides of the bet.
Follow the Queen[edit]
This 7-card stud game uses a wild-card designated as whichever card is immediately dealt (exposed, or face-up) after any queen previously dealt (exposed). In the event that the final card dealt (exposed) is itself a queen, then all queens are wild. If no queens are dealt (exposed), then there are no wilds for that hand. Betting is the same as in normal 7-card stud games. Follow the Queen is a typical game variant in Dealer's Choice poker games.[2][3]
Countdown[edit]
In this 5-card game, the dealer gives each player 5 cards face down. After the first round of betting, each player may choose to replace zero to three cards. A second round of betting follows and then players may opt to replace zero to two cards. Upon completing another round of betting, each player may replace one card of the cards in their hand. After a final round of betting, any remaining players show their hands, and the highest 5 card hand wins. The cost of cards doubles each round. For example, if the dealer says each replacement card costs $10 in the first round, then each card costs $20 in the second round, and $40 in the final round. When players purchase cards to replace ones in their hand, they put the cost of the cards in the pot.[4]
This game will only work with 4 players (or fewer) otherwise you will run out of cards.
Billabong and Shanghai[edit]
Just as Oxford stud is a mixed stud/community card version of Texas hold 'em, Billabong is a mixed version of Manila. Each player is dealt two down-cards and one up-card. Low up-card starts the betting with a Bring-in if you are playing with one, otherwise high card starts the betting. Next, two community cards are dealt, followed by a second betting round, beginning with the player with the best exposed partial poker hand (counting the community cards, as in Oxford stud). Then a third community card is dealt, followed by a third betting round. Finally a fourth community card is dealt, followed by a fourth betting round and showdown. Each player plays the best five-card hand he can make from the three in his hand plus the four on the board in any combination.
Shanghai is the same game with an extra hole card, but no more than two hole cards play. That is, the game begins with each player being dealt three down-cards and one up-card; each player must discard one of his hole cards at some point during the game as determined ahead of time. The most common variation is to discard immediately as in Pineapple; the second most common is to discard just before showdown as in Tahoe.
Gambling dice tattoos. Therefore, a dice tattoo will make a good homage to all the popular board games be it the classic Ludo or the ever-favorite DnD. However, one thing you have to keep in mind is that dice can represent a unique meaning depending on the context of the tattoo. Dice tattoo meaning can range from Risks taking nature to gambling habits. 75 Dice Tattoos For Men – The Gambler's Paradise Known As Life 1. Forearm Dice Tattoos 2. Bicep Dice Tattoos 3. Arm Dice Tattoos 4. Sleeve Dice Tattoos 5. Wrist Dice Tattoos 6. Chest Dice Tattoos 7. Back Dice Tattoos 8. Side Dice Tattoos 9. Calf Dice Tattoos 10. Leg Dice Tattoos 11.
Guts[edit]
Guts is a family of games that are cousins of poker rather than poker variants. They usually involve hands of 3 or fewer cards, ranked similarly to hands in poker, and multiple successive rounds of betting each of which consist of the decision to be 'in' or 'out', and each with its own showdown. The losers of rounds of guts generally match or double the pot, which grows rapidly.
Five-O poker[edit]
Five-O Poker is a heads-up poker variant in which both players must play five hands of five cards simultaneously. Four of the five cards in each hand are face-up. Once all five hands are down, there is a single round of betting. The winner is determined by matching each hand to the corresponding hand of the opponent. The player with the stronger poker hand in three (or more) out of the five columns, wins, unless a player folds on a bet that was made. If a player beats their opponent with all five hands, this is called a 'Five-O' win.
Chinese poker[edit]
Chinese poker is a 2-4 player poker game with thirteen cards. The idea is to make three poker hands with increasing rank : two with five cards and one with three cards. If one of the hands does not adhere to increasing rank (i.e. is mis-set), the hand is declared dead and results in some sort of penalty.
Kuhn poker[edit]
Kuhn poker, using a three card deck, is more of game theory problem than an actual game people play, but it can be played by two players.[5]
See also[edit]
References[edit]
- ^Pagat.com: Roll Your Own
- ^Pokernews.com: Fun Home Poker Game Rules - Follow the Queen
- ^Pokerrules.net: How to Play Follow the Queen
- ^Pokerrules.net: How to Play Countdown Poker
- ^'A Parameterized Family of Equilibrium Profiles for Three-Player Kuhn Poker'(PDF).