Holdem Point System
Points and Payout Calculator. If you hate having to do the math and work out the payout and points to award for your home poker game/tournament, this calcualtor will make your life a little easier. Input the number of poker players and buy in amount and the calcultor will spit out a points and payout structure for you. It will also let you. In the ten-player game for which this system is designed, the early and middle positions comprise the first six seats to the left of the blinds. If you are seated in late position (the next two seats) you should do the following: If your score is under 26 add five points, otherwise add one point. The most popular games that you can ever play within a casino site is slot Holdem Point System games. Slots are reported to be casinos most played Holdem Point System because of their gaming rules that are very simple and easy to keep up with. Not forgetting to mention that their games are predominantly based off the movie culture and industry, meaning players can connect to their gaming. In poker, players form sets of five playing cards, called hands, according to the rules of the game. Each hand has a rank, which is compared against the ranks of other hands participating in the showdown to decide who wins the pot. In high games, like Texas hold 'em and seven-card stud, the highest-ranking hands win.In low games, like razz, the lowest-ranking hands win.
This page describes the ranking of poker hands. This applies not only in the game of poker itself, but also in certain other card games such as Chinese Poker, Chicago, Poker Menteur and Pai Gow Poker.
- Low Poker Ranking: A-5, 2-7, A-6
- Hand probabilities and multiple decks - probability tables
Standard Poker Hand Ranking
There are 52 cards in the pack, and the ranking of the individual cards, from high to low, is ace, king, queen, jack, 10, 9, 8, 7, 6, 5, 4, 3, 2. In standard poker - that is to say in the formal casino and tournament game played internationally and the home game as normally played in North America - there is no ranking between the suits for the purpose of comparing hands - so for example the king of hearts and the king of spades are equal. (Note however that suit ranking is sometimes used for other purposes such as allocating seats, deciding who bets first, and allocating the odd chip when splitting a pot that can't be equally divided. See ranking of suits for details.)
A poker hand consists of five cards. The categories of hand, from highest to lowest, are listed below. Any hand in a higher category beats any hand in a lower category (so for example any three of a kind beats any two pairs). Between hands in the same category the rank of the individual cards decides which is better, as described in more detail below.
In games where a player has more than five cards and selects five to form a poker hand, the remaining cards do not play any part in the ranking. Poker ranks are always based on five cards only, and if these cards are equal the hands are equal, irrespective of the ranks of any unused cards.
Some readers may wonder why one would ever need to compare (say) two threes of a kind of equal rank. This obviously cannot arise in basic draw poker, but such comparisons are needed in poker games using shared (community) cards, such as Texas Hold'em, in poker games with wild cards, and in other card games using poker combinations.
1. Straight Flush
If there are no wild cards, this is the highest type of poker hand: five cards of the same suit in sequence - such as J-10-9-8-7. Between two straight flushes, the one containing the higher top card is higher. An ace can be counted as low, so 5-4-3-2-A is a straight flush, but its top card is the five, not the ace, so it is the lowest type of straight flush. The highest type of straight flush, A-K-Q-J-10 of a suit, is known as a Royal Flush. The cards in a straight flush cannot 'turn the corner': 4-3-2-A-K is not valid.
2. Four of a kind
Four cards of the same rank - such as four queens. The fifth card, known as the kicker, can be anything. This combination is sometimes known as 'quads', and in some parts of Europe it is called a 'poker', though this term for it is unknown in English. Between two fours of a kind, the one with the higher set of four cards is higher - so 3-3-3-3-A is beaten by 4-4-4-4-2. If two or more players have four of a kind of the same rank, the rank of the kicker decides. For example in Texas Hold'em with J-J-J-J-9 on the table (available to all players), a player holding K-7 beats a player holding Q-10 since the king beats the queen. If one player holds 8-2 and another holds 6-5 they split the pot, since the 9 kicker makes the best hand for both of them. If one player holds A-2 and another holds A-K they also split the pot because both have an ace kicker.
3. Full House
This combination, sometimes known as a boat, consists of three cards of one rank and two cards of another rank - for example three sevens and two tens (colloquially known as 'sevens full of tens' or 'sevens on tens'). When comparing full houses, the rank of the three cards determines which is higher. For example 9-9-9-4-4 beats 8-8-8-A-A. If the threes of a kind are equal, the rank of the pairs decides.
4. Flush
Five cards of the same suit. When comparing two flushes, the highest card determines which is higher. If the highest cards are equal then the second highest card is compared; if those are equal too, then the third highest card, and so on. For example K-J-9-3-2 beats K-J-7-6-5 because the nine beats the seven.If all five cards are equal, the flushes are equal.
5. Straight
Five cards of mixed suits in sequence - for example Q-J-10-9-8. When comparing two sequences, the one with the higher ranking top card is better. Ace can count high or low in a straight, but not both at once, so A-K-Q-J-10 and 5-4-3-2-A are valid straights, but 2-A-K-Q-J is not. 5-4-3-2-A, known as a wheel, is the lowest kind of straight, the top card being the five.
6. Three of a Kind
Three cards of the same rank plus two unequal cards. This combination is also known as Triplets or Trips. When comparing two threes of a kind the rank of the three equal cards determines which is higher. If the sets of three are of equal rank, then the higher of the two remaining cards in each hand are compared, and if those are equal, the lower odd card is compared.So for example 5-5-5-3-2 beats 4-4-4-K-5, which beats 4-4-4-Q-9, which beats 4-4-4-Q-8.
7. Two Pairs
A pair consists of two cards of equal rank. In a hand with two pairs, the two pairs are of different ranks (otherwise you would have four of a kind), and there is an odd card to make the hand up to five cards. When comparing hands with two pairs, the hand with the highest pair wins, irrespective of the rank of the other cards - so J-J-2-2-4 beats 10-10-9-9-8 because the jacks beat the tens. If the higher pairs are equal, the lower pairs are compared, so that for example 8-8-6-6-3 beats 8-8-5-5-K. Finally, if both pairs are the same, the odd cards are compared, so Q-Q-5-5-8 beats Q-Q-5-5-4.
8. Pair
Hold'em Point System
A hand with two cards of equal rank and three cards which are different from these and from each other. When comparing two such hands, the hand with the higher pair is better - so for example 6-6-4-3-2 beats 5-5-A-K-Q. If the pairs are equal, compare the highest ranking odd cards from each hand; if these are equal compare the second highest odd card, and if these are equal too compare the lowest odd cards. So J-J-A-9-3 beats J-J-A-8-7 because the 9 beats the 8.
9. Nothing
Five cards which do not form any of the combinations listed above. This combination is often called High Card and sometimes No Pair. The cards must all be of different ranks, not consecutive, and contain at least two different suits. When comparing two such hands, the one with the better highest card wins. If the highest cards are equal the second cards are compared; if they are equal too the third cards are compared, and so on. So A-J-9-5-3 beats A-10-9-6-4 because the jack beats the ten.
Hand Ranking in Low Poker
There are several poker variations in which the lowest hand wins: these are sometimes known as Lowball. There are also 'high-low' variants in which the pot is split between the highest and the lowest hand. A low hand with no combination is normally described by naming its highest card - for example 8-6-5-4-2 would be described as '8-down' or '8-low'.
It first sight it might be assumed that in low poker the hands rank in the reverse order to their ranking in normal (high) poker, but this is not quite the case. There are several different ways to rank low hands, depending on how aces are treated and whether straights and flushes are counted.
Ace to Five
This seems to be the most popular system. Straights and flushes do not count, and Aces are always low. The best hand is therefore 5-4-3-2-A, even if the cards are all in one suit. Then comes 6-4-3-2-A, 6-5-3-2-A, 6-5-4-2-A, 6-5-4-3-A, 6-5-4-3-2, 7-4-3-2-A and so on. Note that when comparing hands, the highest card is compared first, just as in standard poker. So for example 6-5-4-3-2 is better than 7-4-3-2-A because the 6 is lower than the 7. The best hand containing a pair is A-A-4-3-2. This version is sometimes called 'California Lowball'.
When this form of low poker is played as part of a high-low split variant, there is sometimes a condition that a hand must be 'eight or better' to qualify to win the low part of the pot. In this case a hand must consist of five unequal cards, all 8 or lower, to qualify for low. The worst such hand is 8-7-6-5-4.
Deuce to Seven
The hands rank in almost the same order as in standard poker, with straights and flushes counting and the lowest hand wins. The difference from normal poker is that Aces are always high , so that A-2-3-4-5 is not a straight, but ranks between K-Q-J-10-8 and A-6-4-3-2. The best hand in this form is 7-5-4-3-2 in mixed suits, hence the name 'deuce to seven'. The next best is 7-6-4-3-2, then 7-6-5-3-2, 7-6-5-4-2, 8-5-4-3-2, 8-6-4-3-2, 8-6-5-3-2, 8-6-5-4-2, 8-6-5-4-3, 8-7-4-3-2, etc. The highest card is always compared first, so for example 8-6-5-4-3 is better than 8-7-4-3-2 even though the latter contains a 2, because the 6 is lower than the 7. The best hand containing a pair is 2-2-5-4-3, but this would be beaten by A-K-Q-J-9 - the worst 'high card' hand. This version is sometimes called 'Kansas City Lowball'.
Ace to Six
Many home poker players play that straights and flushes count, but that aces can be counted as low. In this version 5-4-3-2-A is a bad hand because it is a straight, so the best low hand is 6-4-3-2-A. There are a couple of issues around the treatment of aces in this variant.
- First, what about A-K-Q-J-10? Since aces are low, this should not count as a straight. It is a king-down, and is lower and therefore better than K-Q-J-10-2.
- Second, a pair of aces is the lowest and therefore the best pair, beating a pair of twos.
It is likely that some players would disagree with both the above rulings, preferring to count A-K-Q-J-10 as a straight and in some cases considering A-A to be the highest pair rather than the lowest. It would be wise to check that you agree on these details before playing ace-to-six low poker with unfamiliar opponents.
Selecting from more than five cards
Note that in games where more than five cards are available, the player is free to select whichever cards make the lowest hand. For example a player in Seven Card Stud Hi-Lo 8 or Better whose cards are 10-8-6-6-3-2-A can omit the 10 and one of the 6's to create a qualifying hand for low.
Poker Hand Ranking with Wild Cards
A wild card card that can be used to substitute for a card that the holder needs to make up a hand. In some variants one or more jokers are added to the pack to act as wild cards. In others, one or more cards of the 52-card pack may be designated as wild - for example all the twos ('deuces wild') or the jacks of hearts and spades ('one-eyed jacks wild', since these are the only two jacks shown in profile in Anglo-American decks).
The most usual rule is that a wild card can be used either
- to represent any card not already present in the hand, or
- to make the special combination of 'five of a kind'.
This approach is not entirely consistent, since five of a kind - five cards of equal rank - must necessarily include one duplicate card, since there are only four suits. The only practical effect of the rule against duplicates is to prevent the formation of a 'double ace flush'. So for example in the hand A-9-8-5-joker, the joker counts as a K, not a second ace, and this hand is therefore beaten by A-K-10-4-3, the 10 beating the 9.
Five of a Kind
When playing with wild cards, five of a kind becomes the highest type of hand, beating a royal flush. Between fives of a kind, the higher beats the lower, five aces being highest of all.
The Bug
Some games, especially five card draw, are often played with a bug. This is a joker added to the pack which acts as a limited wild card. It can either be used as an ace, or to complete a straight or a flush. Thus the highest hand is five aces (A-A-A-A-joker), but other fives of a kind are impossible - for example 6-6-6-6-joker would count as four sixes with an ace kicker and a straight flush would beat this hand. Also a hand like 8-8-5-5-joker counts as two pairs with the joker representing an ace, not as a full house.
Wild Cards in Low Poker
In Low Poker, a wild card can be used to represent a card of a rank not already present in the player's hand. It is then sometimes known as a 'fitter'. For example 6-5-4-2-joker would count as a pair of sixes in normal poker with the joker wild, but in ace-to-five low poker the joker could be used as an ace, and in deuce-to-seven low poker it could be used as a seven to complete a low hand.
Lowest Card Wild
Some home poker variants are played with the player's lowest card (or lowest concealed card) wild. In this case the rule applies to the lowest ranked card held at the time of the showdown, using the normal order ace (high) to two (low). Aces cannot be counted as low to make them wild.
Texas Holdem Point System
Double Ace Flush
Some people play with the house rule that a wild card can represent any card, including a duplicate of a card already held. It then becomes possible to have a flush containing two or more aces. Flushes with more than one ace are not allowed unless specifically agreed as a house rule.
Natural versus Wild
Some play with the house rule that a natural hand beats an equal hand in which one or more of the cards are represented by wild cards. This can be extended to specify that a hand with more wild cards beats an otherwise equal hand with fewer wild cards. This must be agreed in advance: in the absence of any agreement, wild cards are as good as the natural cards they represent.
Incomplete Hands
In some poker variants, such as No Peek, it is necessary to compare hands that have fewer than five cards. With fewer than five cards, you cannot have a straight, flush or full house. You can make a four of a kind or two pairs with only four cards, triplets with three cards, a pair with two cards and a 'high card' hand with just one card.
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The process of comparing first the combination and then the kickers in descending order is the same as when comparing five-card hands. In hands with unequal numbers of cards any kicker that is present in the hand beats a missing kicker. So for example 8-8-K beats 8-8-6-2 because the king beats the 6, but 8-8-6-2 beats 8-8-6 because a 2 is better than a missing fourth card. Similarly a 10 by itself beats 9-5, which beats 9-3-2, which beats 9-3, which beats a 9 by itself.
Ranking of suits
In standard poker there is no ranking of suits for the purpose of comparing hands. If two hands are identical apart from the suits of the cards then they count as equal. In standard poker, if there are two highest equal hands in a showdown, the pot is split between them. Standard poker rules do, however, specify a hierarchy of suits: spades (highest), hearts, diamonds, clubs (lowest) (as in Contract Bridge), which is used to break ties for special purposes such as:
- drawing cards to allocate players to seats or tables;
- deciding who bets first in stud poker according to the highest or lowest upcard;
- allocating a chip that is left over when a pot cannot be shared exactly between two or more players.
I have, however, heard from several home poker players who play by house rules that use this same ranking of suits to break ties between otherwise equal hands. For some reason, players most often think of this as a way to break ties between royal flushes, which would be most relevant in a game with many wild cards, where such hands might become commonplace. However, if you want to introduce a suit ranking it is important also to agree how it will apply to other, lower types of hand. If one player A has 8-8-J-9-3 and player B has 8-8-J-9-3, who will win? Does player A win by having the highest card within the pair of eights, or does player B win because her highest single card, the jack, is in a higher suit? What about K-Q-7-6-2 against K-Q-7-6-2 ? So far as I know there is no universally accepted answer to these questions: this is non-standard poker, and your house rules are whatever you agree that they are. Three different rules that I have come across, when hands are equal apart from suit are:
- Compare the suit of the highest card in the hand.
- Compare the suit of the highest paired card - for example if two people have J-J-7-7-K the highest jack wins.
- Compare the suit of the highest unpaired card - for example if two people have K-K-7-5-4 compare the 7's.
Although the order spades, hearts, diamonds, clubs may seem natural to Bridge players and English speakers, other suit orders are common, especially in some European countries. Up to now, I have come across:
- spades (high), hearts, clubs, diamonds (low)
- spades (high), diamonds, clubs, hearts (low)
- hearts (high), spades, diamonds, clubs (low) (in Greece and in Turkey)
- hearts (high), diamonds, spades, clubs (low) (in Austria and in Sweden)
- hearts (high), diamonds, clubs, spades (low) (in Italy)
- diamonds (high), spades, hearts, clubs (low) (in Brazil)
- diamonds (high), hearts, spades, clubs (low) (in Brazil)
- clubs (high), spades, hearts, diamonds (low) (in Germany)
As with all house rules, it would be wise to make sure you have a common understanding before starting to play, especially when the group contains people with whom you have not played before.
Stripped Decks
In some places, especially in continental Europe, poker is sometimes played with a deck of less than 52 cards, the low cards being omitted. Italian Poker is an example. As the pack is reduced, a Flush becomes more difficult to make, and for this reason a Flush is sometimes ranked above a Full House in such games. In a stripped deck game, the ace is considered to be adjacent to the lowest card present in the deck, so for example when using a 36-card deck with 6's low, A-6-7-8-9 is a low straight.
Playing poker with fewer than 52 cards is not a new idea. In the first half of the 19th century, the earliest form of poker was played with just 20 cards - the ace, king, queen, jack and ten of each suit - with five cards dealt to each of four players. The only hand types recognised were, in descending order, four of a kind, full house, three of a kind, two pairs, one pair, no pair.
No Unbeatable Hand
In standard poker a Royal Flush (A-K-Q-J-10 of one suit) cannot be beaten. Even if you introduce suit ranking, the Royal Flush in the highest suit is unbeatable. In some regions, it is considered unsatisfactory to have any hand that is guaranteed to be unbeaten - there should always be a risk. There are several solutions to this.
In Italy this is achieved by the rule 'La minima batte la massima, la massima batte la media e la media batte la minima' ('the minimum beats the maximum, the maximum beats the medium and the medium beats the minimum'). A minimum straight flush is the lowest that can be made with the deck in use. Normally they play with a stripped deck so for example with 40 cards the minimum straight flush would be A-5-6-7-8 of a suit. A maximum straight flush is 10-J-Q-K-A of a suit. All other straight flushes are medium. If two players have medium straight flushes then the one with higher ranked cards wins as usual. Also as usual a maximum straight flush beats a medium one, and a medium straight flush beats a minimum one. But if a minimum straight flush comes up against a maximum straight flush, the minimum beats the maximum. In the very rare case where three players hold a straight flush, one minimum, one medium and one maximum, the pot is split between them. See for example Italian Poker.
In Greece, where hearts is the highest suit, A-K-Q-J-10 is called an Imperial Flush, and it is beaten only by four of a kind of the lowest rank in the deck - for example 6-6-6-6 if playing with 36 cards. Again, in very rare cases there could also be a hand in the showdown that beats the four of a kind but is lower than the Imperial Flush, in which case the pot would be split.
Hand probabilities and multiple decks
The ranking order of poker hands corresponds to their probability of occurring in straight poker, where five cards are dealt from a 52-card deck, with no wild cards and no opportunity to use extra cards to improve a hand. The rarer a hand the higher it ranks.
This is neither an essential nor an original feature of poker, and it ceases to be true when wild cards are introduced. In fact, with a large number of wild cards, it is almost inevitable that the higher hand types will be the commoner, not rarer, since wild cards will be used to help make the most valuable type of hand from the available cards.
Mark Brader has provided probability tables showing the frequency of each poker hand type when five cards are dealt from a 52-card deck, and also showing how these probabilities would change if multiple decks were used.
On This Page
Introduction
Casino Hold 'Em is a poker variation, similar to Texas Hold 'Em, that is played in Egypt, Russia, South Africa, Holland, Latvia, Estonia, Ireland, Morocco, Malta, Ukraine, Panama, and Romania. It is also available to play online at casinos using Net Gaming, Real Time Gaming, Playtech, Gamesys, and Galewind Software.
The game also goes by the name Casino Hold 'Em Open. Under this name, the rules are the same except the player hole cards are dealt face up. In normal Casino Hold 'Em they are dealt face down.
Rules
The rules are as follows.
- Play begins with each player making an Ante wager. There is also an optional Progressive Jackpot side bet.
- The dealer gives the player and himself two hole cards and three community cards face up on the table.
- Each player must decide to either fold or call. If the player folds, then he gives up his cards and his Ante bet. If the player calls, then the Call bet must be equal to two times the Ante bet.
- The dealer will then deal two more community cards, for a total of five. The dealer will then turn over his own two cards.
- Both hands shall be scored according the highest poker value of the two hole cards and five community cards.
- The dealer must have a pair of fours or better to qualify. If the dealer does not qualify then the Ante will pay according to the Ante pay table below and the Call bet will push.
- If the dealer qualifies and beats the player, then the player will lose both the Ante and Call.
- If the dealer qualifies and the player beats the dealer then the Ante will pay according to the Ante pay table below and the Call bet will pay 1 to 1.
- If the dealer qualifies and the player ties the dealer then both Ante and Call bets will push.
- The Progressive Jackpot side bet pays based on the player's final seven card hand only, even if the player folded or loses to the dealer. More on this bet at the bottom of the page.
Ante Pay Table
| Hand | Table 1 | Table 2 | Table 3 | Table 4 |
|---|---|---|---|---|
| Royal flush | 20 | 25 | 100 | 100 |
| Straight flush | 20 | 25 | 20 | 49 |
| 4 of a kind | 10 | 12 | 10 | 17 |
| Full house | 3 | 3 | 3 | 3 |
| Flush | 2 | 2 | 2 | 2 |
| All other | 1 | 1 | 1 | 1 |
Caribbean Hold 'Em Warning
Be warned that Realtime Gaming has an imitation of this game called Caribbean Hold 'Em. However, they pay 1 to 1 on the Ante if the dealer doesn't qualify, as opposed to the full Ante Bonus pay table. Nowhere is this rule change disclosed in their game rules, I might add.
Analysis
The following table shows the number of combination, probability, and contribution to the return of all possible outcomes under ante pay table 3, which I'm told is the most frequently used. The lower right cell shows a house edge of 2.16%.
Return Table — Pay Table 3Expand
| Hand | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Player wins with royal flush | 102 | 736259040 | 0.000026 | 0.002700 |
| Player has royal flush, dealer doesn't qualify | 100 | 119892960 | 0.000004 | 0.000431 |
| Player wins with straight flush | 22 | 6001122284 | 0.000216 | 0.004747 |
| Player has straight flush, dealer doesn't qualify | 20 | 1089672828 | 0.000039 | 0.000784 |
| Player wins with four of a kind | 12 | 41419896552 | 0.001489 | 0.01787 |
| Player has four of a kind, dealer doesn't qualify | 10 | 909499320 | 0.000033 | 0.000327 |
| Player wins with full house | 5 | 589505037660 | 0.021195 | 0.105973 |
| Player wins with flush | 4 | 505131419580 | 0.018161 | 0.072645 |
| Player wins with straight or less | 3 | 6426670016572 | 0.23106 | 0.693181 |
| Player has full house, dealer doesn't qualify | 3 | 24601676832 | 0.000885 | 0.002654 |
| Player has flush, dealer doesn't qualify | 2 | 168883536432 | 0.006072 | 0.012144 |
| Player has straight or less, dealer doesn't qualify | 1 | 5521376219148 | 0.198512 | 0.198512 |
| Tie | 0 | 678596916580 | 0.024398 | 0 |
| Player folds | -1 | 5009067102600 | 0.180093 | -0.180093 |
| Player loses | -3 | 8839701755612 | 0.317817 | -0.953451 |
| Total | 27813810024000 | 1 | -0.021576 |
The following return table is four pay table 4. The lower right cell shows a house edge of 0.35%. This pay table can be found at Internet casinos using Gamesys N.V. software titled 'Casino Hold 'Em with Zero House Edge.' As you can see, the 'Zero House Edge' part is a misnomer. The player must pay a 10% commission on any net gambling win per session. A 'session' ends after a period of one hour with no bet or 24 hours, whichever happens first.
The owner of Casino Hold 'Em wishes for me to state that Gamesys N.V. is using his game without permission.
Return Table — Pay Table 4Expand
| Hand | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Player wins with royal flush | 102 | 736,259,040 | 0.000026 | 0.002700 |
| Player has royal flush, dealer doesn't qualify | 100 | 119,892,960 | 0.000004 | 0.000431 |
| Player wins with straight flush | 51 | 6,031,161,932 | 0.000217 | 0.011059 |
| Player has straight flush, dealer doesn't qualify | 49 | 1,096,758,936 | 0.000039 | 0.001932 |
| Player wins with four of a kind | 19 | 41,421,337,056 | 0.001489 | 0.028295 |
| Player has four of a kind, dealer doesn't qualify | 17 | 909,634,104 | 0.000033 | 0.000556 |
| Player wins with full house | 5 | 589,638,417,816 | 0.021199 | 0.105997 |
| Player wins with flush | 4 | 505,727,272,920 | 0.018183 | 0.072730 |
| Player wins with straight or less | 3 | 6,429,871,396,516 | 0.231175 | 0.693526 |
| Player has full house, dealer doesn't qualify | 3 | 24,601,738,176 | 0.000885 | 0.002654 |
| Player has flush, dealer doesn't qualify | 2 | 169,051,416,912 | 0.006078 | 0.012156 |
| Player has straight or less, dealer doesn't qualify | 1 | 5,526,154,486,512 | 0.198684 | 0.198684 |
| Tie | 0 | 679,763,871,140 | 0.024440 | 0.000000 |
| Player folds | -1 | 4,984,375,678,920 | 0.179205 | -0.179205 |
| Player loses | -3 | 8,854,310,701,060 | 0.318342 | -0.955027 |
| Total | 27,813,810,024,000 | 1.000000 | -0.003511 |
I would like to thank Stephen How of Discount Gambling for supplying the combinations in pay table 4.
The only pay tables fully analyzed are 3 and 4, because it takes my computer about a month to cycle through all possible combinations. However, assuming the player was following optimal strategy under pay table 3 but playing under pay table 1 or 2, the house edge under pay table 1 would be 2.40%, and under pay table 2 would be 1.96%. The actual house edge under pay tables 1 and 2 would be slightly less or equal to these figures.
Strategy
Unfortunately, there is no easy way to quantify optimal strategy for this game. I can say that the optimal strategy player will raise 82% of the time. So only in the worst 18% of hands should the player fold. In general these are when the player has two singletons in the hole that are low compared to the flop, with little or no chance for a straight or flush.
Side Bets
The only side bet I am aware of for this game is known as the AA+. It pays based on the poker value of the player's hand after the flop. There are three known pay tables, as follows:
AA+ Pay Tables
| Hand | Pay Table 1 | Pay Table 2 | Pay Table 3 |
|---|---|---|---|
| Royal Flush | 25 | 100 | 100 |
| Straight flush | 25 | 50 | 50 |
| 4 of a kind | 25 | 40 | 40 |
| Full house | 25 | 30 | 30 |
| Flush | 25 | 20 | 20 |
| Straight | 7 | 7 | 10 |
| Three of a kind | 7 | 7 | 8 |
| Two pair | 7 | 7 | 7 |
| Pair of aces | 7 | 7 | 7 |
| House edge | 6.40% | 6.26% | 2.97% |
Pay tables 1 and 2 can be found in land casinos. Pay table 3 is used by Internet casinos using Gamesys software.
As an example, following is the full return table for Pay Table 1.
AA+ Side Bet — Pay Table 1
| Hand | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Royal Flush | 25 | 4 | 0.000002 | 0.000038 |
| Straight flush | 25 | 36 | 0.000014 | 0.000346 |
| 4 of a kind | 25 | 624 | 0.000240 | 0.006002 |
| Full house | 25 | 3744 | 0.001441 | 0.036014 |
| Flush | 25 | 5108 | 0.001965 | 0.049135 |
| Straight | 7 | 10200 | 0.003925 | 0.027473 |
| Three of a kind | 7 | 54912 | 0.021128 | 0.147899 |
| Two pair | 7 | 123552 | 0.047539 | 0.332773 |
| Pair of aces | 7 | 84480 | 0.032505 | 0.227537 |
| Other | -1 | 2316300 | 0.891241 | -0.891241 |
| Total | 2598960 | 1 | -0.064023 |
Progressive Jackpot
The Progressive Jackpot bet shall pay based on the player's two hole cards and the five community cards only. It does not matter whether or not the player folds or loses to the dealer. In the event of a straight flush or royal flush on the board, all players who made the Progressive Jackpot bet shall split the win.
The following table shows the probability and contribution to the return for each event. Obviously, the return from the top two awards will depend on the jackpot size, so are treated as unknowns.
Progressive Jackpot
| Hand | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Royal flush | Jackpot | 4,324 | 0.000032 | x |
| Straight flush | 10% of Jackpot | 37,260 | 0.000279 | y |
| 4 of a kind | $100.00 | 224,848 | 0.001681 | 0.168100 |
| Full house | $10.00 | 3,473,184 | 0.025961 | 0.259610 |
| Other | $0.00 | 130,044,944 | 0.972047 | 0.000000 |
| Total | $0.00 | 133,784,560 | 1.000000 | 0.487931+x+y |
The table above shows the fixed wins return 42.77% of the amount bet. Assuming the player is playing alone, for every $1,000 in the meter the return will increase by 6.02%. Under the same assumption, the break-even point is $9,503.22. Due to jackpot sharing, the return will go down slightly according to the number of other players making the bet.
Jumbo Jackpot
There is another progressive jackpot called the 'Jumbo Jackpot.' The following table shows the wins, probabilities and the contribution to the return for each type of winning hand.
Jumbo Jackpot
| Hand | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| 7-card straight flush | ? | 32 | 0.00000024 | x |
| 6-card straight flush | $5,000.00 | 752 | 0.00000562 | 0.028105 |
| 5-card straight flush | $250.00 | 40,800 | 0.00030497 | 0.076242 |
| 4 of a kind | $50.00 | 224,848 | 0.00168067 | 0.084034 |
| Full house | $5.00 | 3,473,184 | 0.02596102 | 0.129805 |
| Flush | $4.00 | 4,047,644 | 0.03025494 | 0.121020 |
| Straight | $2.00 | 6,180,020 | 0.04619382 | 0.092388 |
| Other | $0.00 | 119,817,280 | 0.89559871 | 0.000000 |
| Total | $0.00 | 133,784,560 | 1.00000000 | 0.531593 |
The return for the top award depends on the amount in the jackpot. I can say that all the other wins return 53.16% of money bet. For every 100,000 bet units in the meter the return increases by 2.39%. At a jackpot of $1,958,300.75 the return reaches 100%.
Progressive Jackpot Side Bet
There is yet another side bet based on the player's first two cards and the three-card flop. I put information about it in my page titled Casino Hold Em Progressive Jackpot Side Bet'.
Casino Razz Bonus
I believe this side bet pays according to the poker value of the player's two hole cards and the three cards on the flop -- the lower the poker value, the more it pays. For all the rules and analysis, please see my page on Casino Razz Bonus.
Methodology
The above analysis was performed using a brute force combinatorial program that analyzed all 27,813,810,024,000 possible outcomes, and played every hand according to optimal player strategy. It took my computers about a month to crank though the 27.8 trillion hands.
External Links
The web site for Casino Hold'em, as well as other games, is www.casinopokergames.com.
There is a good Casino Hold 'Em calculator at beatingbonuses.com.
Texas Holdem Point System
Written by:Michael Shackleford