There are 2,598,960 many possible 5-card Poker hands. Thus the probability of obtaining any one specific hand is 1 in 2,598,960 (roughly 1 in 2.6 million). The probability of obtaining a given type of hands (e.g. Three of a kind) is the number of possible hands for that type over 2,598,960. Thus this is primarily a counting exercise. Eliminating identical hands that ignore relative suit values leaves 6,009,159 distinct 7-card hands. The number of distinct 5-card poker hands that are possible from 7 cards is 4,824. Perhaps surprisingly, this is fewer than the number of 5-card poker hands from 5 cards because some 5-card hands are impossible with 7 cards (e.g. Straight flush 40 There are four suits (spades, hearts, diamond, clubs). Using TABLE 1, 4(10) = 40.

1. Hands Of Poker In Order
2. List Of Best Poker Hands
3. Number Of Unique Poker Hands Symbols

This page is based partly on information from Ka Lun, Anthony Horsley Sr, Don Smolen, Richard Dewhirst, Alan Ho, Brandon Bahti and several anonymous correspondents.

Introduction

This Chinese gambling game is popular in Hong Kong and parts of Southeast Asia and is also played to some extent in the USA. It is known by several different names.

• In Cantonese it is called Sap Sam Cheung (十三張), which means 13 cards, and in Vietnamese it is known by the similar name Xập Xám Chướng.
• In Chinese, it is also sometimes called Luosong Pai Jiu (羅宋牌九), which I think means Russian Pai Gow. The game is indeed distantly related to Pai Gow.
• In the USA it is often known as Chinese Poker or sometimes Russian Poker, but note that some people also use the name Chinese Poker to refer to the climbing game Big Two. In Hawaii it is called Pepito.
• In the Phillipines it is known as Pusoy, again not to be confused with Pusoy Dos, which is Big Two. Another name sometimes used is Good, Better, Best, referring to the three hands of a player.

The aim is to arrange your 13 cards into three poker hands - two of five cards and one of three cards - which will beat the corresponding poker hands made by the other players.

A recent development is Open Face Chinese Poker, in which after the first five cards, hands are built face up one card at a time.

Players, Cards, Stakes and Deal

I’m assuming on the basis of your calculation that you’re talking about five-card hands from a standard deck. There are 13 ways to choose the rank of the triplet, and 4 ways to choose which of the four suits is not reprsented in it. There are then 48 cards of the other ranks, so there are 48 ways to choose one of them. In this unique poker variant, players are dealt three cards and can decide to play their hand or not by simultaneously dropping a chip in the centre of the table. The winner takes the pot, and the losers match it.

There are four players, each playing for themselves. A standard 52 card pack is used.

Before playing it is necessary to agree on a stake. Below I will describe the payments in terms of units; one unit can be worth whatever the players agree in advance - $1, $10, $100, etc.

The cards are shuffled, cut and dealt out singly: 13 cards to each player.

Arrangement of cards

Each player must divide their 13 cards into a 'back' hand of 5 cards, a 'middle' hand of 5 cards and a 'front' hand of 3 cards. Considered as poker hands, the back hand must be better than the middle hand, and the middle hand must be better than the front hand. The standard poker ranking is used - so the hand types from high to low are: royal flush, straight flush, four of a kind, full house, flush, straight, three of a kind, two pairs, one pair, high card (see the page on ranking of poker hands). There are no wild cards.

Since the front hand has only 3 cards, only three hand types are possible: three of a kind; one pair; high card. There is no value in having a front hand with three consecutive cards or three cards of the same suit: 'straights' or 'flushes' in the front hand do not count.

Players place their three hands face down in front of them, the front hand nearest the centre of the table and the back hand nearest themselves.

Showdown and Scoring

When everyone is ready, all the players expose their three hands and each pair of players compares the corresponding hands. In the simplest system of payments, you win one unit for each corresponding hand of another player that you beat and lose one for unit each hand that beats you. When the hands are equal you neither win nor lose. Here is an example:

The result would be as follows:

Players	front winner	middle winner	back winner	North	East	South	West
North v East	North	North	North	+3	-3
North v South	South	South	North	-1		+1
North v West	North	North	West	+1			-1
East v South	South	South	East		-1	+1
East v West	East	West	West		-1		+1
South v West	South	South	West			+1	-1
Total				+3	-5	+3	-1

Notice that although West's back hand is the overall best hand (aces full), West loses on balance because of the weaker middle and front hands. East could have done slightly less badly by putting the sevens in the middle hand, which would then have beaten West. Notice also that it is not legal for East to put the jacks in the front hand, because it would then not be possible to make a middle hand that was better and a back hand that was better still from the remaining ten cards.

Special Hands

It is possible to play using just the payments described above. However, many players add two further features to the stakes: increased payments for certain hands, and some special 13-card hands that win automatically. If you are playing with these it is important to agree in advance exactly which ones are allowed and how much each is worth.

A typical scale of increased payments is as follows:

• If you win the front hand with three of a kind, you receive 3 units instead of 1 for that hand.
• If you win the middle hand with a full house, you receive 2 units instead of 1 for that hand.
• If you win the back (or middle) hand with 4 of a kind, you receive 4 units instead of 1.
• If you win the back (or middle) hand with a royal flush or straight flush you win 5 units instead of 1.

These bonuses only count for you for hands that you win. For example if A and B each have a 3 of a kind in front, but B's is higher, A will pay B 3 units for it. A's 3 of a kind will still count against the other players if it wins.

Example:A has 6-6-6, 4-4-4-9-9, K-K-K-8-8 and B has Q-Q-7, J-J-J-2-2, 5-5-5-5-A. A wins 3 for the front hand, but B wins 2 for the middle and 4 for the back, so altogether A pays 3 units to B.

When special hands are allowed, the following 13-card hands win automatically against any ordinary hand, if declared before the hands are exposed. When two special hands come up against each other, the higher wins the full specified amount and the lower loses its value (though it can still win against the other players). After the special hands have been dealt with, the remaining players expose their cards and settle up among themselves in the normal way. A typical schedule of special hands, in ascending order, is:

• Six pairs: a hand with six pairs and one odd card. When two players have six pair hands, compare the highest pair; if the highest pairs are equal compare the second highest pair, and so on. Win 3 units.
• Three straights: the back and middle hands are five card straights and the front hand is a three card straight (i.e. three cards of consecutive rank). If two players have three straights, compare the highest (back) straights first, then if these are equal the middle straights, and finally, if all else is equal, the front straight. Win 3 units.
• Three flushes: the back and middle hands are flushes, and the front hand is a three-card flush (three cards of one suit). If two players have this, the player with the better back hand wins; if tied the better middle hand; if those are also tied, the better front hand. Win 3 units.
• Complete straight: the hand has one card of each rank: A-2-3-4-5-6-7-8-9-10-J-Q-K. Suits can be mixed. If two players have this, they are tied. Win 13 units.

A player who has a special hand can choose not to declare it, but instead to set three hands of 5, 5 and 3 cards in the normal way. This loses the right to an automatic win, but it may occasionally be possible to win more units in the normal settlement, when extra payments can be won.

Variations

There seem to be numerous variations in the way the payments are organised. Here are the ones I have so far discovered.

Playing against the house

One player, probably the dealer, is the house (bank, casino). The other players compare their hands with the house, but not with each other, and pay or receive accordingly. When an individual hand is tied, the house wins it.

Extra payment for sweep

Some play that a player who wins all three hands against another player is paid an extra 1 unit (or sometimes 3 units) for a sweep.

Higher payment in the middle

Some play that winning with four of a kind or a straight flush in the middle is worth an extra point, so 5 in the middle or 4 at the back for quads and 6 in the middle or 5 at the back for a straight flush.

The overall point

Some play that between each pair of players, the net winner wins one additional unit - the overall point. This makes it more important to try to win two hands out of three whenever possible. If playing with extra payments for straight flush, quads, etc., these are taken into account in deciding who gets the overall point.

Single winner

Anthony Horsley Sr reports a version of Pusoy played in the Philippines in which apparently there is just one winner of each deal. In order to win, you have to beat each of the other players on at least two out of three hands. Presumably if no one achieves this, no one wins.

Extra payments counted for losing hands

Some play that instead of the increased payments for certain types of winning hand, the following extra payments count, irrespective of whether the hand in question wins or loses:

• Three of a kind in the front hand: 2 extra units
• Full house in the middle hand: 1 extra unit
• Four of a kind in the back or middle hand: 3 extra units
• Straight or royal flush in the back or middle hand: 4 extra units

This variation is often combined with the overall point variation above.

Surrender

Some play that a player with a poor hand can surrender before the hands are exposed. If you surrender, you pay each of the other players as though you had lost two out of three hands - one unit each, or two units each if you play the version with the overall point. If playing with a banker, then of course a surrendering player just pays the banker, and a surrendering banker pays each of the players.

Winning from a pool

Some play that each player contributes 3 units to a pool before the deal. Instead of comparing the hands between pairs of players, whichever of the four players has the best front hand collects 4 units, the player with the best middle hand collects 4 units, and the player with the best back hand collects 4 units. Some play that if one player wins all three hands, the collect the whole pool and each of the other players has to pay them an additional 3 units.

No pictures

I have been told that some people regard a hand containing no pictures as a special hand giving an automatic win, but I don't know how many units it is worth or how it ranks with respect to the other special hands.

Malayan Sap Sam Cheung

In his book 'Gambling Games of Malaya', C.T.Dobree describes a version of Sap Sam Cheung in which three players play against the bank. The bank wins ties on individual hands as usual. Extra payments count irrespective of whether the hand wins or loses, as follows:

• Three of a kind in the front hand: 2 extra units
• Full house in the middle hand: 2 extra units
• Four of a kind in the back hand: 4 extra units
• Four of a kind in the middle hand: 6 extra units
• Straight or royal flush in the back hand: 6 extra units
• Straight or royal flush in the middle hand: 8 extra units

The special hands, in ascending order, are:

• Three flushes: 3 units
• Three straights: 4 units
• Six and a half pairs: 4 units
• Five pairs and one three of a kind: 5 units
• Four threes of a kind and an odd card: 6 units
• All cards are the same colour: 10 points
• Small: all cards are 2, 3, 4, 5, 6, 7, 8: 10 points
• Big: all cards are 8, 9, 10, J, Q, K, A: 10 points
• Three fours of a kind and one odd card: 16 units
• Three straight flushes: 18 units
• All 12 picture cards plus any 13th card: 18 units
• All thirteen cards of one suit: 26 units

A special hand, if declared before the cards are exposed, beats any normal hand and wins the number of units specified in the table (a player wins from the bank, or the bank wins from all players). If the bank and a player both have special hands, the holder of the higher scoring hand wins the difference between their values.

Vietnamese Version

Phong Le gives the special scores for the Vietnamese game Xập Xám as follows:

• Three of a kind in front: 3 units instead of 1
• Full house in the middle: 2 units instead of 1
• Four of a kind at the back: 4 units; in the middle: 8 units
• Straight flush at the back: 5 units; in the middle: 10 units

Some play that a player who wins all three hands against one opponent is paid double; a player who wins all three hands against all opponents is paid triple.

The scores for special hands are:

• Three straights: 3 units
• Three flushes: 3 units
• Six pairs: 3 units
• Five pairs and one triplet: 6 units
• Complete straight A to K with mixed suits: 13 units; if all 13 cards are of one suit: 26 units.

Hands Of Poker In Order

I am told that in some places there is the tradition that if anyone is dealt a complete suit of 13 cards, all those present, including both players and non-players who may be watching the game, have to empty their pockets and give all their money to the winner.

Singapore Version

Alan Ho describes a version played in Singapore.

The special 13-card hands are known as Claims. The 13-card straight is known as a Dragon (Yi Tiao Long: 一条龙) and wins 13 units (or according to some players 26 units). Six and a half pairs, three straights, or three flushes each worth 3 units as usual. There is an additional hand called 'small cards', in which all 13 cards must be in the range 2 to 9 (or according to some players 2 to 10): this also wins 3 units from each opponent.

If two of these 3-point special hands come up against each other, neither player pays the other. However a Dragon beats any other hand and is paid the full 13 (or 26) units.

The payments for winning with strong hands in front, middle and back are:

• Three of a kind in front: 3 units instead of 1
• Full house in the middle: 2 units instead of 1
• Four of a kind at the back: 4 units; in the middle: 8 units
• Straight flush at the back 7 units; in the middle: 14 units

List Of Best Poker Hands

Some play that a player who wins all three hands against all opponents is paid double - that is 6 points each instead of 3, assuming that no special hands are involved.

Some play that if no one is willing to deal, the player who held the Ace of Spades must deal the next hand, and is paid 1 unit compensation by each opponent for this extra work.

Hawaiian Gardens Casino version

Brandon Bahti describes a version played at the Hawaiian Gardens Casino in California. The special 13-card hands are:

• Three straights: 4 units
• Three flushes: 4 units
• 12 red cards and 1 black or 12 black and 1 red: 4 units
• All black or all red: 6 units
• Six pairs: 4 units
• Complete straight A to K with mixed suits: 13 units
• All 13 cards of one suit: 39 units

If two special hands come up against each other, the holder of the lower valued hand pays the difference (if they are equal there is no payment between these two players).

A player wins two out of three hands against an opponent receives 1 unit from that opponent. For winning all three hands the payment is 6 units. A player who wins all three hands against every other player is paid 9 units (instead of 6) by each. For winning with particular hands in particular positions there are additional payments as follows:

• Straight flush: 5 units at the back; 10 units in the middle
• Four of a kind: 4 units at the back; 8 units in the middle
• Full house: 2 units in the middle
• Three of a kind: 3 units at the front

A player who surrenders pays 3 units to each opponent.

Some play with an extra side bet on the number of aces held. One aces is worth 1, two aces 2, three aces 6, four aces 8. Between two players, the player with fewer aces pays the difference in units, in addition to the payments for the Chinese Poker game.

Payments are made in chips and it is not possible to win or lose more chips than you had in front of you at the start of the deal. Settlement is in clockwise order staring with the dealer. Any 13-card special hands are settled first, followed by all other payments. Specifically, if the players in clockwise order are A (dealer), B, C, D then settlements are made in the order A vs B, A vs C, A vs D, B vs C, B vs D, C vs D. Example: A starts with only 8 chips. A wins all three hands against B and loses all three against C. B pays A 6 chips, but A pays only 2 chips to C, because each chip is either doubled or lost, and A's first 6 chips have already been 'used' to justify the win from B. Therefore A ends up with 8+6-2=12 chips. A neither pays to nor receives from D since the transactions with B and C have already accounted for all A's chips. Players can buy additional chips from the house after the settlement and before the next deal.

The casino takes a fixed rake per hand, and part of this is used to build jackpots that are offered for certain unusual events - for example when a player has a straight flush, three of a kind, and a pair and loses all three hands to another player.

Open Face Chinese Poker

This variant, which became popular worldwide in 2012, is now described on a separate page.

Other Chinese Poker web pages

Further information can be found on Don Smolen's Chinese Poker page. From there you can also order his excellent book on the tactics of this game, and obtain his CPOKER computer program.

Rules for a version of Chinese Poker can also be found under the name Pusoy on this archive copy the Bicycle Cards web site.

Rules for Chinese Poker can also be found at the Asian Games Site vinagames.com, where it is possible to play Chinese Poker on line.

Playing Chinese Poker Online

Number Of Unique Poker Hands Symbols

With Phong Le's Chinese Poker Analyser you can compare the power of alternative divisions of 13 cards into three hands, and play Chinese Poker (Xap Xam) against one, two or three computer players.