Poker Hand Rankings. How to Play Poker. General Rules. Hand Rankings. Today, CardPlayer.com is the best poker information portal for free poker content.
- 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. 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.
- Poker Hand Rankings. How to Play Poker. General Rules. Hand Rankings. Today, CardPlayer.com is the best poker information portal for free poker content.
For a great training video on poker combinatorics, check out this poker combos video.
'Combinatorics' is a big word for something that isn’t all that difficult to understand. In this article, I will go through the basics of working out hand combinations or 'combos' in poker and give a few examples to help show you why it is useful.
Oh, and as you’ve probably noticed, 'combinatorics', 'hand combinations' and 'combos' refer to the same thing in poker. Don’t get confused if I use them interchangeably, which I probably will.
What is poker combinatorics?
Poker combinatorics involves working out how many different combinations of a hand exists in a certain situation.
For example:
- How many ways can you be dealt AK?
- How many ways can you be dealt 66?
- How combinations of T9 are there on a flop of T32?
- How many straight draw combinations are there on a flop of AT7?
Using combinatorics, you will be able to quickly work these numbers out and use them to help you make better decisions based on the probability of certain hands showing up.
Poker starting hand combinations basics.
- Any two (e.g. AK or T5) = 16 combinations
- Pairs (e.g. AA or TT) = 6 combinations
If you were take a hand like AK and write down all the possible ways you could be dealt this hand from a deck of cards (e.g. A K, A K, A K etc.), you would find that there are 16 possible combinations.
- See all 16 AK hand combinations:
Similarly, if you wrote down all the possible combinations of a pocket pair like JJ (e.g. JJ, JJ, JJ etc.), you would find that there are just 6 possible combinations.
- See all 6 JJ pocket pair hand combinations:
So as you can see from these basic starting hand combinations in poker, you’re almost 3 times as likely to be dealt a non-paired hand like AK than a paired hand. That’s pretty interesting in itself, but you can do a lot more than this…
Note: two extra starting hand combinations.
As mentioned above, there are 16 combinations of any two non-paired cards. Therefore, this includes the suited and non-suited combinations.
Here are 2 extra stats that give you the total combinations of any two suited and any two unsuited cards specifically.
- Any two (e.g. AK or 67 suited or unsuited) = 16 combinations
- Any two suited (AKs) = 4 combinations
- Any two unsuited (AKo) = 12 combinations
- Pairs (e.g. AA or TT) = 6 combinations
You won’t use these extra starting hand combinations nearly as much as the first two, but I thought I would include them here for your interest anyway.
It’s easy to work out how there are only 4 suited combinations of any two cards, as there are only 4 suits in the deck. If you then take these 4 suited hands away from the total of 16 'any two' hand combinations (which include both the suited and unsuited hands), you are left with the 12 unsuited hand combinations. Easy.
Fact: There are 1,326 combinations of starting hands in Texas Hold’em in total.
Working out hand combinations using 'known' cards.
Let’s say we hold KQ on a flop of KT4 (suits do not matter). How many possible combinations of AK and TT are out there that our opponent could hold?
Unpaired hands (e.g. AK).
How to work out the total number of hand combinations for an unpaired hand like AK, JT, or Q3.
Method: Multiply the numbers of available cards for each of the two cards.
Word equation: (1st card available cards) x (2nd card available cards) = total combinations
Example.
If we hold KQ on a KT4 flop, how many possible combinations of AK are there?
There are 4 Aces and 2 Kings (4 minus the 1 on the flop and minus the 1 in our hand) available in the deck.
C = 8, so there are 8 possible combinations of AK if we hold KQ on a flop of KT4.
Paired hands (e.g. TT).
How to work out the total number of hand combinations for an paired hand like AA, JJ, or 44.
Method: Multiply the number of available cards by the number of available cards minus 1, then divide by two.
Word equation: [(available cards) x (available cards - 1)] / 2 = total combinations
Example.
How many combinations of TT are there on a KT4 flop?
Well, on a flop of KT4 here are 3 Tens left in the deck, so…
C = 3, which means there are 3 possible combinations of TT.
Thoughts on working out hand combinations.
Working out the number of possible combinations of unpaired hands is easy enough; just multiply the two numbers of available cards.
Working out the combinations for paired hands looks awkward at first, but it’s not that tricky when you actually try it out. Just find the number of available cards, take 1 away from that number, multiply those two numbers together then half it.
Note: You’ll also notice that this method works for working out the preflop starting hand combinations mentioned earlier on. For example, if you’re working out the number of AK combinations as a starting hand, there are 4 Aces and 4 Kings available, so 4 x 4 = 16 AK combinations.
Why is combinatorics useful?
Because by working out hand combinations, you can find out more useful information about a player’s range.
For example, let’s say that an opponents 3betting range is roughly 2%. This means that they are only ever 3betting AA, KK and AK. That’s a very tight range indeed.
Now, just looking at this range of hands you might think that whenever this player 3bets, they are more likely to have a big pocket pair. After all, both AA and KK are in his range, compared to the single unpaired hand of AK. So without considering combinatorics for this 2% range, you might think that the probability break-up of each hand looks like this:
- AA = 33%
- KK = 33%
- AK = 33%
…with the two big pairs making up the majority of this 2% 3betting range (roughly 66% in total).
However, let’s look at these hands by comparing the total combinations for each hand:
- AA = 6 combinations (21.5%)
- KK = 6 combinations (21.5%)
- AK = 16 combinations (57%)
So out of 28 possible combinations made up from AA, KK and AK, 16 of them come from AK. This means that when our opponent 3bets, the majority of the time he is holding AK and not a big pocket pair.
Now obviously if you’re holding a hand like 75o this is hardly comforting. However, the point is that it’s useful to realise that the probabilities of certain types of hands in a range will vary. Just because a player either has AA or AK, it doesn’t mean that they’re both equally probable holdings - they will actually be holding AK more often than not.
Analogy: If a fruit bowl contains 100 oranges, 1 apple, 1 pear and 1 grape, there is a decent range of fruit (the 'hands'). However, the the fruits are heavily weighted toward oranges, so there is a greater chance of randomly selecting an orange from the bowl than any of the 3 other possible fruits ('AK' in the example above).
This same method applies when you’re trying to work out the probabilities of a range of possible made hands on the flop by looking at the number of hand combinations. For example, if your opponent could have either a straight draw or a set, which of the two is more likely?
Poker combinatorics example hand.
You have 66 on a board of A J 6 8 2. The pot is $12 and you bet $10. Your opponent moves all in for $60, which means you have to call $50 to win a pot of $82.
You are confident that your opponent either has a set or two pair with an Ace (i.e. AJ, A8, A6 or A2). Don’t worry about how you know this or why you’re in this situation, you just are.
According to pot odds, you need to have at least a 38% chance of having the best hand to call. You can now use combinatorics / hand combinations here to help you decide whether or not to call.
Poker combinatorics example hand solution.
First of all, let’s split our opponent’s hands in to hands you beat and hands you don’t beat, working out the number of hand combinations for each.
Adding them all up…
Seeing as you have the best hand 79% of the time (or 79% 'equity') and the pot odds indicate that you only need to have the best hand 38% of the time, it makes it +EV to call.
So whereas you might have initially thought that the number of hands we beat compared to the number of hands we didn’t beat was close to 50/50 (making it likely -EV to call), after looking at the hand combinations we can see that it is actually much closer to 80/20, making calling a profitable play.
Being able to assign a range to your opponent is good, but understanding the different likelihoods of the hands within that range is better.
Poker combinatorics conclusion.
Working out hand combinations in poker is simple:
- Unpaired hands: Multiply the number of available cards. (e.g. AK on an AT2 flop = [3 x 4] = 12 AK combinations).
- Paired hands: Find the number of available cards. Take 1 away from that number, multiply those two numbers together and divide by 2. (e.g. TT on a AT2 flop = [3 x 2] / 2 = 3 TT combinations).
By working out hand combinations you can gain a much better understanding about opponent’s hand ranges. If you only ever deal in ranges and ignore hand combinations, you are missing out on useful information.
It’s unrealistic to think that you’re going to work out all these hand combinations on the fly whilst you’re sat at the table. However, a lot of value comes from simply familiarising yourself with the varying probabilities of different types of hands for future reference.
For example, after a while you’ll start to realise that straight draws are a lot more common than you think, and that flush draws are far less common than you think. Insights like these will help you when you’re faced with similar decisions in the future.
The next time you’re doing some post session analysis, spend some time thinking about combinatorics and noting down what you find.
Poker combinatorics further reading.
Hand combinations in poker all stem from statistics. So if you’re interested in finding out more about the math side of things, here are a few links that I found helpful:
- Combinations video - Youtube (all the stuff on this channel is awesome)
If you’re more interested in finding out more about combinations in poker only, here are a few interesting reads:
Also, I’d highly recommend you check out the Mathematics of NL Hold’emEp. 2 and Ep. 6 by WiltOnTilt at DeucesCracked for some great video tutorials (and examples) on using hand combinations in poker.
Go back to the awesome Texas Hold'em Strategy.
Can You Afford Not To Use
Poker Tracker 4?
“I wouldn’t play another session of online poker without it”
“I play $25NL, and in under 1 week PT4 had paid for itself”
Comments
Please enable JavaScript to view the comments powered by Disqus.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 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
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.
Best Poker Hands Ever
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.
- 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.
- 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
- 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.
- 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
- 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
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.
Best Poker Hands To Play
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.
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
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.