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Poker is mostly a game of mathematics in which a strong understanding of the underlying principles gives you a big edge, and one of the core elements you need to master is combinatorics.
This principle involves counting the possible combinations of cards in any given situation.
Understanding poker combinations allow you to bluff more successfully, make better hero calls, and get value in thin spots with higher precision. In this article, we are going to look more closely at this concept and teach you how to count your poker combos and make them work for you.
Understanding poker combinations is not that difficult because we are talking about the simplest mathematical operation, counting. We know that the game of poker is played with a deck made up of 52 cards in total, which are divided into 13 different ranks and four different suits.
Each player at the table is dealt two hole cards at the start of the hand, and there is a total of 1,326 poker combinations each player can receive, to begin with.
Each possible hand combo can be either suited or offsuit, and there are a few key concepts to remember:
Knowing these few simple things and keeping them in your mind as you play poker will help you quite a bit, and we will show you how to use them to get the most value from your knowledge.
So how do poker hand combinations help me make better decisions at the table? Well, it’s actually quite simple!
When deciding what to do with your hand, one of the key things to consider is what your opponent might be holding.
We have long stopped trying to determine the exact hand another player can have and should instead think in terms of the possible range of hands they could be holding.
For instance, a player who opens the pot from UTG in a full-ring game usually holds a strong range of hands, as opposed to one who raises from the button. But what exactly does that mean, and what hands could be in that range? This is exactly where poker hand combinations come into play.
When constructing your opponent's range, you should consider every action they took throughout the hand and think about all possible combinations that could fit that pattern.
As streets go by, you should consider which poker combinations are still in their range and why. Were they bluffing with a flush draw, and would they continue firing, having completely missed the board?
Poker combinations may allow you to narrow down a player’s range quite significantly by the river.
By the time that last community card is dealt, you should have a pretty good idea of which combos are still in their range and which ones aren't, which is of great help in your decision-making process.
Even before the flop is dealt, you can start counting the possible combos your opponents have and discounting certain combinations from their range. Most players follow certain patterns when playing preflop, and deviating from them too much will usually mean they are too tight or too loose.
Against players playing a balanced strategy, you should have a pretty good idea which poker hand combinations they have when they raise from each position, call preflop raises, or playback against the original raiser.
With each new raise or bet, you can discount certain hand combinations even before the flop, often discounting the offsuit variations of hands first, as these are the more likely hands for a player to fold.
As the flop comes down, it becomes that much easier to start discounting combos. Players will usually only continue when they have connected with the board somehow, significantly diminishing the number of hand combos still in play.
Let us imagine a player from the middle position opening for a standard $15 raise in a $2/5 live cash game and getting called by you in the big blind.
With $32 in the pot, the flop comes down Ks8d5d. You check, and the player fires out a continuation bet of $12, to which you respond with a $45 raise.
When the player fires out the $12 continuation bet, you can still assume they have the same range they opened the hand with.
After all, there is little reason not to c-bet on this fairly dry board, and they can expect you to fold a ton of hands. Their range contains more Kx type hands, making the bluff much more likely to work.
However, your raise is where things start to get interesting. Assuming we are talking about a reasonable thinking player, they should now fold a whole ton of poker hand combinations.
For example, Ax type hands in suits that are neither diamonds nor spades should fold every time, while many spade combos should also be folding out. Other hands, such as offsuit broadways and small pocket pairs, should also be folding, significantly reducing the number of hand combinations left in your opponent's range.
Assuming your opponent does call, you can reduce their range to hands like Kx, 8x, 76, and a variety of diamond combos.
At this point, you can quite literally start counting their hand combinations and thinking about how many of those hands are made hands and how many are draws.
Since you know your opponent is not opening a hand like K4 or K7 of the offsuit variety from his position preflop, you can completely discount these hands from their range.
Their best-made hands will be the three combos of KK, 88, and 55, along with hands like K8s, K5s, and 85s, assuming they are raising all of these preflop.
On the other hand, their drawing range will be made up of at least four 76s and possibly 12 more offsuit versions of this hand, along with a whole bunch of diamond draws (AdXd, QdJd, QdTd, Qd9d, Jd9d, JdTd, Jd8d, Td9d, etc.).
Being able to count these poker combinations exactly will help you decide how to proceed when various cards hit the turn and river and make even better decisions on each consecutive street.
A relatively “new” concept in the world of poker, but one that’s completely changed how we see the construction of opponent ranges, are called blockers. Essentially, blockers are cards that we know our opponent can't have because we are holding those cards in our hand.
Sometimes, we can also know that a card is not in play because the dealer exposed it or it was exposed in another way. Cards are rarely exposed in this way, but it does happen in live poker.
In either case, knowing that a card cannot be in our opponent’s hand can be very important in how we proceed and how we count their hand combinations.
For example, on the Ks8d5d board we discussed, let us imagine our hand was Ad7s. While this hand is certainly not strong on this board, there are a few key things to consider.
We are holding the Ad, so there is no chance our opponent has the nut flush draw. What’s even more, the overall number of flush draws in their range drops dramatically, as Ax suited is a big part of their suited opening range.
We are also holding the 7s, a card that’s part of the 7s6s combo, which is quite a strong draw on this board, as well as some 76 combos that are not suited.
If we place our raise on this board and get called while holding this hand, we can immediately assume our opponent’s range consists of more value hands.
The exact opposite would be if we held a hand like Kc5c. In this case, we hold two of the key value cards while all the possible draws are unblocked and still in our opponent's range.
This concept also works across all other boards and textures, and you need to carefully consider it when deciding whether to make raises, calls, or folds.
Holding blockers to our opponent's strongest bluffs makes a hand less valuable as a bluff-catcher while unblocking such draws makes it a stronger bluff-catching candidate.
As a general rule of thumb, you want your opponent to have all the possible missed draws in their range when making a hero call or deciding to bluff them on later streets in a hand.
We went over how to count poker hand combinations and what they are, but we haven't given a concrete example of counting combos in a poker hand. So, let us once again use our example of a single raised pot with a Ks8d5d board to try and count all the possible strong hand combos and draws.
Let’s count strong made hand combos first:
All sets are still possible when our opponent c-bets. There are 6 combos of each pocket pair in total, but that number goes down to just three once a card hits the flop.
The more interesting thing to consider is the difference between K8s and 85s. There are two combos of K8s and K5s available, while there are three combos of 85s. You may be wondering why?
If you think more carefully, you will realize that both spades and diamonds are out of the question for suited combos of K8 and K5, while 8d5d is still very much possible.
These are the nuances you should consider when trying to count combos. Of course, our opponent can also have a variety of Kx combos, but we won't count those as super-strong hands at this point.
Also note that some hands, like AA, will have fewer combos available in cases when we hold an ace ourselves, such as in the previous example we gave when talking about blockers.
Now let’s take a look at some possible drawing hands our opponent could have:
Some other notable draws on this board would include 9d7d, 9d6d, and 7d4d, all of which contain both a gutshot straight draw and a flush draw.
When thinking about these hands, it is key to consider how likely our opponent is to play those hands for a raise before the flop, especially ones like 9d6d.
You will also want to consider other flush draws, such as QdJd and JdTd, which only have a naked flush draw without much to fall back on.
Counting poker hand combinations should become second nature to you after a while, and doing it every time you are in a hand will work miracles for your game.
We highly recommend practicing counting combos when you are not playing, using examples of hands you have played, and trying to figure out what your opponent can have and how likely they are to be bluffing in various spots.
In the long run, always thinking about poker hand combinations will make you a better poker player and help you achieve better results when you face competent opponents who know what they are doing at the tables.
If you have the feeling you need to sharpen up your game then Pokercode is a great place to start. Sign up for a free account and set your first steps towards becoming a better poker player.
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