If you’re looking to up your poker game, then you need to know about the best poker combos for winning at the tables. These combinations will give you an edge over your opponents and help you take home the pot!
Combinatorics is a big term for something that is easy to understand. This article will cover the basics of how to calculate hand combinations or poker combos. We’ll also share some examples of why it is so useful in the game.
Oh, and you probably noticed that “poker combinatorics,” “hand combinations,” and “combos” all refer to the same thing when it comes to poker. They can be interchanged, but don’t be confused.
What are poker combos?
Combinatorics is the art of determining how many possible combinations of a hand exist in a given situation.
Take, for example:
- What are the possibilities for dealing AK?
- How many ways are there to deal 66?
- What combinations of T9 can you find on a T32 flop?
- How many straight draw combinations can you find on a flop at AT7?
Poker combinatorics will allow you to quickly calculate these numbers and make better decisions based upon the likelihood of certain hands appearing.
Basics of poker starting hand combinations
- Any two (e.g. AK or T5 = 16 combinations.
- Pairs (e.g. AA or TT) = 6 combinations.
Take a hand like AK and list all possible ways that you could get this hand from a deck, you will see that there are 16 combinations possible.
You can also write down all possible combinations of a pocket-pair like JJ and you will see that there are only 6 combinations.
As you can see, these basic starting hands in poker are almost three times more likely to be dealt a nonpaired hand like AK than a paired one. This is quite interesting, but there are many other options.
There are two additional starting hand combinations.
There are 16 combinations of any two nonpaired cards, as mentioned above. This includes both non-suited and suited combinations.
These stats give you the total combination of any two suited and any two unsuited cards.
- Any two (e.g. AK or 67 suited/unsuited) = 16 combinations
- Any two suited AKs = 4 combinations
- Any two unsuited (AK) = 12 combinations
- Pairs (e.g. AA or TT) = 6 combinations
These extra starting hand combinations won’t be used nearly as often as the first two but they were worth sharing.
It is easy to see that there are only four suited combinations of any two cards. There are only four suits in the deck. The remaining 12 unsuited combinations can be found if you subtract these 4 suited combinations from the total of 16 “any two” hand combinations. Easy.
The fact is there are 1,326 total combinations of starting hands in Texas Hold’em.
Creating poker combos with “known” cards
Let’s say that we hold KQ on the flop of KT4 (suits don’t matter). What are the possible combinations of AK and TT that your opponent could hold?
Unpaired hands (e.g. AK)
How do you calculate the total number of hand combinations in an unpaired hand such as AK, JT, or Q3?
Multiply the number of cards for each of the two cards.
For example, how many AK combinations can you make if you hold KQ on a KT4 flop?
There are 4 Aces and 2 Kings (4 minus the 1 on the flop and minus the 1 in your hand).
If C = 8, then here are 8 possible combinations of AK if KQ is held
Paired hands (e.g., TT)
How do you calculate the total number of hand combinations in a paired hand such as AA, JJ, or 44?
Multiply the number of available cards by available cards minus 1, then divide the result by two.
For example, how many combinations of TT can you find on a KT4 flop?
After a flop with KT4, there are still 3 tens in the deck.
If C = 3, then there are 3 possible combinations for TT.
It is simple enough to work out the possible combinations of unpaired hands. Just multiply the two numbers of available cards.
Although it may seem difficult to figure out the combinations for paired hand combinations, it is not difficult once you try it. Find the number of cards available, subtract 1 from it, multiply those numbers together, then half it.
Note: This method can also be used to calculate the preflop starting hand combinations that were mentioned earlier. If you want to work out the number of AK poker combos, there are 4 Aces and 4 Kings so then 4 x 4 = 16 AK combinations.
What is the purpose of poker combinatorics?
You can learn more about a player’s range by working out hand combinations.
Let’s say, for example, that a rival’s 3-betting range is approximately 2%. This means they are only 3-betting AA, KK, and AK. This is a very tight range.
Just by looking at
- AA = 33%
- KK = 33%
- AK = 33%
…with the two major pairs accounting for the majority of the 2% 3-betting range or roughly 66%.
- AA = 6 combinations (21.5%).
- KK = 6 combinations (21.5%).
- AK = 16 combinations (57%).
Out of the 28 combinations that can be made from AA, KK, and AK, 16 come from AK. This means that if your opponent 3-bets, he is likely holding AK and not a pocket pair.
This is not comforting, especially if your hand is 75.
The point is that the probabilities of different types of hands in a range can vary. Having AA or AK doesn’t necessarily mean they are equally likely to hold – in fact, they will be holding AK more often.
Here’s an analogy: A fruit bowl containing 100 oranges, 1 pear, 1 apple, and 1 grape will have a decent range of fruits (hands). But some fruits are heavier than others so it is more likely that you will choose an orange from the bowl than any of the other three fruits.
The same approach applies to determining the probabilities
More examples of poker combos
On a board of As Jh 6d 8d 2c, the pot is $12 and you wager $10. Your opponent moves all-in for $60. This means that you must call $50 to win an $82 pot.
You are confident that your opponent has a set, or two pairs with an Ace (i.e. AJ, A8, A6, or A2). You don’t have to worry about how or why you know this.
According to pot odds, you must have a minimum of 38% chance to have the best hand to call. To help you decide whether to call, you can use combinatorics.
Let’s first divide our opponent’s hand into hands that you can beat and hands that you don’t beat. Then work out the number of hand combinations for each.
If you have the best hand 79% of the time, and the pot odds suggest that you only need to have the highest hand 38% of all the time, that makes +EV to call.
Although you may have thought that the ratio of hands we beat to those we didn’t beat was close at 50/50, we can now see that it is closer to 80/20. This makes calling a profitable play.
It is great to be able to give a range to your opponent, but it is much better to understand the probabilities of the hands within that range.
It is easy to calculate hand combinations in poker:
- Unpaired hands: Multiply the number of cards. (e.g., AK on an AT2 flop = [3 x 4] = 12 AK combinations.
- Paired hands: Take 1 away from the number of available cards, multiply the two numbers together, and divide by 2. (e.g. TT on an AT2 flop = [3 x 2] / 2 = 3 combinations of TT.
You can better understand your opponent’s hand ranges by working out hand combinations. You are missing valuable information if you only deal in ranges and don’t consider hand combinations.
After a while, you’ll realize that straight draws are much more common than you think and that flush draws are much less common. These insights will be helpful when you have to make similar decisions in the future.
When you do your post-session analysis, think about combinatorics. Keep track of what you find.
So, what are the best poker combos for winning at the tables? Well, that depends on your playing style. But, in general, you want to have a mix of strong starting hands and good drawing hands.
That way, you’ll be able to take down pots regardless of the situation.
Remember, practice makes perfect! So make sure to drill these combos into your head and put them into action at the table. You’ll be surprised at how much they can help improve your game.