For a great training video on poker combinatorics, check out this poker combos video.

How Many Possible Starting Hands In Texas Hold'em
How Many Starting Hands In Texas Holdem
How Many Starting Hands Are There In Texas Holdem

'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.

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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?

In poker terms, the river is the name for the fifth card dealt, face-up on the board. In total, there are 2,598,960 possible poker hands with 52 cards. The odds of getting four of a kind in Texas Hold ‘Em is 4164 to 1. With two hole cards, you have 1,326 possible starting hands, including duplicates like Ace-Seven of Hearts and Ace-Seven of Diamonds. With four hole cards, you have 270,725 possible starting hands and many more different ways to connect with the board.

Six-plus hold 'em (also known as Short-deck hold 'em) is a community card poker game variant of Texas hold 'em, where cards 2 through 5 are removed. Each player is dealt two cards face down and seeks make his or her best five card poker hand using from any combination of the seven cards (five community cards and their own two hole cards).
In the case of Texas Hold'em, there's the 2 pocket cards and 5 on the board. This way of working out the probabilities would be the more accurate way - however, just to note, the probabilities worked out on 5 of 52 are practically the same, and far easier to calculate.
As you can see, half of all profits are generated by only 5 of the 169 starting hand combinations. And with a total of 14 of the 169 starting hands (6.3% of all hole cards dealt), 80% of all profits are made. So this should make it obvious that you should only play few hole cards in Texas Hold’em Cash Games.

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

How many starting hands are there in texas holdem

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:

How Many Possible Starting Hands In Texas Holdem

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.

How Many Possible Starting Hands In Texas Hold'em

Fact: There are 1,326 combinations of starting hands in Texas Hold’em in total. Wrest point casino revolving restaurant dinner menu.

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.

How Many Starting Hands In Texas Holdem

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.

How Many Possible Starting Hands In Texas Holdem