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

1. Worst Starting Hands In Texas Holdem
2. How Many Possible Starting Hands In Texas Holdem
3. Possible Starting Hands In Texas Holdemas Hold Em

'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.

There are over one hundred possible starting hands in Texas Holdem ranging from the all powerful pocket aces to the fairly worthless 2/3 offsuit. Every one of these opening hands carries with it a unique set of strategies, strengths, weaknesses and other facets for when you decide to play those cards. Starting hands In Texas Hold'em, a player is dealt two down card (or pocket cards). The first card can be any one of 52 playing cards in the deck and the second card can be any one of the 51 remaining cards.

Obviously, the quality of your hand also depends on the rank of the pair and it follows that the best starting hand in Texas Hold’em is a pair of aces. They look beautiful, and every Texas Hold’em player goes to sleep and dreams of finding nothing but aces in the hole. A pocket pair can often win a hand of Texas Hold’em without needing to.

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:

Go back to the awesome Texas Hold'em Strategy.

Comments

There are over one hundred possible starting hands in Texas Holdem ranging from the all powerful pocket aces to the fairly worthless 2/3 offsuit. Every one of these opening hands carries with it a unique set of strategies, strengths, weaknesses and other facets for when you decide to play those cards.

While it would be impossible to go over every possible opening hand to decide how best to play those cards, we can narrow the list down to a few tricky hands and cover how to play them. These cards were picked by me personally as opening hands I totally misplayed or succeeded at playing well. Ultimately, I learned a lot from them and I think you can learn from them, too.

Just be careful. It’s impossible to discuss every situation that will arise over the course of a full game of poker. In the end, you still need to use your best judgment and remember that bad beats will happen. Still, I think I can show you how to handle these opening hands better more often than not.

1- Pocket Kings

According to some charts I’ve seen, if you’re dealt pocket kings, you actually have an 83% percent chance to win the hand. Personally, I would like to find whoever put that that chart together and have some very strong words about what, exactly, I feel about being dealt pocket kings. Maybe I’m just the 17%, but I’ve never actually won when I’m dealt them.

Though, if I am being honest, a lot of the reason I lose with pocket kings is my own fault. It just feels like such a strong hand. Having a pair of anything in the hole is clearly better than having nothing in the hole when you start. (Even pocket 2s have a better than 50% chance of winning the day.) Still, pocket kings is far from unbeatable especially when your opponents are likely to play any hand with a pocket ace.

Even though I personally haven’t had luck with pocket kings, the strategy for playing them is fairly straight forward. If you don’t have position, you have enough firepower that you can play a strong opening bet. You don’t want to bet the farm, but you can definitely raise pre-flop with what you have if you’re aggressive, but definitely stay in the hand.

If you have position, pay attention to your opponents.

As far as the rest of the hand goes, you can continue to be aggressive, but be on the lookout for an ace. If a single ace hits the board, more than likely someone else is going to use that to make a pair of aces. Sadly, that is the voice of experience talking. If no ace hits the board, then you may be able to ride pocket kings to victory.

2- Ace/King Suited

Ace/king is another of those poker hands that gets a bad rap around the community. I think the reason for this is largely psychological because an ace and a king feel pretty good (they are the highest and second highest card in the game after all.) Unfortunately, they’re also not worth much because together they don’t even form a pair. So, their strength is largely illusory without some help.

With that said, there’s almost no reason that you don’t stay in with ace/king. I would have to be at a final table with everyone else going all in before I’d even think about folding ace/king and then I’d still probably push my stack and see what happened.

That’s really the key with ace/king: you’re not going to win pre-flop. You need help from the board to win, but you’re sitting in a really good position to let the board help you go on to poker glory. Therefore, as long as your bankroll management limit can support it, call any reasonable amount to stay and see what the flop gives you for it is on the flop that you will make your money.

Once the flop is down, that’s when you have a decision to make.

If any of that happens, stay in the game and bet according to the strength of your hand. If the other players are betting aggressive, you can back off, but you have a good chance of winning. On the other hand, if you flop nothing in your suit and nothing higher than a 9, you might want to get out of the hand since there’s a good chance someone else is working on a better hand than you.

Continue that logic through the next two cards. If you chances to win are high or if you have something, keep betting. If the cards aren’t falling your way, then don’t risk your money. Live to fight another day.

3- Ace/King Off Suit

Unsurprisingly enough, the strategy for ace/king off suit is largely the same as it is for ace/king suited, however the number of good post-flop hands fall off pretty dramatically since you will need at least four cards on the board to make a flush and, quite frankly, if you’re making a flush that way, so is everyone else.

Because of this, when I have ace/king off suit, I am mainly looking for flops that give me that chance at a straight. I certainly don’t mind pairs, but the table is likely to hold on to their hands if they have either a king or an ace. Therefore, if I have a pair, they probably have a pair and I end up splitting the pot. A straight is a much better way to ensure victory even though they are more rare.

4- Queen/Seven

Queen/seven isn’t the greatest starting hand, but having a face card to your name isn’t a bad thing, right? Actually, this is a deceptively poor hand and when you see this combination show up, the best thing you can do is fold.

I say “deceptively” because if this were a game of blackjack, a combined score of 17 is a pretty good hand (in fact, Queen/seven is the highest-scored blackjack hand that you want to fold.)

According to computer simulations, queen/seven will only win about fifty percent of the time, which makes it unreliable.

Worst Starting Hands In Texas Holdem

Ultimately, that unreliability is this hand’s undoing. Even if you have position and everyone else is tepid, resist temptation and throw in your cards. The only reason to stay in is if you were the big blind and no one else bet. Then you could at least see if there’s something pre-flop.

5- Five/Four Suited

This is an autofold, right? Strangely enough, if you have position, five/four suited is the worst hand you could possibly consider keeping at least until you see the flop.

Why would you keep this hand? It offers two interesting ways to win. First, it sits in the middle of a straight (though clearly five/six suited would be better because then your hold cards could begin or end a straight) and it can be a nice seed for building out a flush. There’s also a very small chance a pair of fives win if most of the other players miss their draws.

I’m definitely not saying that you should play this hand every time. If you don’t have the position or if the table is betting fiercely, you don’t have a lot of strength in your hand and you probably won’t win any money. On the other hand, if the action is lukewarm, then it might make sense to stay in the hand and see what the flop gives you.

If the flop gives you four of the five cards you need for a straight, at that point, you can start to bet accordingly because chances are no one else has 4/5 in the hole and is not going for the same straight you are. Of course, if the flop doesn’t cooperate, fold and live to bet another day.

Conclusion

How Many Possible Starting Hands In Texas Holdem

Poker can be cruel sometimes and the hands you think are the best sometimes just are not. That’s okay. That’s why you have a bankroll and that’s why you fold early so you can bet more later.

Possible Starting Hands In Texas Holdemas Hold Em

Still, hopefully when you are dealt any of the five hands above, you now have a better idea of whether you should stay in the game or runaway to play again later. Good luck and happy pokering.