• 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.

1. How Many Starting Hands In Texas Holdem
2. How Many Starting Hands Are There In Texas Holdem
3. How Many Possible Starting Hands In Texas Hold'em

Hand Combinations -- The Basics

Texas Hold’em: a game in which it is easy to learn the basics, but considerably harder to master. For now, let's cover a basic part of the game - starting hands.

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). For any given starting hand, there are 50 × 49 ÷ 2 = 1,225 hands that an opponent can have before the flop (after the flop, the number of possible hands an opponent can have is reduced by the three community cards revealed on the flop to 47 × 46 ÷ 2 = 1,081 hands).

How Many Starting Hands In Texas Holdem

Hand combinatorics isn't as scary as it sounds.

It's not some big, complex math technique that only a select few guys with PhDs can understand.

It's an easy, highly useful technique that we poker players can use to help put our opponents on hand ranges.

The technique works kind of like it sounds -- we want to calculate the number of combinations of hands our opponent can be holding in a given scenario.

Let's walk through the process of calculating combinations step-by-step. By the time you're done reading this article, you'll be able to more accurately assess what an opponent's hand range could be.

Combinatorics 101: What's a Combination?

A combination is simply a way to put a set of items together where all the items are drawn from a larger set.

In simple English, a combination is a way to pick some stuff out of a bigger pool of stuff.

Say we have a set of objects A, where A = {1, 2, 3, 4, 5}. We want to figure out the number of 2-object subsets we can form out of A; that is, the number of combinations of 2-object subsets we can pick from the set of objects A.

Calculating this turns out to be pretty simple. All we need to do is follow this simple formula:

n = total # of objects in the set
x = number of items we want to choose
C = combinations of x in set n

C = n! / x! * (n-x)!

Plugging in our numbers for set A into this equation, we get:

n = 5
x = 2

C = 5! / 2! * (5-2)! = 10

So there are 10 unique combinations of 2 items that we might choose from set A.

Now, let's say we have a set of 52 items that we want to draw from. As a basic set of 52 objects, B can be the deck of 52 cards for example.

We just plug the total number of objects in the set (52) into our magic equation, along with the number of items we want to include in each chosen subset (2), and get:
n = 52
x = 2
C = 52! / 2! * (52-2)! = 1326

So there are 1,326 unique combinations of 2 items that we might choose from set B.

You will probably find these numbers to be familiar. If so, good! It's probably because 1,326 is the number of possible starting hands in Holdem poker. What we were acually determining in the above calculation was how many combinations of 2 cards we can pick from a 52-card deck.

Keeping with poker, let's examine a more applicable form of calculating combinations, and some situations in which such a method would be useful.

Combinatorics 101: Combinations of Poker Hands

There's obviously no way you'll be able to whip out a calculator at the poker table and calculate combinations. Luckily, there are some more compact ways of calculating combos that don't require calculators or intense math. We can use these benchmarks to help refine our estimates of opponents' ranges.

There are three basic numbers you need to know:

• There are 12 combinations of any given offsuit unpaired hand in Holdem.
• There are 6 combinations of any given paired hand in Holdem.
• There are 4 combination of any given suited unpaired hand in Holdem.

How we arrive at these numbers is pretty basic:

• There are 4 of any card of a given suit in a deck, and 3 of another particular card of a different suit. So we multiply 4 by 3 to obtain 12, the number of combos for a given offsuit unpaired hand.
• There are 4 of any card of a given suit in a deck, and 3 additional cards left in the deck of that rank. So we multiply 4 by 3 to obtain 12. When counting pairs, there are going to be two ways to make each unique combination of pair; for example, 6c6s and 6s6c. So we must divide 12 by 2 to eliminate double-counts. So 12/2 = 6, the number of combinations of a given pair preflop.
• There are 4 of any card of a given suit in a deck, and only one card after that that can make the suited hand. So (4)(1) = 4, the number of combinations for a given suited hand.

A Practical Example

Say you're playing against an opponent whose range you estimate to be {JJ+, AKo, AQs+} in a given situation. You want to break down the number of hand combinations in his range. You'll calculate the combinations as such:

So there are a total of 44 hand combos in your opponent's range, 24 of which are pocket pairs and 20 of which are unpaired hands.

His range looks a lot scarier when we view it as 4 pocket pair hands and 3 unpaired hands, doesn't it? In reality, it's 50/50 that he's got matching cards in the hole; which can change our equity, and thus our correct action, drastically.

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For a certain segment of new hold’em players, starting hand charts can be fascinating. Even those with many years of experience who have little need to consult such charts still find them interesting as debate-starters.

In hold’em there are 169 different combinations of hands you can be dealt. For those of us who enjoy working with numbers or creating lists with which to organize our lives, there’s something appealing about the idea of ranking all of those hands from 1 to 169, even if we know such a list probably might have only limited value when it comes to actual game play.

In truth, there are actually a lot more possible combinations of hole cards in hold’em — 1,326 of them, in fact. But that total also considers suits as distinct, when in fact before the community cards come the suits are all essentially of equal value.

That is to say, is of the same value as when playing preflop, while and are also of equivalent value. So, too, are the different combinations producing the same pocket pairs all equal before the flop in terms of their relative worth. While there are six different ways to get pocket aces — , , , , , — you're equally happy no matter what suits the cards are.

So we get rid of all of those redundant hands and say that in Texas hold'em there are 169 “non-equivalent” starting hands, breaking them down as follows:

• 13 pocket pairs
• 78 non-paired suited hands (e.g., with two cards of the same suit like or )
• 78 non-paired unsuited hands (e.g., with two cards of different suits like or )

Notice now the non-paired combinations of hole cards neatly divide into equal groups, both of which are six times as large (78) as the smaller group of pocket pairs (13). The total of 169 combinations represents a square, too — 13 x 13 — another curious symmetry when it comes to hold'em hands.

Still, that’s a lot of starting hand combinations — too many for most of us humans to keep in our heads — which is one reason hand ranking charts are appealing and even can be useful, since they help players think about certain two-card combos as “strong” or “average” or “weak” as possible starters.

Setting aside the idea of actually ranking the 169 hands from best to worst, we might think for a moment about other ways of categorizing starting hands in hold’em, using that initial breakdown of hands into pocket pairs, non-paired suited hands, and non-paired unsuited hand as a first step toward coming up with further, smaller groups that are easier to remember.

The 13 pocket pairs we might group as big or “premium” (, , and ), medium ( through ), and small ( through ).

Meanwhile, we might divide each of the other groups into “connectors,” “one-gappers,” and “two-gappers” (and so on), further thinking of them also as “big,” “medium,” and “small” while also keeping separate suited and non-suited combinations.

These categories of non-paired hands are created by thinking about straight-making possibilities (affected by connectedness) and flush-making possibilties (affected by suitedness). There are more ways to make straights with “connectors” — that is, two cards of consecutive rank like — than with two-gappers, three-gappers, and so on. So, too, do you have a better chance of making a flush with suited hole cards than with non-suited hole cards.

Another possible group to create would include “ace hands” — i.e., non-paired hands containing one ace — that can be thought of as “big aces” (e.g., , ), “medium aces” ( down to ), and “small aces” ( to ). Or “king hands,” too. We like keeping these groups in mind, as hands with big cards like an ace or king can connect with flops to make big pairs.

In any case, you can see how these criteria for making categories can help when it comes to building those starting hand charts. And in fact most of those charts feature a similar ordering of hands, with...

• the premium pocket pairs and the big aces (suited and non-suited) up at the top;
• medium and small pocket pairs and big-to-medium suited connectors and one-gappers in the middle;
• and non-paired hands with less potential to make big pairs, straights, or flushes toward the bottom.

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However, there are problems with relying so heavily on starting hand charts that you don’t take into account factors that can make a given hand gain or lose value. Such as the flop. Or the turn. Or the river. Or other factors — including how your opponents are playing their hands — that can quickly affect the value of your starting hands.

After all, as anyone who’s played even a few hands of hold’em well knows, even if is the highest-ranking starting hand and a non-suited ranks as 169th, a couple of deuces among the community cards is all it takes to make the best hand worst and the worst hand best.

Learning the relative value of starting hands is definitely an important first step when it comes to getting started in hold’em. Other aspects of game play such as the importance of position, knowing when and how much to bet or raise, and thinking about opponents’ holdings and playing styles as hands proceed are good to learn, too, and help show how a great starting hand might not be so great five community cards later.

How Many Starting Hands Are There In Texas Holdem

Poker is not blackjack, a game in which similar hand-ranking guides are sometimes used to inform players’ decisions about how to play. In poker you want to be wary about becoming too reliant on those pretty starting hand charts. They can be great for indicating which hands might be worth playing (and which should be thrown away), but troublesome if allowed to outweigh all of the other important factors that arise as a hand plays out.

That said, starting hand charts can be useful, especially for those new to hold’em. They also can be a big help when picking up other games, too, like pot-limit Omaha or the various stud games, if only to get an early idea what hands tend to play better than others.

But for many such charts ultimately are only themselves a way to get started, before the experience of playing helps players more instinctively recognize both hand groupings and how hands tend to compare in terms of profitability.

How Many Possible Starting Hands In Texas Hold'em

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