Everything You Wanted to Know about Poker Hand Combinations and Hand Reading

An Introduction to Poker Hand Combinations and Poker Card Combinations

What is your objective when you play poker? To win and make some money, right. Of course, you also need to enjoy the game and have some fun along the way. But, the objective for most poker players is simple – win and earn money! And how do you win? By forming the best possible poker hand combinations, isn’t it? Be it any variant of poker, and the winner is primarily decided by the poker card combinations he/she holds. In some poker variants such as the Hi Lo version for Omaha, it may not just be the best possible poker hand combination, but, also the lowest possible poker hand combination that wins.

What does all of this mean? That you need to have a good understanding of poker hand combinations if you wish to succeed regularly in poker games. This game does involve some luck, but it does require tremendous skills with regards to your capability to read hands from the initial betting rounds when you are exposed to minimal cards. For example, when you get your hole cards, you need to decide which of the top poker hand rankings can be achieved as the game progresses, with cards you have. So, it is not about the combination you have at the start, but the card combination that you can form towards the end which can fetch you a win.

During this article, we shall study the various hand combinations possible in a given situation and the way this knowledge can be used to make better decisions in different rounds of a poker game. Let us deep dive into this concept of poker hand combinations that can be critical to you becoming a more solid poker player.

Best Poker Hand Combinations

If you have been playing poker for a while, you would have already come to terms with the best poker hand combinations (or poker hand rankings), out of which you aim to achieve one of them with the cards you receive. These best poker hand rankings (or combinations) in descending order are as described under:

• Royal Flush

It is the best possible poker hand combination, and nothing can beat this in poker. It comprises of Ace, King, Queen, Jack, and 10 – all belonging to the same suit.

• Straight Flush

This is the second-best possible card combination in a game of poker. Here, the combination consists of five cards of the same suit, in a consecutive rank (peculiar numerical order). For example, the card combination can be 5,6,7,8, and 9 of hearts. If there are two players with straight flush combination, the player who has a higher denomination of cards is the winner!

• Four of a Kind

Here, only four cards of your set of five cards can be used to form a combination. This combination will comprise of four cards of the same rank (equal rank), and each of them can be of a different suit. For example, you can have four Aces and a three as one of the ‘four of a kind’ combinations.

• Full House

This poker hand combination consists of three cards of the same rank and the other two cards of identical rank, i.e., three of a kind and a pair. It is also known as full boat. For example, you can have three Queens (as your three of a kind) and two 9s (as your pair).

• Flush

The Flush combination comprises of five different cards of the same suit. These cards need not be in any specific sequence or order. For example, you can have 2,4,8,10 and Ace of diamonds.

• Straight

In poker, a straight combination comprises of five consecutive cards (continuous numerical order) belonging to any suit. For instance, your straight hand combination could be 6, 7, 8, 9, and 10 (and these cards could be a mix of diamonds, spades, hearts, and clubs).

• Three of a kind/set

This combination refers to three cards of identical rank and belonging to different suits (three of a kind), and the remaining two cards can be from any suit.

• Two Pair

This combination consists of two card pairs – where each pair will be of the same rank (value). The last card can be of any suit and any rank.

• One Pair

Here, you need to form one pair (two cards of the same rank) and the remaining three cards can be from any suit and of any rank.

• High Card

This combination considers the highest value card in your hand as the high card. You can rarely win from such a hand, but even then, you need to have an Ace or a King as your high card.

Overview of Combinatorics

Now that you have checked out the best possible hand rankings in poker, you need to be aware about how to decide which hands are possible for the cards dealt to you and cards yet to be received. You also need to take cognizance of the cards that are dealt face-up to other players and determine the range for every player on the table. This is where hand reading comes into the picture. You need to have the ability to assign a range to other players and then you need to aim to narrow down the range to make decisions based on the probability of certain hands coming up. This is achieved via ‘combinatorics’ or ‘hand combinations’.

In simple terms, combinatorics refers to the process of working out the various different combinations of a hand that exist in a specific situation. Let us check out some of the below examples that denote combinatorics concept:

• How many different ways can you be dealt AK (Ace and King) in a game of poker?
• How many different straight draw combinations are there on the flop of AT7?

Combinatorics helps you to answer these queries by working out these numbers for the possible combinations.

Starting Hand Combinations

A deck has 52 cards, with 13 of every suit, and 4 of every rank. For this deck, you can have:

• 16 possible hand combinations for every unpaired hand like AK (Ace and King of same as well as different suits)
• 6 possible hand combinations for every pocket pair like QQ (Queen and Queen of different suits)
• 12 possible hand combinations for every unpaired hand which is not of the same suit
• 4 possible hand combinations for every suited hand

Going by these possibilities of hand combinations and comparing these with the poker hand rankings discussed earlier, you can have some conclusions like:

• Suited hands are very valuable as there is less number of combinations for them. For example, you have three times more probability of being dealt with an unsuited hand (12 possible combinations) as compared to a suited hand (4 possible combinations).
• Flushes are extremely hard to form, and that’s the reason they are harder to defeat. So, having a suited hand as a starting hand combination gives you a good chance at winning the pot.
• For a game of Texas Hold’em, there are about 1326 different combinations of starting hands.

Calculating Poker Hand Combinations for Known Cards

Scenario#1

Let us assume that you have a scenario where you are holding KQ (King and Queen) on a flop of KT4 (where suits are not relevant). In such a case, how many possible combinations of an unpaired hand like AK (Ace and King) exist that can be held by your opponent out there?

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This calculation can be done as under:

Possible combinations (C ) = Available cards for the first card (Ace here) x Available cards for the second card (King here)

As you are not holding any Ace card, there are 4 Aces available. Since you are already holding two of the kings, only 2 Kings are available.

Thus, Possible combinations = 4 x 2 = 8

So, you have 8 possible hand combinations of AK while holding KQ on a flop of KT4.

Scenario#2

Now, consider that instead of the unpaired hand AK, you have to calculate the possible card combinations of paired hand TT as you hold KQ on a flop of KT4. Over here, you have only 1 ten (T) card with you, so there are about 3 T cards available.

The formula for possible combinations (C ) will be:

C = [(Available cards) x (Available cards – 1)] / 2

Thus, possible combinations = [(3) x (3-1)]/2 = 6/2 = 3

So, you have 3 possible hand combinations of TT as you hold KQ on a flop of KT4.

Thus, the scenario#1 above highlights the formula for calculating the starting hand combinations for an unpaired hand and the scenario#2 highlights the formula for calculating the starting hand combinations for a paired hand. Similar formulas can be used for calculating the pre-flop combinations.

This concept of combinatorics is useful to identify useful information about a player’s range in poker, i.e., it helps you to know your opponent’s hand ranges much better. Of course, it is not possible for you to work out all of this information (about the combinations and player’s range) during gameplay at the poker table. But, you get used to the probabilities of various different types of hands for later reference and relate to them as you play more games. For instance, you will start realizing that flush draws quite less common than you think and straight draws are much more common than you think. This kind of knowledge will enable you to make better decisions during poker tournaments.

You will have to practise using the concept of combinatorics after your game by doing post session analysis. Check out the hand history and apply the concept of card removals and blockers for calculating combinations and deducing your opponent’s potential holdings during late stage poker. How is it possible? You can simply check the card rank (and suit) you are holding, track the card rank (and suit) that is face-up on the table, and you are left with the pending card of that rank (or suit). Using this kind of comparison, you can possibly block certain hands for your opponents as well as remove certain cards from your opponent’s range.

This method of card blocker and removal along with combinatorics information will help you to deduce the value hands against bluffs of your opponents during poker gameplay.

The Verdict

If you wish to make your poker game more solid and become a very tough player to beat during cash games or poker tournaments, you have to start implementing the combinatorics concept for calculation of poker hand combinations possible at different situations. The combinatorics concept might seem tough to start off with. Still, you will be able to familiarize yourself to the various possible combinations as you keep using it more and more. You need to work on it right away by heading to the Spartan Poker online platform, download the poker app and playing your preferred versions of poker!