Hand Combinations in Poker

Introduction

Combinatorics may sound intimidating, but it is just a fancy word for hand combinations. It helps you determine different poker hands you can use in a specific situation, like the flop or the community cards. Understanding hand combinations is important as it will help you make the best hand in poker and win. It also improves your gameplay if you are a beginner. This article will help you understand poker combinations and why they are essential.

Objective

The article's objective is to explain the hand combinations and their metrics.

What is Hand Combinations in Poker?

Also known as combinatorics or combos, combinations poker refers to the number of possible hand combinations in a particular round. This will help you understand the number of AK variations you can hold in a specific spot.

There are 52 cards in a standard deck, 13 of each suit and 4 of each rank. This means there are 16 possible hand combinations for every unpaired hand, 12 hand combinations for unpaired suit, four for suited hands, and six combinations for pocket pair.

To evaluate these combinations, we usually use two types of matrix: The hand matrix and the card matrix.

A grid represents the hand and card matrix.  The hand matrix states that Holdem has 1326 possible starting hand combinations.

Poker Combinations Chart: Highest to Lowest

Here’s the ranking of each poker combination to realise the strength compared to others:

• Royal Flush: The highest-ranking hand in the poker hand rankings. It includes the top five cards of the same suit, such as A ♦️ K ♦️ Q ♦️ J ♦️ 10♦️.
• Straight Flush: Five consecutive cards of the same suit make a straight flush, for example, 9♠️ 8♠️ 7♠️ 6♠️ 5♠️.
• Four of a kind: Four cards of the same rank along with an additional fifth card of any rank.
• Full House: A combination of Three of a kind and a pair.
• Flush: Five cards of the same suit not necessarily in the same order.
• Straight: Five consecutive cards of different suits.
• Three of a kind: three cards of the same rank and two other cards.
• Two Pair: A hand with two sets of pairs, with an unrelated fifth card.
• Pair: Two cards of the same rank with three unrelated cards.
• High Card: When you are unable to make any of the above-mentioned hands, the highest card in your hand becomes your high card.

What Are Blockers In Poker?

Blockers are the cards that make it impossible for you to make a certain hand. At times, it makes it impossible for a hand to exist.

The Hand Matrix

There are 1326 starting hand combinations in Texas Holdem, represented by a grid. There are 6 combinations of each:

• Pocket pair: A♠️A♥️, A♠️A♦️, A♠️A♣️, A♥️A♦️, A♥️A♣️, A♦️A♣️, 
• 4 combinations of suited hand: A♠️K♠️, A♥️K♥️, A♦️K♦️, A♣️K♣️.
• 12 combinations of offsuit hand: A♠️K♥️, A♠️K♦️, A♠️K♣️, A♥️K♠️, A♥️K♦️, A♥️K♣️, A♦️K♠️, A♦️K♥️, A♦️K♣️, A♣️K♠️, A♣️K♥️, A♣️K♦️.

This means there are 78 pocket pairs, 312 suited, and 936 offsuit hand combinations.

The Card Matrix

Dead Cards

These are cards that are not in a player's hand. For example, when cards are dealt in the flop, they are considered dead, as no player can hold them.

Other Card Removal Examples

In poker, dead cards and blockers are two different concepts. Dead cards are visible to everyone, whereas blockers are the private cards you hold, which can affect your opponent's game.

Simple Blocker Example

Blockers can either help you win the game or lose it. They help eliminate special hand combinations from your opponent's ranges. Suppose you have K♠️; this reduces the chance of your opponent making a Flush.

Strategic vs. Actual Frequencies

The difference between what should happen and what happens is based on the blocker. If you have a card, it changes the likelihood of your opponent making a certain hand. However, this needs to be reflected in the general strategy guide. Hence, it is important to consider both the strategic and actual frequencies.

Card Bunching

Card Brunching: Card brunching happens when your opponent Folds. This indicates that they have a weak hand, while others have a stronger one.

Why Combinatorics Is Essential in Poker?

Poker is a strategy game; you need data or numbers to build a strategy. Understanding these poker combinations will help you develop a good plan and gameplay. It will also help you in understanding your opponent’s gameplay. You can decide when to Call, Raise, or Fold. Lastly, you can analyse your opponent’s cards and better understand poker ranges.

How Many Hand Combinations Are There?

There are 169 hand combinations, including 78 paired hands, 312 suited unpaired hands, and 936 off-suited unpaired hands. All these are represented in a grid with different colours.

Combinatorics and Hand Range Charts

Combinatorics is a fancy term for counting possibilities. It helps us understand and gives more insights about the game. For example, you can determine which hand to play using the combinatorics chart.

Let’s say you are playing from the button position. You want to know what hands to play. Assume there are 534 combinations from that position, and we already know there are 1,326 starting hand combinations. This means your range is about 40% of all the possible starting hands.

You can use the same matrix to determine the hand combinations from the small bling position.

Using Combinatorics at the Bottom of Hand Ranges

There are guidelines regarding the number of hands you can play from each position. For example, if you are the first to act, you can play around 15% of the hands you are dealt.

Here are some things you should consider:

• Several good hands you have to bet?
• How often have you been in this situation with a busted straight draw?
• Out of those busted straight draws, how many are suited (same suit), and how many aren't?

To solve the abovementioned problems, you should have two and a half solid hands for every bluff. If you have 20 goods to bet with, you should have 5 to 10 bluffs.

Let's say the cards on the table can make different straights, and if you have all the possible combinations, you can end up with many hands to bluff. But realistically, you can only have some of the possible combinations. Now you have to choose which ones you bluff with.

The best ones to bluff with usually make it easier for your opponent to have a good hand.

Combinatorics: Poker Hand Probability Explained

Combinatorics is just a fancy word for counting different probabilities. To understand this, we will take an example of four-of-a-kind. Four-of-a-kind is when you have four cards of the same ranks, like four Kings.

Now, if the community cards already have two kings, only one combination of cards is left to make a four-of-a-kind: the remaining two kings in your hand. But if there are three-of-a-kind cards on the community cards, then more combinations exist to make a four-of-a-kind. 

To figure this out, we can multiply the one card we need for four-of-a-kind by the number of cards left in the deck after the flop. This will give you the number of combinations you have to make four-of-a-kind. Remember, you will not have all the combinations in your starting hands.

Post-Flop Hand Combinations

In poker, hand combinations also tell you how many difference ways you can have a specific hand based on the cards you know like the community cards. After the flop you can use math and figure out how likely your opponent is to have certain hands.

This is important because some cards showing on the flop make it less likely that your opponent has certain hands.

Let’s say player A called pre-flop with a bunch of hands and then the flop comes T♠️ 3♦️ 2♦️. Now, we will look at the how many combinations of hands in his range match this flop.

Combinatorics of Top Pair

There are fewer ways to make top pair because one T is already on the board.

• Player A 15 combinations that hit top pair.
• Player A has 36 combinations that didn’t hit anything.
• So only 29% of his unpaired hands made top pair.  This means top pair isn't super common unless someone was holding a T already.

Combinatorics of Flush Draws

Let’s ay player A started with two diamonds, then the player might be on a flush draw (waiting for one more diamond).

• Player A has 9 combinations with a diamond flush draw.
• If the flop had two lower diamonds, player A has 14 combos. This shows the exact cards on the board affect how likely flush draws are.

If the turn card is a J♦️, that’s bad for player As flush as four of player A’s possible flush draws used that card, so he loses those combos. Now, only 5 flush combos left out of 89 hands, the chances are about 6% flushes.

But if the But if the turn is 4♦️, then player A can keep all 9 flush draw hands. This is almost double.

Combinatorics of Sets

Sets are avery strong hand, but hard to make. To amke a set, player A needs 33 or 22. These are usually 6 combos of each, but with one of each card already on the flop, only 3 combos each are left.

Poker Combinations: Things to Remember

Royal Flush- Strongest and Unbeatable Poker Combination

The above-mentioned table shows that royal flush is the highest and strongest hand in poker. It can beats all other poker hands. If you have made a royal flush, consider yourself a winner.

High Card- Weakest Poker Combination

The high card is the lowest and weakest poker hand. It has no suited cards to complete a sequence or a pair. The strength of a hig card is determined the cards in your hand. For xample, player A has A♣️ 2♣️ J♥️ 10♠️ 6♦️ and player B has K♣️ Q♠️ 3♦️ 9♠️ 10♦️. Player A’s high card will be Ace and player B’s high card will be K. In this case Player A wins as ace is higher than k in holdem.

Higher Ranking Hands Beat Lower Ranked Hands

As per the standard poker rules, the highest hand beats the lowest hand.  Tis means Flush beats the straight, and two pair beats the pair. It is advisable to memorise the hand rankings to play your had strength appropriately.

Role of Kicker in Poker Combinations

A kicker the next highest card that helps decide the winner in case of a tie. Let’s understand this with an example:

Example 1: High Card Tie

• Player 1: A♥️ K♠️
• Player 2: A♦️ 9♣️
• Board: Q♥️ J♣️ 8♠️ 5♦️ 2♠️

Both have Ace as their best card, let’s look at the kicker. Player 1 wins because their kicker (K) is higher than Player 2’s (9).

Example 2: Same Three of a Kind

• Player 1: K♥️ Q♣️
• Player 2: K♠️ 10♥️
• Board: K♣️ A♦️ 9♠️ K♦️ 6♣️

Both players have Three Kings, but, Player 1 wins because their kicker (Q) beats Player 2’s kicker (10).

How Combinatorics Affects Bluffing Frequencies

If you want to bluff after betting in previous rounds, you’ll have to make the balance between your strong hand and your bluffs. You should have one bluff for every 2 or 2.5 strong hands you are betting.

To bluff, consider the number of unsuccessful hands you have that could be a potential bluff. Let’s say the board has Q-J-7-6-2; this shows the number of straight draws with cards like AK, KT, or 98. But you cannot bluff with every combination, or you’ll be bluffing too much. You should bluff with strong block hands.

You can also look at the type combinations you have. The suited hands have four combinations, whereas off-suited hands have 12 combinations.

Lowball Poker Combination Methods

Here’s how the strength of poker combinations changes in Lowball poker games:

• Ace to Five Low: The best and strongest hand is A-2-3-4-5 in Ace to five low. You can win by making a straight and flushes with the lowest cards 
• Deuce-to Seven Low– This poker variation got its name from its strongest hand i.e. is 7-5-4-3-2. The hand is formed regardless of the suit.
• Ace to Six Low: Alos known as Chicago Wheel, A-2-3-4-6 the best possible hand you can make in Ace to six low. It is the strongest hand, followed by A-2-3-5-6, A-2-4-5-6 and so on.

Frequently Asked Questions

How many hand combinations are there in poker?

There are a total of 1326 combinations of hands in poker.

How many combos of KK?

There are a total of 6 possible combinations of KK.

How many flops are possible in poker?

19,600 flops are possible in poker.

What are the poker hand ranking combinations?

In a standard poker game, the hands are rankd from highest to lowest as follows: Royal Flush, Straight Flush, Four-of-a-Kind, Full House, Flush, Straight, Three-of-a-Kind, Two Pair, One Pair, and High Card.

Conclusion

Mastering hand combinations is essential, especially if you're a beginner. This will help you understand your cards and give you an idea about your opponent's gameplay. You can even make informed decisions about your actions, such as when to bet, raise, call, or fold. Just remember that practice and patience are the key. So, keep learning and start practising to master the game.