**Explanation of Combination**

The term “**combinations**” (combos for short) is mostly used when discussing either Hold’em or Omaha variants, although it can presumably be used to describe a specific **combination** of cards in any variant.

Check out our story about the different combinations in poker.

There are 1326 unique **combinations** of two cards that can be dealt preflop in Hold’em. This includes cards which are otherwise identical aside from the suits. I.e both **7**♣**8**♣ and **7**♦**8**♦ are different **combinations** of hole-cards despite the fact that they are identical in strength. If we ignore any suits, there are actually 169 unique holdings that can be dealt preflop in Hold’em.

There a 4 **combinations** of each suited hand, e.g. **7**♠**8**♠

There are 12 **combinations** of each unsuited hand (not including pocket pairs), e.g. **A**♣**Q**♦.

There are 6 **combinations** of each pocket pair, e.g. **6**♠**6**♥

Of course, the possible **combinations** of each starting hand change after the community cards are dealt. For example, on a KT6 flop there are no longer 6 **combinations** of TT that may appear as a player’s hole cards. (More on counting **combinations** in the strategy application section).

In a four-card variant of poker such as Pot Limit Omaha, the number of possible starting hand **combinations** increases exponentially. There are 270,725 possible combinations of four-card starting hands in PLO.

**Example of Combination used in a sentence ->** (Hold’em) On a K72 board there are 3 combinations of each possible set for a total of 9 set combos.

**How to Use Combination as Part of Your Poker Strategy**

Here we will discuss how to count combinations in a postflop Hold’em scenario. Before we do so, let’s answer a relevant question. *Why would we want to count combinations in Hold’em?* By considering the precise number of certain types of holding within our opponent’s range we can gain insights into what the best play might be. Employing combinatorics usually implies we are in a close situation. If our decision was easy, then counting our opponent’s combinations would be unnecessary. Consider the following example -

Our opponent makes a half pot bet on the river in a situation where we just hold a bluffcatcher. We calculate that he has 15 legitimate value **combinations**. How many bluff **combinations** does he need to show up with in order for us to have a profitable bluff-catch?

To answer this question, we firstly need to calculate our pot-odds. If we made the call we would be investing 25% of the total pot, meaning we need to win more than 25% of the time in order to make profit. (Also expressed as 3:1 pot odds). We hence need our opponent to be bluffing at least 25% of the time in order for our call to break even. If our opponent hence had 5 bluff combos our call would break even. If he had additional bluff combos, our call would begin to make a profit.

If we figured it was a close spot, we might do the combinatorics work. But if we have a read that our opponent never bluffs in a certain spot, we have a clear fold without the need of any **combination** counting.

__Counting Postflop Combinations in Hold’em__

__Unpaired Holdings__

To calculate the remaining **combinations** of a certain unpaired (preflop) hand, we multiply the number of first card remaining in the deck, with the number of the second card remaining in the deck. To make this clear, let’s see an example.

Example – How many **combinations** of KJ are there on the following textures?

**1) A25
2) K23
3) KJJ**

1) There is no King or Jack out there on the board, meaning there are four Kings and four Jacks left in the deck. 4 * 4 = 16 **combinations** of KJ.

2) There is a King already out there meaning that there are only three Kings left in the deck. 4 * 3 = 12 **combinations **of KJ.

3) There are two Jacks, and three Kings left in the deck. 3 * 2 = 6 **combinations** of KJ.

__Paired Holdings__

By “paired” holdings in this context we are referring specifically to pocket pairs. The rules for determining the number of paired **combinations** left in the deck are a little different. We look at the number of cards remaining of that specific rank and multiply it by “itself minus one” and then divide by two. Let’s see that expressed as a formula.

Where X = the number of cards of a specific rank left in the deck.

Number of **combinations** of a certain pocket pair = (x * (x-1)) / 2

Example – How many **combinations** of 66 are there on the following textures?

**1) 552
2) 622
3) 662**

1) There are no Sixes on the board texture meaning there are 4 left in the deck. (4 * (4-1))/2 = 6 **combinations** of 66.

2) There is already one Six out there meaning that there are 3 left in the deck. (3 * (3-1))/2 = 6 **combinations** of 66.

3) There are already two Sixes out there meaning that there are 2 left in the deck. (2 * (2-1))/2 = 1 **combination** of 66.

**Combinations** can be hence used to ascertain the weighting of certain types of hands. For example, it may often surprise players to learn that on boards with a possible straight, there are more **combinations** of straights than flushes. On an AQT texture there are 16 possible combinations of straights but only 9 **combinations** of possible sets.

**See Also**