Explanation of Combination
The phrase \" combinations \" or its abbreviated form \"combos\" is primarily employed during conversations that involve either poker variants or specific hands within any type of variant. Holdem or Omaha In Texas Hold'em, this term encompasses all cards dealt before the flop, including those that only differ by suit. For example, both 7 ♣ 8 ♣ and 7 ♦ 8 ♦ represent unique combinations of hole-cards even though they share the same rank. Notably, without considering suits, there are actually 169 distinct holdings available before the flop in Hold'em.
There are 1326 unique combinations of two cards There are 4 combinations for every suited hand, such as 7 ♠ 8 ♠.
For each unsuited hand that isn’t a pocket pair, like A ♣ Q ♦, there are 12 possible combinations .
When it comes to pocket pairs, there are 6 combinations available, for example, 6 ♠ 6 ♥.
It’s important to note that once the community cards are revealed, the potential combinations for each starting hand will change. For instance, with a K6T flop, the 6 combinations of TT are no longer relevant since they can’t appear as a player’s hole cards. (Further details on counting combinations will be covered in the strategy application section).
In variations such as Pot Limit Omaha (PLO), the total number of potential starting hand combinations skyrockets. In fact, there are a staggering 270,725 different combinations of four-card starting hands possible in PLO.
In a four-card variant of poker Example of Combination used in a sentence -> (In Hold’em) With a K72 board, there are 3 combinations for each potential set, culminating in a total of 9 set combos.
Integrating Combinations into Your Poker Strategy
This section will focus on how to effectively count combinations in a postflop setup in Hold’em. Before diving into that, let’s address a pertinent question. What’s the benefit of counting combinations in Hold’em? By identifying how many specific types of holdings exist within an opponent's playable range, we can glean valuable insights that inform our best move. Employing combinatorial analysis typically indicates we are facing a close decision. In simpler situations, counting our opponent's combinations becomes unnecessary. Take the following scenario -
Suppose our opponent places a half-pot bet on the river while we possess only a bluffcatcher. We determine he has 15 valid value combinations . How many bluff combinations does he need to have to make our bluff-catching profitable?
To find the answer, we first need to assess our pot odds. If we choose to call, we would be putting in 25% of the entire pot, which requires us to win over 25% of the time to break even. This is equivalent to having pot odds of 3:1. Therefore, we need our opponent to bluff at least 25% of the time for our call to be justifiable. If we believe he only has 5 bluff combos, our call would yield break-even results. More bluff combos would lead to a profitable call.
If we think the situation is close, we might perform the combinatorial calculations. But if we suspect our opponent never bluffs in a particular situation, it would be a straightforward decision to fold without further analysis.
Calculating Postflop Combinations in Hold’em poker combination counting.
To determine the remaining combinations of a specific unpaired (preflop) hand, you multiply the count of the first card remaining in the deck by the count of the second card remaining. To clarify, consider the following example.
Unpaired Holdings
Example – What is the number of combinations for KJ under various board textures?
1) With no King or Jack present on the board, there remain four Kings and four Jacks in the deck. So, 4 * 4 = 16 combinations of KJ.
1) A25
2) K23
3) KJJ
2) If there is one King on the board, only three Kings will be left in the deck. Therefore, it's 4 * 3 = 12 combinations of KJ.
3) If there are two Jacks and three Kings remaining in the deck, it results in 3 * 2 = 6 combinations of KJ.
When referring to “paired” holdings in this case, we specifically mean pocket pairs. The method to calculate how many paired combinations are still available in the deck differs slightly. We take the number of cards left of that rank, multiply it by one less than itself, and then divide the result by two. Here’s the formula expressed clearly.
Paired Holdings
Where X stands for the count of cards of a specific rank remaining in the deck.
The number of combinations of a specific pocket pair can be calculated as follows: (x * (x-1)) / 2.
Example – Evaluating how many combinations of 66 can be found under different board conditions.
1) If there are no Sixes visible on the board, four remain in the deck. Thus, (4 * (4-1))/2 = 6 combinations of 66.
1) 552
2) 622
3) 662
2) With one Six already on the board, only three remain in the deck. Therefore, (3 * (3-1))/2 = 6 combinations of 66.
3) If there are two Sixes exposed, only two remain. So, (2 * (2-1))/2 = 1 combination of 66.
Combinations are valuable for measuring the prevalence of certain hand types. For example, players are often astonished to find out that on boards where a straight is possible, the number of combinations of straights surpasses those of flushes. For instance, on an AQT board, there are 16 possible combinations of straights compared to just 9 combinations of potential sets.
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