Poker Combinaison Possible

On a two-tone board we know he will have 1 combo of each suited hand that can make a flush-draw. But we obviously don't just count all possible flush-draws; we have to think about which of these are actually in his range. So in most situations we can discount holdings like 2 7. Final Note on Poker Combinatorics. He has been crushing the game ever since his historical 2009 SCOOP chop for $470,000, a $3,000 tournament which he satellited into during his college years. Nowadays, you can find him playing live tournaments and cash games in America while hosting live webinars where he provides hand analysis and top-level poker strategy content to our readers. I'm trying to figure out how I can work out the number of possible valid hand combinations of a poker game that a player (opponent) could possibly have when the flop has been dealt on the table. So I'm guessing that I have to take the probability that each hand can occur and then see which one is the highest one that could possibly be?

A combination is when you have a certain number of items in a set, and you want to know how many different ways you can choose a specific number of those items.

In mathematics, this is written in the format 'n choose r' meaning there are n options to choose from, and we want to pick r of them. The formula needed to evaluate a statement of this form is the following:

We'll be using this formula in our discussion of poker probabilities relating to hand combinations. However, if you aren't comfortable writing out the math on your own, you can still use a calculator to find the value of combinations. Typing '52 choose 4' into Google, for example, will tell you how many different ways you can be dealt a four-card starting hand in Omaha.

Five Card Poker Hands

In games like five card stud and five card draw, we need to be able to figure out the chance of getting a certain hand by just being dealt five random cards.

The following chart shows the chance of being dealt these hands right off the bat by listing the number of combinations possible for each poker hand rank.

To find the total number of combinations of a five card hand, you'll do 52 choose 5 as follows:

You divide the number of combinations of a single hand by this value to get the chance of being dealt that hand with five random cards from a deck. This will tell you how likely you are to be dealt a specific hand which is an exceptionally important piece of information in games that use five cards.

Seven Card Poker Hands

Playing with seven card poker hands is very interesting, and this is what happens with holdem and Omaha (2 hole cards + 5 community cards), the two most popular games played today.

In these games, poker combinations and math are less about knowing the chances of being dealt a specific hand but about using these ideas to figure out the probability of your opponents having certain holdings.

Unique and Non-unique Starting Hands in Omaha

If you have the hand A♠A♥K♠K♥ in Omaha, that's known as a distinct or unique combination of cards because there's only one way you can be dealt that hand. However, if you just say that you were dealt AAKK double-suited, then there could be several different ways of being dealt that particular hand, and you would have to figure out how many different unique combinations there were by using two combinations of suits like so:

Each of these six examples are unique combinations because there are no other ways to be dealt the hand. The reason that unique combinations are so important is that they help you to find the probability of actually being dealt those hands as you're about to see.

Finding the Probability of Texas Holdem Hands Using Combinations

Poker Combinaison Possible Extreme

In Texas holdem, you have the best opportunities for using the poker combinations probability to increase your chances of winning because it's how you evaluate what your opponents might be holding. You can also use it to determine how often you will be dealt certain hands.

Hand reading in Texas Holdem requires you to know the relative chances of your opponent having different hands in different situations.

For example, how many ways can you be dealt AA? Look at the possible combinations of suits to figure this out: spade-club, spade-heart, spade-diamond, club-heart, club-diamond and heart-diamond. That's a total of six. Remember that A♠A♥ is the same thing as A♥A♠, so they aren't counted as two different hands.

To figure out how many total ways you can be dealt a starting hand, you'll calculate the combination 52 choose 2 to find the total number of possible starting hands, and then you do the division to find the chances of being dealt AA:

So there's a 0.45 percent chance of being dealt AA, and this process can be repeated for any pocket pair since they will all have an equal chance of being dealt.

There are 16 ways to be dealt a non-pair hand, and you can use the same process as above to find that there's a 1.21 percent chance of being dealt a specific one.

Poker in 2018 is as competitive as it has ever been. Long gone are the days of being able to print money playing a basic ABC strategy.

Today your average winning poker player has many tricks in their bags and tools in their arsenals. Imagine a soldier going into the heat of battle. Without his weapons, he is practically useless, and chances of survival are extremely low.

If you sit down at a poker table without any preparation or general understanding of poker fundamentals, the sharks are going to eat you alive. Sure you may get lucky once in a blue moon, but over the long term, things won’t end well.

With the evolution of poker strategy, you now have many tools at your disposal. Whether it be online poker training sites, free YouTube content, poker coaching, or poker vlogs, there’s no excuse to be a fish in today's game.

Some of the essential fundamentals you need to be utilizing that every poker player should have in their bag of tricks whether you are a Tournament or Cash Game Player are concepts such as hand combinations (Also known as hand combinatorics or hand combos).

Hand Combinations and Hand Reading

If you were to analyze a large sample of successful poker players you would notice that they all have one skill set in common: Hand Reading

What does hand reading have to do with hand combinations you might ask?

Well, poker is a game of deduction and to be a good hand reader, you need to be good at correctly ranging your opponents.

Once you have assigned them a range, you will then need to start narrowing that range down. Combinatorics is one of the ways we do this.

So what is combinatorics? It may sound like rocket science and it is definitely a bit more complex than some other poker concepts, but once you get the hang of combinatorics it will take your game to the next level.

Combinatorics is essentially understanding how many combos each of your opponent's potential holdings are and deducing their potential holdings utilizing concepts such as removal and blockers.

There are 52 cards in a deck, 13 of each suit, and 4 of each rank with 1326 poker hands in total. To simplify things just focus on memorizing all of the potential combos to start:

• 16 possible hand combinations of every unpaired hand
• 12 combinations of every unpaired offsuit hand
• 4 combinations of each suited hand
• 6 possible combinations of pocket pairs

Here is a short video example of using combinatorics to count the number of ways a non-paired hand AK can be arranged (i.e. how many combos there are):

So now that we have this memorized, let's look at a hand example and how we can apply combinatorics in game.

We hold A♣Q♣ in the SB and 3bet the BTN’s open to 10bb with 100bb stacks. He flats and we go heads up to a flop of

Poker Combinaison Possible Double

A♠ 5♦ 4♦

We check and our opponent checks back with 21bb in the middle

Turn is the 4♥

We bet 10bb and our opponent calls for a total pot of 41bb

The river brings the 9♠

So the final board reads

A♠ 5♦ 4♦ 4♥ 9♠

We bet 21bb and our opponent jams all in leaving us with 59bb to call into a pot of 162bb resulting in needing at least 36% pot equity to win.

Our opponent is representing a polarized range here. He is either nutted or representing missed draws so we find ourself in a tough spot. This is where utilizing combinatorics to deduce his value hands vs bluffs come into play. Now we need to narrow down his range given our line and his line. Let's take a look at how we do this...

Poker Combinaison Possible Games

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Blockers and Card Removal Effects

First, let's take a look at the hands we BLOCK and DON’T BLOCK

Since we hold an Ace in our hand and there is an Ace on the board, that only leaves 2 Ace’s left in the deck. So there is exactly 1 combo of AA.

We BLOCK most of the Aces he can be holding, so we can REMOVE some Aces from his range.

We do not BLOCK the A♦ as we hold A♣Q♣, and the A on the board is a spade, so it is still possible for him to have some A♦x♦ hands.

We checked flop to add strength to our check call range (although a bet with a plan to triple barrel is equally valid in this situation SB vs BTN) and because of this our opponent may not put us on an A here.

If he is a thinking player his jam can exploit our thin value bet on the river turning his missed straight/flush draws into a bluff to get us to fold our big pocket pairs and even make it a tough call with our perceived weak holdings.

The problem in giving him significant credit for this part of his bluffing range is the question of would he really shove here with good SDV (Showdown Value)?

These are the types of questions we must ask ourselves to further deduce his range along with applying the combinatoric information we now have.

Now, let's look at all the nutted Ax hands our opponent can have.

If he has a nutted hand like A4 or A5, and we assume he is only calling 3bets with Axs type hands, the only suited combo of those hands he can have are exactly A♥5♥. He can’t have A♦5♦ or A♦4♦ because the 4 and the 5 are both diamonds on the board blocks these hands.

Lets take a look at all of this value hands:

There is only 1 combo of 44 left in the deck, 2 combos of A9s, 3 Combos of 55, 3 Combos of 99, 2 Combos of 45s - some of these hands may also be bet on the flop when facing a check.

So to recap we have:

1 Combo A5s, 2 Combos of A9s, 3 Combos of 55 (With one 5 on board, the number of combinations of 55 are cut in half from 6 combos to 3 combos), 1 Combo of 44, 2 Combos of 45s, 3 Combos of 99

Total: 12 Value Combos

Now we need to look at our opponent's potential bluffs

Based on the villain's image, this is the range of bluffs we assigned him:

K♦Q♦(1 Combo), J♦T♦ (1 Combo), T♦9♦ (1 Combo), 67s (4 Combos)

He may also turn some other random hands with little showdown value into bluffs such as A♦2♦/A♦3♦

Total: 9 Bluff Combos

9(Bluff Combos) + 12(Value Combos) = 22

9/21 = 42% of the time our opponent will be bluffing (assuming he always bets this entire range)

11/21 = 58% of the time our opponent will be value raising

Now, this is the range we assigned him in game based on the action and what we perceived our opponents range to be.

We are not always correct in applying the exact range of his potential holdings, but so long as you are in the ballpark of that range you can still make quite a few deductions to put yourself in the position to make the correct final decision.

According to the range we assigned him, he has 11 Value Combos and 9 Bluff Combos which gives us equity of 42%. This would result in a positive expected value call as we only need 36% pot odds to call.

However, unless you are playing against very tough opponents you will not see someone bluffing all 9 combos we have assigned - most likely they will bluff in the range of 4-6 combos on average which gives equity in the range of 20-30% equity. This is not enough to call.

Poker Combinaison Possible Game

We ultimately made our decision based on the fact that we felt our opponent was much less likely to jam with his bluffs in this spot. Given that it was already a close decision to begin with, we managed to find what ended up being the correct fold.

Now this all may seem a bit overwhelming, but if you just start taking an extra minute on your big decisions you’d be surprised how quickly you can actually process all this information on this spot.

A good starting point is to simply memorize all of the possible hand combinations listed above near the beginning of the article.

Get access to our 30-minute lesson on Combinatorics and PokerStove by clicking on one of the buttons below:

Conclusion On Combinatorics

Eventually accounting for your opponent's combos in a hand will become second nature. To get to the point that , a lot of the work needs to be done off the table and in the lab. As you spend more time studying it and reviewing hand histories like the one above, you will find yourself intuitively and almost subconsciously using combinatorics in your decision making tree.

But the work will be worth the effort, as being able to count combos on the fly will add a new dimension to your game, allow you to make more educated decisions, become a tougher opponent to play against and move away from playing ABC poker.

Want more content like the ones in this blog post on poker combinatorics? Check out our Road to Success Course where we have almost 100 videos like this to help take your game to the next level. You can also get the first module of the Road To Success Course for Free - for more details see the free poker training videos page by TopPokerValue.com.