There is a small amount of poker math needed to become a professional or winning poker player. It includes a rudimentary understanding of poker combinatorics.
Poker Combinatorics Rule #1
There are in total 1326 poker hands that can be dealt in Texas Hold’em.
The first number and most important poker combinatorics number you need to know is 1326. This is the number of possible starting hand combinations that can be dealt with in no-limit Hold’em. This is derived from the mathematical equation of 52C2! (pronounced 52 choose 2) then divide this by 2. You divide by two because it doesn’t matter in which order you receive the two cards. It is not necessary that you understand how this number is derived. Simply remembering it will more than sufficient.
Poker Combinatorics Rule #2
There are 16 combinations of any unpaired hand in Texas Hold’em, each representing 1.2% of all possible hands.
The next poker combinatorics number you need to remember is 16. If you are dealt AK, there are 16 possible combinations. There are four aces in every deck, and each ace can be paired with four kings. Four multiplied by four gives us our number 16. Now if we look back at rule #1, we can see that we will be dealt AK (or any other unpaired combination) 16 times out of 1326, or 1.2% of the time. Another way to look at this is: the odds of being dealt AK is about 82:1. If you are being dealt 30 hands per hour, you should get AK just under once every three hours.
Poker Combinatorics Rule number #3
There are 6 combinations of any pocket pair hands in Texas Hold’em, each representing 0.45% of all possible hands.
The next important number is 6. This is the number of pocket pair combinations there are. This is represented by the mathematical notation of 4P2! (pronounced 4 permutations 2). If you need to visualize this, look at pocket aces as an example. These are the combinations: AsAh; AsAd; AsAc; AhAd; AhAs; AdAc.
An alternative way to think of this is: the odds of being dealt pocket is aces 6 times out of every 1326 hands or one time in every 221 hands. At 30 hands an hour, it will take you on average just over 7 hours to be dealt pocket aces.
Poker Combinatorics Rule number #4
There are 4 combinations of any suited unpaired hands in Texas Hold’em, each representing 0.30% of all possible hands.
It should be obvious now that there are 4 combinations of any suited unpaired hands. A common hand to which this is relevant is, JT. It is a hand that is often correctly folded when unsuited and raised when suited.
Example
So in the following example, you are using a strategy that recommends going all-in with the following hands. AK, AQs, AA, KK, QQ and JJ. How many combinations do you have? The correct notation for this range is {AQs+, JJ+}.
You have one combination of unpaired hands (AK) for 16. You have one combination of a suited unpaired hand (AQs) for 4. You also have four pocket pairs for 6 combinations each, or 24. That is a total of 44 combinations out of 1326 or 3.3% of all possible hands. In this example, it can be said that you are playing a 3.3% Range, or R{AQs+, JJ+} = 3.3%
Learning to make these types of calculations during a hand is an important skill for a winning poker player. Over time and with repetition, it becomes quite easy. Learning to make these poker combinatorics calculations quickly is a stepping stone to more advanced and useful calculations.
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