Grinderschool Free Poker Strategy Articles
Introduction to Hand Combinations
Let me give you all a quick introduction to card combinations. First, remember that there are 4 suits of every card:
A, A, A, A
To figure out how many combinations are possible for an un-paired hole card, multiply the number of combinations per card together. For example, in calculating the number total AK hands we know that there are 4 A's and 4 K's in the deck:
4 Aces * 4 Kings = 16 total combinations of Ace-King
There are only 4 combinations for any suited cards: A K; A K; A K; A K
So that leaves 12 combinations of un-suited, un-paired Ace-King (otherwise known as Ace-King Offsuit).
Each pair has 6 combinations to it, so as an example QQ: Q Q; Q Q; Q Q; Q Q; Q Q; Q Q
You have A Q and the flop is: Q J 2. If your opponent is loose/passive pre-flop, what is the number of combinations he can have per a specific hand?
QQ = 1 Combination: Q Q; He can't have the Q because it is in our hand or the Q because it is on the flop.
JJ = 3 Cominations: J J; J J; J J; He can't have any hand with the J in it because it is on the flop.
22 = 3 Cominations: (Same as Above).
There are only 6 combinations of: QJ (2 Queens * 3 Jacks), Q2 (2 Queens * 3 Deuces) and AQ (3 Aces * 2 Queens)
He can also have 6 combinations of KK, but only 3 combinations of AA possible since we have the A.
There are 9 combinations of: J2 (3 Jacks * 3 Deuces), AJ (3 Aces * 3 Jacks)and A2 (3 Aces * 3 Deuces) possible.
There are 8 combinations of: KQ (4 Kings * 2 Queens), QT (2 Queens * 4 Tens) and Q9 (2 Queens * 4 Nines) possible.
There are 16 combinations of: KT (4 Kings * 4 Tens), T9 (4 Tens * 4 Nines), K9 (4 Kings * 4 Nines) and 98 (4 Nines * 4 Eights) possible.
There are also 12 combinations of AK (3 Aces * 4 Kings), AT (3 Aces * 4 Tens) and A9 (3 Aces * 4 Nines) possible if you choose to include those hands in his range.
The total number of combinations pre-flop in a 52 Card Deck is 1326. However, there are only 169 different specific hands since we don't differentiate between suits pre-flop. We can calculate the likelihood of getting dealt a specific hand by dividing the number of combinations for that hand by the total combinations in the deck. For Example:
AA: 6/1326 = 1/221 or 0.45%
AKs: 4/1326 = 1/331.5 or 0.30%
AK: 16/1326 = 1/82.875 or 1.21%
This was a quick introduction to hand combinations; hopefully this will give you a starting point to understanding hand combinations to a further degree in your poker progress.