Combinations Part II: Starting Hands

Hey

Last posts I posted was about the basics of combinations. This post is going to be about how combinations are used when trying to figure out texas holdem starting hands.

People keep saying there are 1326 possible starting hands. How do they get this number?

There is 52 cards in a deck of cards. When I am dealt my first card for my starting hand there is 52 possibilities. Then I am dealt my second card for 51 possibilites. (X) Objects Taken From.

Now that we were dealt 2 cards for our starting hand. This is our (Y) At a Time part of the formula.

The formula looks like this:
(52)
(2)

52 x 51-------2652
_______ = ________ = 1326 number of possible starting hands
2 x 1------------2



Have you ever wondered? Why people say being dealt any pocket pair in texas holdem is 220 to 1?

There is 52 cards in the deck, I am dealt a pocket pair. When I was dealt my first card, There were 4 possibilities of getting this card. Then my second card dealt to me was the same rank. There were 3 possibilites of me getting another card of the same rank. These two possibilies is what we call our (X) Objects Taken From.

Since we are choosing 2 cards at a time. This would be our (Y) At a Time - part of the formula. Remember were dealt our 1st card. Then dealt our 2nd card. Which would represent 1 x 2 = 2.

Our formula for being dealt a pocket pair is below.
(4)
(2)

4 x 3-----------12
______ = __________ = 6
2 x 1------------2

Now, that we figured out the combination for pocket pairs. We need to divide this 6 by the total number of starting hands.

6 / 1326 = 221; or 220 to 1 that we will be dealt a pocket pair in holdem.


Now. What is the possibility I am dealt two suited cards? If we are looking for two hearts out of a 52 card deck we then set up our formula as:

(13) We have 13 hearts to Take From
(2) We are only choosing 2 cards At A Time.

13 x 12-------156
_______ = _______ = 78
2 x 1----------2

Now we divide 78 by 1326 the total possible starting hands.

78 / 1326 = 17; or 16 to 1 - that you will be dealt two suited cards that are hearts.


The starting hands fomula's here can be used on further but I will be writing forever. Play with these numbers and see what you come up with. I don't know what my next post will be about.