TPFAP question, pg. 123

In the last paragraph of pg. 123 in TPFAP, Sklansky says that those who don't know how he came up with the 13% figure for the number of 2 card combos that the well known casino owner's 21 year old daughter can go all in with pre-flop should not finish reading TPFAP because he does not know enough about poker to justify doing so. Can anyone please tell how Sklansky came up with the 13% figure? I won't finish reading the book until I know how.

spidey,


I will help you out with combinations, so you can finish reading the book.


First we will start with pairs. There are 13 ranks of cards in a 52 card deck. For illustrative purposes: 2, 3, 4, 5, 6, 7, 8, 9, ten, jack, queen, king, and ace. If you add them all together you will get 13 ranks of cards. Multiply 13 ranks by the 4 suits and you get 52 cards. Simple so far? Right.


In order to figure out all the possible starting hand combinations we will use a simple mathematical formula. To calculate combinations you need to know the total number of cards that are in the deck and the total number of cards you are dealt. So, there are 52 cards available to make a 2 card starting hand. In order to figure out the total amount of possible starting hands use the following equation:


52 total cards multiplied by 51 equals 2652

2 total card starting hand multiplied by 1 equals 2

divide 2652 by 2 and the total number of starting hands is 1326


or


First multiply and then divide


(52 * 51) / (2 * 1) =


2652 / 2 = 1326 Total starting hand combinations


Now, it's time to figure out combinations for pairs. Let's use deuces for this example. There are 4 deuces of different suits. For illustrative purposes:


2s2c, 2s2d, 2s2h, 2c2d, 2c2h, 2d2h


As you can see there are six unique combinations of deuces. The less tedious method to figure this out is to use the combination equation. We are interested in 2 cards for our starting hand and out of those two cards are four of different suits. Here's the equation:


(4 * 3) / (2 * 1) =


12 / 2 = 6 Total starting hand combinations for deuces.


To figure out the total amount of possible pair combinations that we can get we will multiply the total amount of ranks by the possible pair combinations.


13 ranks multiplied by 6 combinations =


78 Total pair combinations.


Now, we will figure out the ace-other suited combinations except for AK


A2, A3, A4, A5, A6, A7, A8, A9, AT, AJ, and AQ gives us a total of 11 ace-other hands. To figure out the total amount of suited ace-other hands we multiply 11 by the number of suits (which is 4).


11 * 4 = 44 ace-other suited combinations.


For ace-king suited we multiply the one ace-king combination by four suits.


1 * 4 = 4 ace-king suited combinations.


For unsuited ace-king combinations we will subtract the total number of suited combinations from the total number of ace-king combinations.


4 aces multiplied by 4 kings equals 16 total ace-king combinations.


16 – 4 = 12 ace-king unsuited combinations.


Lastly, we will figure out the playable suited connectors, excluding 23 and 34.

There are 9 combinations of 4 suits. 45, 56, 67, 78, 89, 9T, TJ, JQ, and QK.


Multiply 9 by the number of suits.


9 * 4 = 36 Combinations of playable suited connectors.


Lets, add up all the combinations and see if the percentage in the book matches.


Pair 78

Ace-other suited 44

Ace-king suited 4

Ace-king unsuited 12

Suited connectors 36

(excluding 23 and 34)


Total playable combinations: 174


Finally, we will figure out the percentage of playable hands by dividing the total playable combinations by the total number of two card starting hands.


174 / 1326 = 0.13122


13.12%


Hope this helps.


Good Luck


Mark

Thanks, Mark. Now I can continue. But I still don't understand how not knowing this can make me a guaranteed loser according to Sklansky.

spidey,


Those genious minds like Sklansky think different than us normal average people. I think it is just his sense of humor maybe?


Anyway, I think that statement is a waste of paper and it should have been excluded. But, in Sklansky's Poker, Gaming, and Life there are a few essays on hold'em essentials that will help you figure out how to mathematically deduce your opponents holdings. I highly recommend getting that book.


Good Luck


Mark