Bayes or not Bayes, that\'s the question....
 

I found an article by David Sklansky in cardplayer online and it made me wonder.

First of all, here is the link:
http://www.cardplayer.com/poker_maga...77&m_id=68

Now there is an interesting part about A-K and pair combinations. A-K can be made from 16 different combinations while a pair can only be made from 6 different combinations.

Looking into PoT (p. 229) I find a reference to Bayes theorem and that the odds of getting A-K instead of A-A are 4:3!

This is true, because of how the cards are dealt. You can make A-A in 6 different ways, starting with 4 different aces = 24. You can make A-K in 16 different ways, starting with either ace or king = 32. 32/24 = 4/3

What I am wondering about is why in the article David only used the pure hand combinations and not the possible combinations how these cards can be dealt, because if you do that you get different results. Quite obvious because Davids math is based on 16/6 while mine is based on 32/24.

HELP!!!

Sorry for my stupidity, but I am 38 years old and I knew I had this all in school, but since it was 20 years ago, I simply forgot it all.

Re: Bayes or not Bayes, that\'s the question....
 

Looks to me that the odds of getting AK vs AA are 16-6 or 8-3. Odds of getting AK vs either AA or KK is 16-12 or 4-3. I don't see that what you're doing with the 32-24 makes any sense.

PairTheBoard

Re: Bayes or not Bayes, that\'s the question....
 

Oh lol, nm...found the mistake. Thanks!

Re: Bayes or not Bayes, that\'s the question....
 

When you talk about the number of ways a hand can be made, you have to be careful to specify whether or not order matters. Is As/Ah the same as Ah/As or not? You can calculate it either way, but you have to be consistent.

There are 16 ways to get AK, but eight of them are the same as the other eight with the card reversed. There are 12 ways to get AA, but six of them are the same as the other six.

So 16:12 or 8:6, 4:3 either way.

Re: Bayes or not Bayes, that\'s the question....
 

Ah well, my mistake was rather simple.

In PoT Sklansky was talking about odds for A-K against A-A and K-K which is two pairs. Those odds are 4:3. In the other text he was talking about the odds A-K against single pairs and I did not notice it.

So I started adding, doubling and such until I got 4:3, because I wanted to get 4:3 [img]/images/graemlins/smile.gif[/img]