# OK, here's the skinny on probabilities...

#### RammerJammer

##### Visionary
Silver Level
A long and rancorous debate has broken out on another thread concerning poker probabilities. (And probabilities in general.) After chastising for not doing their homework those in disagreement with what I knew to be a standard mathematical equation for determining the odds of succession, I decided to practice what I preach. I looked it up. Given that it's good stuff for everyone, I decided to post it here in a new thread instead of 4 pages deep on the old one.

Surprise! We're ALL right! As I repeatedly asserted in the original thread, it completely depends on how you approach the question. It's as much a matter of perspective as pure math. Read on.

Brian Alspach's Mathematics & Poker Page
Professor Emeritus of Mathematics & Statistics
Simon Fraser University
www.math.sfu.ca/~alspach/index.html

"Probabilities for Successive Memorable Hands"
Back-to-Back Identical Hold 'Em Hands

"Back-to-back hands consisting of the same two cards is something a player notices. Another successive occurrence players notice is being dealt back-to-back special hands. For example, back-to-back pocket aces usually draws comments when it happens. When this happens, sometimes you will hear a player ask, 'What are the chances of being dealt successive hands of pocket aces?'

"The problem with the question as asked is that it makes no sense, because it may be interpreted in several ways. The probability of being dealt A-A on a particular deal is 1/221. Thus, if you interpret the preceding question to be asking for the probability of being dealt A-A on two particular successive deals, the answer is

1/221 x 1/221 = 1/48,841

"If, on the other hand, you interpret the preceding question to be asking for the probability of being dealt A-A on the next hand, given that you have just been dealt A-A, then the answer is 1/221. This interpretation is not terribly interesting."

So, the reason why we have stalemated over this probability problem is that you can take either view and be correct. Your odds of drawing a pair of pocket aces is the same on every deal...221 to 1 on that deal. But if you're asking what is the probability that someone actually will be dealt pocket aces on two consecutive deals, it is 1 in 48,841.

#### diabloblanco

##### Legend
Silver Level
Basically, it all depends upon which way you approach the problem. While I completely understand the multiplication of statistical probabilities to determine consecutive outcomes, I saw it as an unnessisary complication of the question at hand. The devil is always in the details. Thanks for researching the question and finding the answer, and although I have done it via PM, I will also say publicly, if I offended members by posts in the other thread, especially you, RJ, I apologize. Some of you guys were politely in disagreement, others not so much. In the end were all here for the advancement of the game and to combine talents to help one another get a leg up in the poker world. Lets get back to the business of making money.

Silver Level

#### Sammyv1

##### Legend
Silver Level
Great work on this subject Rammer. You always do some hard work and research on these hard to awnser Subjects and I appreciate it. By the way did you get a Pacific poker bonus yet! Or were you already a member. I'm still trying to win more so I can cash out more money and use it on another web site!

P

#### pookyman

##### Rising Star
Bronze Level
The probability of someone holding Aces seems to increase when I catch a pair of Kings.