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 06-09-2012, 01:47 AM #1 grinder   Join Date: Dec 2008 Posts: 664 AK and AQ what are the chances If i have AQ and there is one person left to act what are the chances/odds that they have AK? I have learned a lot from you all here, doesn't mean i understand it all. I think i made a mistake when i looked down at AQ with one person left to act directly on my left, and she had hit AK 7 times in 80 hands maybe more that's what i had seen. We were live so when the thought entered my mind that she has had AK so many times already, that was a mistake correct? I just don't fully understand why? I know cards have no memory and every hand is independent from the other etc but then how do they make those probability tables/charts? thanks
 06-09-2012, 10:19 AM #2 Carpal \'Tunnel     Join Date: Feb 2006 Location: Austin, TX Posts: 14,950 Re: AK and AQ what are the chances If we assume that the cards that were folded so far are random, then there are 3 aces and 4 kings left in the deck. This is 12 combos of hands. The total number of combos that could be made is 50*49/2 because there are 50 cards we don't know about, and we have to choose 2. We divide by 2 because the order is not important, i.e. 6c7d = 7d6c So, the chance is 12/1225, and without using a calculator I can see that this is about 1/100. Very small. Now... there is an observed effect that when it folds to you in the small blind, the deck and your opponent's hand are a bit more likely to have an ace in them, because all the folds in front of you indicate people had bad hands.
 06-09-2012, 11:23 PM #3 grinder   Join Date: Dec 2008 Posts: 664 Re: AK and AQ what are the chances Ya you would think! Thanks rusty why did they have 2 have it with a K LOL. Really 100 to 1 it seems it happens more often than that! One other just for s*its and g*ggles is hitting AK 7times in 80 hands unusual? In other words how often should you expect to get dealt AK? I'm thinking it should be about 1 in 50
 06-09-2012, 11:29 PM #4 Carpal \'Tunnel     Join Date: Feb 2006 Location: Austin, TX Posts: 14,950 Re: AK and AQ what are the chances There are 16 ways to make AK and 52*51/2=1326 possible starting hands, so you'll get it about 1/83 hands.
 06-09-2012, 11:48 PM #5 veteran   Join Date: Mar 2009 Location: In the wires Posts: 2,274 Re: AK and AQ what are the chances And the chance to get it 7 times in the next 80 hands starting now is about 1/18K. However, the 80 hand sample here is cherry-picked after the fact. So the chance you have some span of 80 hands containing 7 AK in a long series of hands played (tens of thousands) is much greater, and eventually becomes virtually certain.
 06-10-2012, 06:25 AM #6 old hand     Join Date: Sep 2007 Location: St. ELMO!!! Posts: 1,208 Re: AK and AQ what are the chances Also the chances are 1/83 every hand not 1 out of 83 hands
06-10-2012, 08:44 AM   #7
Carpal \'Tunnel

Join Date: Feb 2006
Location: Austin, TX
Posts: 14,950
Re: AK and AQ what are the chances

Quote:
 Originally Posted by Michaellawre Also the chances are 1/83 every hand not 1 out of 83 hands
When someone says "1 out of X hands" mentally add "on average"

06-12-2012, 01:16 AM   #8
grinder

Join Date: Dec 2008
Posts: 664
Re: AK and AQ what are the chances

Quote:
 Originally Posted by NewOldGuy And the chance to get it 7 times in the next 80 hands starting now is about 1/18K. However, the 80 hand sample here is cherry-picked after the fact. So the chance you have some span of 80 hands containing 7 AK in a long series of hands played (tens of thousands) is much greater, and eventually becomes virtually certain.
I don't know what cherry picked means. She was just sitting to my immediate left through the whole 80 hands of the tourney till i got knocked out (she had AK again! to my AQ) blind vs blind. Why should i not take into consideration how many time she has had AK in that tourney? Not sure why it should not be more unlikely for her to have it since she has had it so many times in the last 80. Did i ask that right?

06-12-2012, 04:44 AM   #9
veteran

Join Date: Mar 2009
Location: In the wires
Posts: 2,274
Re: AK and AQ what are the chances

Quote:
 Originally Posted by apkrnewb I don't know what cherry picked means. She was just sitting to my immediate left through the whole 80 hands of the tourney till i got knocked out (she had AK again! to my AQ) blind vs blind. Why should i not take into consideration how many time she has had AK in that tourney? Not sure why it should not be more unlikely for her to have it since she has had it so many times in the last 80. Did i ask that right?
Cherry picked means that you picked the 80 hand sample after it happened, it is NOT a random sampling of 80 hands. The chance it happened is 100% ("it" being 7 AK). If some other unusual event happened during that 80 hands, you would have noticed that other event instead.

If we pick the NEXT 80 hands played starting now, then the chance it happens again is the calculated probability.

In a nutshell, the probability only applies to a random sample. We can always find some unusual cluster of things if we get to cherry pick the sample.

Last edited by NewOldGuy; 06-12-2012 at 04:54 AM.

 06-13-2012, 11:38 PM #10 centurion     Join Date: Apr 2012 Posts: 128 Re: AK and AQ what are the chances apkrnewb... think of it like this: 1) Simplify the problem - Flipping a coin twice and hitting heads both times. 2) When you look at the situation before you start the trial, the odds of heads coming up each time will be 50% for the first time and 50% for the second time. Calculating that... (.50*.50 = .25) 25% of the time heads will come up both times. 3) Now look at the problem mid-trial after heads came up the first time. You only have to flip one more time and the probability of heads coming up this time is 50%. 4) Analyze. The probability of the coin coming up heads twice in a row is a low 25%, but if the first trial is successfully, heads coming up on the second trial has the normal 50% odds of occurring. 5) Compare. Although the odds of the person to you left having AK so many times in 80 hands is low, those previous hands are in the past and now the odds of her having AK in the hand where you busted revert back to the normal odds of 1/83. In other words... if you look at the situation as a whole you are already in the "low probability realm" because of the number of times the person to your left has had AK over the last 80 hands. That doesn't change the fact that every new event still has the normal probability of occurring one more time. I may have just confused you more... it's probably a good thing I'm not a teacher. Last edited by Hbtn; 06-13-2012 at 11:53 PM.
06-16-2012, 04:33 PM   #11
Pooh-Bah

Join Date: Jul 2005
Location: Phoenix
Posts: 4,677
Re: AK and AQ what are the chances

Quote:
 Originally Posted by NewOldGuy If some other unusual event happened during that 80 hands, you would have noticed that other event instead.
Or, as Bertrand Russel said, we encounter a miracle every time we read the license plate of a passing automobile.

 06-26-2012, 11:45 AM #12 grinder   Join Date: Dec 2008 Posts: 664 Re: AK and AQ what are the chances Actually that did not confuse me more! It was a big help especially when taken in context with what everyone else said! thanks all

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