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 Probability Discussions of probability theory

 06-19-2012, 11:49 AM #1 adept     Join Date: Apr 2012 Location: Check Republic Posts: 1,134 odds to have QQ 4times in a row I was just wondering ... happened to friend in tourney on stars
 06-19-2012, 11:50 AM #2 banned   Join Date: Feb 2012 Posts: 259 4 out of 4 times if it's the first four hands he has ever been dealt. I know that much
 06-19-2012, 11:58 AM #3 adept     Join Date: Apr 2012 Location: Check Republic Posts: 1,134 Re: odds to have QQ 4times in a row I mean mathematically .. like odds to have pocket aces are like 250:1 right ? so its 250*250*250*250 ?
 06-19-2012, 12:09 PM #4 forum-inhabiting degen     Join Date: Mar 2010 Location: spaced out ... Posts: 6,639 Re: odds to have QQ 4times in a row I just got dealt Q3o, 68o, A4o, J9s - what are the odds of that exact sequence of hands coming? The problem with this kind of analysis is that it is after the event, when human pattern recognition has already picked out a pattern. http://forumserver.twoplustwo.com/25/probability/ is the best place to post this to talk with the people who really know about this stuff.
06-20-2012, 02:16 PM   #6
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Re: odds to have QQ 4times in a row

Quote:
 Originally Posted by Mudrc I mean mathematically .. like odds to have pocket aces are like 250:1 right ? so its 250*250*250*250 ?
That kind of math only applies to predicting the chance an event happens on exactly the NEXT x hands starting now. It has no relevance for an event that already happened and was simply cherry picked out of a universe of possible events because it happened and was interesting.

06-21-2012, 10:44 PM   #7

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Re: odds to have QQ 4times in a row

Quote:
 Originally Posted by NewOldGuy That kind of math only applies to predicting the chance an event happens on exactly the NEXT x hands starting now. It has no relevance for an event that already happened and was simply cherry picked out of a universe of possible events because it happened and was interesting.
You are wrong. It is correct math if we assume the cards are dealt randomly. The probability that he was dealt QQ four times in a row is exactly 1/221^4=1/2,385,443,281.

The problem is that people would then look at that large number and then think "wow, he was really lucky then!" But if someone came to the forum and posted "What's the chance I was dealt Q9 4 times in a row" it'd be 1/1326^4=3,091,534,492,176. But it wouldn't be very lucky to be dealt Q9 four times in a row because that hand isn't worth very much.

In my opinion a better question would be "What is the probability that he was dealt QQ or better 4 times in a row" because it's the value of the hand that has meaning in the game. But that question still isn't perfect.

Last edited by Karganeth; 06-21-2012 at 10:50 PM.

06-21-2012, 10:49 PM   #8
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Re: odds to have QQ 4times in a row

Quote:
 Originally Posted by Karganeth You are wrong. It is correct math if we assume the cards are dealt randomly. The probability that he was dealt QQ four times in a row is exactly 1/221^4=1/2,385,443,281.
My statement was still correct. The probability he was dealt 4x QQ on those four hands is 100%. Your number is the probability that it happens again on his very next four hands starting now. It's an important distinction. The latter is random, the former is cherry picked from some unknown population of hands already observed, because it was the interesting part.

Last edited by NewOldGuy; 06-21-2012 at 11:05 PM.

 06-22-2012, 12:26 AM #9 Carpal \'Tunnel     Join Date: Jun 2005 Location: Psychology Department Posts: 7,450 Re: odds to have QQ 4times in a row ^^ See...this is why it is a bad question. We see three different answers in 2 posts all of which can be considered correct in one way or another.
06-22-2012, 09:22 AM   #10

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Re: odds to have QQ 4times in a row

Quote:
 Originally Posted by NewOldGuy The probability he was dealt 4x QQ on those four hands is 100%. Your number is the probability that it happens again on his very next four hands starting now. It's an important distinction. The latter is random, the former is cherry picked from some unknown population of hands already observed, because it was the interesting part.
It doesn't matter if it's cherry picked. Cherry picking cannot change the probability of events occurring. Even if Mudrc only ever posted when he got 4x QQ in a row and kept playing until he was dealt them, the probability still wouldn't change. However, given that we know he made a post to these forums it would be certain that he would be dealt QQ.

Last edited by Karganeth; 06-22-2012 at 09:28 AM.

06-22-2012, 09:28 AM   #11
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Re: odds to have QQ 4times in a row

Quote:
 Originally Posted by Karganeth It doesn't matter if it's cherry picked. Cherry picking cannot change the probability of events occurring. Even if Mudrc only ever posted when he got 4x QQ in a row and kept playing until he was dealt them, the probability still wouldn't change. However, given that we know he made a post to these forums it would be certain that he would be dealt QQ. Honestly, your level of understanding of probability is embarrassing. I'm surprised you haven't yet said "It's 50:50 - it either happens or it doesn't."
Karganeth, it does matter. Because we can change the question slightly to, "what is the probability I get QQ four times in a row in my lifetime" and the probability will change dramatically (assuming one plays lots of hands in one's lifetime). And looking at the thread title, "odds to have QQ 4 times in a row" that is a perfectly legitimate interpretation of the question. Just as your interpretation is. So again...the question is poorly specified therefore there are multiple answers.

What's with the insult BTW?

06-22-2012, 09:46 AM   #12

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Re: odds to have QQ 4times in a row

Quote:
 Originally Posted by Sherman Karganeth, it does matter. Because we can change the question slightly to, "what is the probability I get QQ four times in a row in my lifetime" and the probability will change dramatically (assuming one plays lots of hands in one's lifetime).
But you must recognize that NewOldGuy isn't making that particular interpretation because he says the probability is 100%. No finite number of hands dealt could result with a probability of 100%.

NewOldGuy said "4x QQ on those four hands is 100%". This is false. Lets assign each hand a specific number. So he was dealt QQ on hands 34,444, 34,445, 34,446, 34,447. The probability of being dealt QQ on hand 34,444 is exactly the same as the probability of being dealt it on hand number 20,000. He thinks it changes to 1 because we know that it was QQ.

You could make this argument for the flipping on a coin in real life. Before we flip the coin we think it has a 50% chance of landing on heads. But once it lands on heads, we can sort of imagine that the probability that it landed on heads was 1. This is because had we known the speed at which the coin was going to rotate and its exact angular velocity, we would have been able to calculate it was going to land on heads. So our original 50% calculation was the result of a lack of information.

But in the case of QQ I explicitly stated that the deck was random, so that argument cannot be made here.

06-22-2012, 09:58 AM   #13
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Re: odds to have QQ 4times in a row

Quote:
 Originally Posted by Karganeth It doesn't matter if it's cherry picked. Cherry picking cannot change the probability of events occurring.
Quote:
 Originally Posted by Sherman Karganeth, it does matter. Because we can change the question slightly to, "what is the probability I get QQ four times in a row in my lifetime" and the probability will change dramatically (assuming one plays lots of hands in one's lifetime).
It's a more important difference than that. It is valid to say, "Let's look at this historical set of events and see if we can find event X happening several times consecutively in there. Since our set is a random sample, we know that the chance of finding this specific event consecutively is Y. Now let's look."

That's entirely different than looking first and picking out some unspecified outlier we find that happens to be interesting, and then assigning a retroactive probability to what we find, and then compounding the error by forming conclusions based on that finding.

Sherman in your field you should know that the fallacy I describe above has been used by otherwise smart people to justify terrible policy decisions because they didn't understand their statistical mistake. I'm referring to the cherry picking of "clusters", or data mining basically.

I don't disagree with Karganeth's math, which is obviously correct, the point in my first post that he took issue with, and what I actually said, is that such math has no relevance in this situation. Maybe a better word would be "no usefulness". It is useful for the case I described, predicting the NEXT four hands. It can also be useful if you put it in a streak calculator and use the context of our observed sample size (which is unknown here).

Edit in regard to the post above this one: Also, my statement about the event having a probability of 100% was mildly facetious, but it illustrates the point, and is technically correct too, but not any more useful than the conclusion I initially disagreed with. There's no need for you to have to argue with that point. Obviously I understand the math, but I'm talking about principles.

Last edited by NewOldGuy; 06-22-2012 at 10:27 AM.

 06-22-2012, 10:44 AM #14 Carpal \'Tunnel     Join Date: Jun 2005 Location: Psychology Department Posts: 7,450 Re: odds to have QQ 4times in a row What is the probability of Roger Maris hitting more than 60 home runs in 1961? The answer, 1.0. It already happened. That is all NewOldGuy is saying. I could go throw my hand history database, find a seemingly rare pattern of events and make a post that says, "what is the probability of that?" It is a silly question. It already happened. But Karganeth's interpretation of the question is a sound one also (and I think is the one most people who ask these kinds of questions are looking for). But that question really is, "What is the probability of [insert sequence of events] happening if I start counting right now?" And of course, almost no one who posts these kinds of questions did start counting right now. These questions are making me so crazy I am just not going to respond to any new threads that start with them. I have tried and they just keep coming back. Someone else is going to have to do it.
06-22-2012, 01:30 PM   #15
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Re: odds to have QQ 4times in a row

Quote:
 Originally Posted by Sherman What is the probability of Roger Maris hitting more than 60 home runs in 1961? The answer, 1.0. It already happened. That is all NewOldGuy is saying. .
But, there is a legitimate way to deal with probability of past events that does not necessarily result in a 0 or 1 answer. Suppose someone asked you for the probability that George Washington was born on a Tuesday.

Clearly from a classical probability viewpoint, it is 0 or 1 depending on the actual day of his birth. But, what if someone wanted to bet you and you knew he did not know the actual day? Would you not choose 1/7 as a reasonable probability? Such 'guesses' fall within the realm of subjective probability, an accepted discipline if probability axioms are observed.

Bayesian probability incorporates such probabilities very nicely and, in fact, so does poker analysis, such as when we subjectively assign a villain an opening range based on his manner, age, dress, comments and perhaps observing a few hands.

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