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 23rd May 2012, 04:17 PM #201 jt512 Critical Thinker   Join Date: Sep 2011 Posts: 389 Originally Posted by RandomElement Final reminder: part of my hypothesis is that stronger players will roll better than weaker ones even when no skill is involved. I notice that not one person even attempted a quick prestudy that could be done by merely observing high dollar games in non-contact positions and noting either expected or unexpected results. Why would anyone even bother to a "pre-study," when the laws of physics rule out supernatural hypotheses such as yours. Jay
 23rd May 2012, 04:19 PM #202 sol invictus Philosopher     Join Date: Oct 2007 Location: Nova Roma Posts: 8,419 Originally Posted by jt512 Let's say I really have no idea what P(D|H1), the probability of the data is under the alternative hypothesis, the hypothesis that the sequence is non-random. Since I have no idea whatsoever, the probability could be any number between 0 and 1, and, more specifically, because of my ignorance, it could be any number between 0 and 1 with equal probability. This implies that the best representation of my belief (ie, complete ignorance) about the probability of the data under the alternative hypothesis is that it has a uniform distribution. That is, the best representation of this probability is a weighted average of all the numbers between 0 and 1, with equal weights. That average is, obviously, .5. Gibberish, particularly the bolded parts. In all examples discussed there are many possibly Ds, and since the sum over all Ds of P(D|H)=1, they cannot all be equal to .5. Quote: Now we redo the calculation, under this assumption. Note that we are no longer computing an upper limit on the probability that the sequence is random; we are calculating the probability itself, based on our current state of knowledge. Then, by Bayes' Theorem $2.48\times10^{-59}=\frac{1.24\times10^{-68}}{.5}\times\frac{1-10^{-9}}{10^{-9}}$ So we started out with a prior belief that our letter (or its underlying number) generator was random of 999999999/1000000000, near certainty. After seeing the outcome, a–zA–Z, our belief that it is random is miniscule, on the order of 10–59. More nonsense. You used P(that sequence|generator non-random)=.5, which means the hypothesis you're comparing the null hypothesis to is that the letter generator produces that particular sequence (out of the 10^68 possible sequences) half the time. You're making exactly the same mistake you've made all along, only this time you've "supported" it with some wrong math. If I go out and pick grass blade #231,512,692 out of a huge field at random, your "argument" would lead you to conclude that with overwhelming probability I deliberately picked blade #231,512,692 and couldn't possibly have chosen randomly - and you'd conclude that no matter what blade I picked. Quote: Incidentally, another name for the uniform distribution is the beta(1,1) distribution, and it is a standard choice for P(D|H1). It is the default choice on Jeff Rouder's applet, and its use to represent minimal knowledge a probability is discussed in every standard text on Bayesian hypothesis testing. This is probably the calculation I should have made in the first place. The default distribution used for the "alternate" hypothesis on the website is flat in the number of successes, i.e. any number of successes has the same probability. That's not p=.5, it's p=1/(T+1), where T is the total number of trials. Last edited by sol invictus; 23rd May 2012 at 04:29 PM.
 23rd May 2012, 05:04 PM #203 marplots Philosopher   Join Date: Feb 2006 Posts: 5,401 Originally Posted by RandomElement Final reminder: part of my hypothesis is that stronger players will roll better than weaker ones even when no skill is involved. I notice that not one person even attempted a quick prestudy that could be done by merely observing high dollar games in non-contact positions and noting either expected or unexpected results. I assume you mean, by "strong" and "weak," that would be known going in? How should we then interpret "rolling better?" Would that mean "better in the exact same position" or some other meaning of better? I don't know enough about backgammon to do it.
 23rd May 2012, 05:29 PM #204 SezMe post-pre-born     Join Date: Dec 2003 Location: Santa Barbara, CA Posts: 16,369 RE, is your bad luck limited to backgammon or does it infest other aspects of your life?
 23rd May 2012, 05:54 PM #205 jt512 Critical Thinker   Join Date: Sep 2011 Posts: 389 Originally Posted by sol invictus Gibberish, particularly the bolded parts. Just because you don't understand something doesn't mean it is gibberish; however, I was rushed when I made that post, and I could have explained myself better, so I'll give you the benefit of the doubt, and try to do a better job in this post. Quote: In all examples discussed there are many possibly Ds, and since the sum over all Ds of P(D|H)=1, they cannot all be equal to .5. First of all, the mistake I made yesterday was considering outcomes that did not occur. In Bayes Theorem, D is the data that actually occurred; it does not include data that hypothetically could have occurred, but did not. So I was wrong to even try to take into consideration other non-random-looking sequences. The only one that should enter into the calculation is the actual outcome, the sequence a–zA–Z. So, actually, there is only "one D" in Bayes Theorem, the data that actually occurred. The form of Bayes' Theorem that I used in my original (and wrong) calculation contains the term P(D|H1), the probability of the data D under the alternative hypothesis H1, that is, the probability that a non-random number generator would generate the sequence a–zA–Z. We don't know what that probability is. To handle our uncertainty, we treat D as a bernoulli random variable with parameter p, and we treat p as a random variable with pdf f(p), which represents our knowledge about what values p are likely to take on. In the present case, though, we have no knowledge about p at all. The probability that a non-random number generator would generate the sequence we got depends on the behavior of a population of non-random number generators about which we are completely ignorant. p could be 1—for all we know every non-random number generator puts out the sequence we got every time, or it could be any other probability—maybe there is a huge number of non-random 52-letter sequences that non-random number generators put out. Therefore, the best we can say is that p could be any number between 0 and 1, and since we have no reason to favor any set of values in that range over any others, we should treat all values of p as equally likely. That means that the best way to express our uncertainty about p is to make f(p) the uniform density, f(p) = 1, 0 ≤ p ≤ 1. To accommodate the fact that we are treating p as a continuous random variable, we have to use a more general form of Bayes Theorem: $\frac{P(H_0|D)}{P(H_1|D)} = \frac{P(D|H_0)}{\int_0^1pf(p|H_1)\,dp} \times \frac{P(H_0)}{P(H_1)},$ where the denominator of the Bayes' factor is now explicitly written as a marginal likelihood. Since f(p) is the unifiorm pdf, $\int_0^1pf(p|H_1)\,dp=\int_0^1p\,dp=.5\,.$ This does not mean that P(D|H1)=.5—P(D|H1) no longer appears in the equation. It has been replaced by the marginal likelihood of p|H1, which is essentially a continuous weighted average of the values that p can take on, where the weights are f(p). But in our case, since f(p) is the uniform density, the weights are all 1, so the weighted average is just the simple average value of p, .5. But, again, this does not mean we are assigning a probability of .5 to anything. Quote: The default distribution used for the "alternate" hypothesis on the website is flat in the number of success, i.e. any number of successes has equal probability. That's not p=.5, it's p=1/(T+1), where T is the total number of trials. No. Per the website: "Alternative Model: p~Beta(a,b)," and the default values for a and b are each 1. Therefore the default alternative model is Beta(1,1), which is the uniform distribution. Jay
 23rd May 2012, 07:45 PM #206 Kevin_Lowe Penultimate Amazing     Join Date: Feb 2003 Location: Queensland Posts: 10,283 I wish I had the card manipulation skills to play poker with Sol Invictus. After the fifteenth time I dealt myself a royal flush he'd still be there muttering "I wish I knew the exact odds that Kevin would deal himself a royal flush if he were cheating, because without that information I cannot make any estimate at all of the probability that he is cheating". I might try to explain to him that the exact odds didn't matter because the odds of fifteen royal flushes are so astronomically low that absolutely any reasonable estimate would still lead to a very high degree of confidence that I was cheating, but I doubt it would make any difference. __________________ Thinking is skilled work....People with untrained minds should no more expect to think clearly and logically than people who have never learned and never practiced can expect to find themselves good carpenters, golfers, bridge-players, or pianists. -- Alfred Mander
 23rd May 2012, 07:55 PM #207 RandomElement Critical Thinker   Join Date: Mar 2006 Posts: 300 Originally Posted by jt512 Why would anyone even bother to a "pre-study," when the laws of physics rule out supernatural hypotheses such as yours. Jay More time was spent writing 6 pages of posts. Besides, a live study of this nature has never been done.
 23rd May 2012, 08:06 PM #208 jt512 Critical Thinker   Join Date: Sep 2011 Posts: 389 Originally Posted by Kevin_Lowe I wish I had the card manipulation skills to play poker with Sol Invictus. After the fifteenth time I dealt myself a royal flush he'd still be there muttering "I wish I knew the exact odds that Kevin would deal himself a royal flush if he were cheating, because without that information I cannot make any estimate at all of the probability that he is cheating". I might try to explain to him that the exact odds didn't matter because the odds of fifteen royal flushes are so astronomically low that absolutely any reasonable estimate would still lead to a very high degree of confidence that I was cheating, but I doubt it would make any difference. Sol doesn't think that probabilities can be calculated after the data have been seen, so you'd be safe cheating him for two full sessions: he'd need the first session to formulate a hypothesis, and the second session to test it. Jay
 23rd May 2012, 09:00 PM #209 marplots Philosopher   Join Date: Feb 2006 Posts: 5,401 Originally Posted by Kevin_Lowe After the fifteenth time I dealt myself a royal flush he'd still be there muttering "I wish I knew the exact odds that Kevin would deal himself a royal flush if he were cheating, because without that information I cannot make any estimate at all of the probability that he is cheating". I might try to explain to him that the exact odds didn't matter because the odds of fifteen royal flushes are so astronomically low that absolutely any reasonable estimate would still lead to a very high degree of confidence that I was cheating, but I doubt it would make any difference. The psychology of cheating uses just this idea. You don't cheat in an "obvious" way, just enough to gain a real, but unnoticed advantage. The purpose being not to scare off your opponent so that they stop playing. Using your example, of course it was random chance, for no one who could actually control the cards would be foolish enough to deal all those royal flushes. This is the same logic used to decide that you were cheating in the first place, an assumption about whether a deal is under your control or not. The only difference is the assumption -- either dealing the RFs is to the cheater's advantage or it isn't. But it's still just an assumption. So why does it seem so powerful? I think because we are wired to see patterns and agency, even when we are not justified in doing so without further information. It's the same reason we might think that, instead of cheating, you were just "blessed by the Holy God of Gambling" or something. The appearance of agency is so strong, we will make one up out of whole cloth rather than believe it could be chance. What the string of RFs does call for is further investigation. But in truth, even if the cards appeared random, or were running in my favor (they call that "white hat" cheating) I would have no justification in saying you were not cheating without further investigation. Which, I wonder, is more likely -- the 15 RFs in a row, or me writing, and you reading, this post on this forum in this world at this exact time? I believe you may be cheating to orchestrate either of those two things, both being so unlikely. Well, you, or God. And I might do so if I didn't understand that my own sense of pattern and purpose is not very accurate. Last edited by marplots; 23rd May 2012 at 09:01 PM.
 23rd May 2012, 09:08 PM #210 jt512 Critical Thinker   Join Date: Sep 2011 Posts: 389 Originally Posted by marplots The psychology of cheating uses just this idea. You don't cheat in an "obvious" way, just enough to gain a real, but unnoticed advantage. The purpose being not to scare off your opponent so that they stop playing. Using your example, of course it was random chance, for no one who could actually control the cards would be foolish enough to deal all those royal flushes. This is the same logic used to decide that you were cheating in the first place, an assumption about whether a deal is under your control or not. The only difference is the assumption -- either dealing the RFs is to the cheater's advantage or it isn't. But it's still just an assumption. So why does it seem so powerful? I think because we are wired to see patterns and agency, even when we are not justified in doing so without further information. It's the same reason we might think that, instead of cheating, you were just "blessed by the Holy God of Gambling" or something. The appearance of agency is so strong, we will make one up out of whole cloth rather than believe it could be chance. What the string of RFs does call for is further investigation. But in truth, even if the cards appeared random, or were running in my favor (they call that "white hat" cheating) I would have no justification in saying you were not cheating without further investigation. Which, I wonder, is more likely -- the 15 RFs in a row, or me writing, and you reading, this post on this forum in this world at this exact time? I believe you may be cheating to orchestrate either of those two things, both being so unlikely. Well, you, or God. And I might do so if I didn't understand that my own sense of pattern and purpose is not very accurate. Wait, are you saying that your opponent dealt himself 15 royal flushes in a row, that you could not conclude that he was cheating without doing further investigation? Or have I misunderstood you? Jay
 23rd May 2012, 09:10 PM #211 OnlyTellsTruths     Join Date: Sep 2007 Posts: 5,797 Originally Posted by jt512 Originally Posted by Kevin_Lowe I wish I had the card manipulation skills to play poker with Sol Invictus. After the fifteenth time I dealt myself a royal flush he'd still be there muttering "I wish I knew the exact odds that Kevin would deal himself a royal flush if he were cheating, because without that information I cannot make any estimate at all of the probability that he is cheating". I might try to explain to him that the exact odds didn't matter because the odds of fifteen royal flushes are so astronomically low that absolutely any reasonable estimate would still lead to a very high degree of confidence that I was cheating, but I doubt it would make any difference. Sol doesn't think that probabilities can be calculated after the data have been seen, so you'd be safe cheating him for two full sessions: he'd need the first session to formulate a hypothesis, and the second session to test it. Jay I'm quite sure you both are mis-representing Sol's position. Sol would be sure you were cheating after seeing that the first hand is a royal flush. Just maybe not 100%. I should just wait for Sol, but I will try and explain it how I understand it (and I'll probably be wrong ). There's a difference between saying you know the odds are 99.99999 (lots of 9s) % and Sol saying you can't be so sure. It could be as low as 99.5 (as an example) depending on many unknown factors. That's what happens when you try and make a probability claim after the fact. Just because he says the odds against it happening are lower than you say doesn't mean he is saying it a complete unknown. Exactly how much it is lower is what is unknown or unknowable. __________________ ________________________
 23rd May 2012, 09:17 PM #212 marplots Philosopher   Join Date: Feb 2006 Posts: 5,401 Originally Posted by jt512 Wait, are you saying that your opponent dealt himself 15 royal flushes in a row, that you could not conclude that he was cheating without doing further investigation? Or have I misunderstood you? Jay Yes, but more nuanced. I'm saying you couldn't conclude it mathematically. But that's not what you do, is it? What you really do is use your previous experience with cards, the game and humans to come to that conclusion. Arguably, no one would bother to "do the math" before accusing someone. It's only when you bring math into it to support your case that you have a problem. WHen the math comes in, we are modeling something in the conceptual realm instead of in the shoot-from-the-hip, instinctual realm. Here's one where it seems the guy wasn't cheating -- or was he? Quote: From wiki, Charles Wells (gambler): In July 1891 Wells went to Monte Carlo with Ł4,000 that he had defrauded from investors in a bogus invention, a "musical jump rope." In an eleven-hour session Wells 'broke the bank' twelve times, winning a million francs. At one stage he won 23 times out of 30 successive spins of the wheel. Wells returned to Monte Carlo in November of that year and won again. During this session he made another million francs in three days, including successful bets on the number five for five consecutive turns. Despite hiring private detectives the Casino never discovered Wells's system; Wells later admitted it was just a lucky streak. His system was the high-risk martingale, doubling the stake to make up losses. Last edited by marplots; 23rd May 2012 at 09:22 PM.
 23rd May 2012, 09:21 PM #213 marplots Philosopher   Join Date: Feb 2006 Posts: 5,401 The reason the card cheat example is attractive is because we know that some people can cheat at cards. We don't, however, bring up astronomical probabilities in examples where we go in not knowing how cheating could be accomplished. So, for example, I am the product of the chances of a single sperm of millions fertilizing an egg. So was my dad, the guy who produced the semen (at least I hope so). Take that back a few generations and you get some pretty long odds. But I can't construct a "cheater" so I just assume it was all circumstance. If you believe in God, you have the ultimate cheat and might think differently.
 23rd May 2012, 09:28 PM #214 jt512 Critical Thinker   Join Date: Sep 2011 Posts: 389 Originally Posted by marplots Yes, but more nuanced. I saying you couldn't conclude it mathematically. But that's not what you do, is it? What you really do is use your previous experience with cards, the game and humans to come to that conclusion. Arguably, no one would bother to "do the math" before accusing someone. It's only when you bring math into it to support your case that you have a problem. WHen the math comes in, we are modeling something in the conceptual realm instead of in the shoot-from-the-hip, instinctual realm. Here's one where it seems the guy wasn't cheating -- or was he? If someone deals themselves 15 royal flushes in a row, they're manipulating the cards. The probability of that occurring by chance is so minute that it is, for all practical purposes, physically not possible. It has never happened by chance in the history of poker, and it never will. Jay
 23rd May 2012, 09:38 PM #215 marplots Philosopher   Join Date: Feb 2006 Posts: 5,401 Originally Posted by jt512 If someone deals themselves 15 royal flushes in a row, they're manipulating the cards. The probability of that occurring by chance is so minute that it is, for all practical purposes, physically not possible. It has never happened by chance in the history of poker, and it never will. Jay That's pretty good on the instinct and the hunch side, and even exceeds the "beyond a reasonable doubt" that a jury might use as a standard. But you know enough math to calculate the odds that it would happen. Is your claim that mathematically the odds are zero? I'm also interested in if you think you could make the same claim, should poker continue to be played regularly for the next billion or trillion or whatever years? Would there come a point in time where you would have to say, "Well, I guess by now it could have happened somewhere." I don't mind the "practically impossible" or "I suspect it is extremely likely they are manipulating the cards" -- as long as we stay away from any kind of mathematical certainty and stick with human suspicion.
 23rd May 2012, 09:46 PM #216 OnlyTellsTruths     Join Date: Sep 2007 Posts: 5,797 Originally Posted by jt512 If someone deals themselves 15 royal flushes in a row, they're manipulating the cards. The probability of that occurring by chance is so minute that it is, for all practical purposes, physically not possible. It has never happened by chance in the history of poker, and it never will. Jay All good until the highlighted part. You have to say "and it very probably never will". Or something like that. __________________ ________________________
 23rd May 2012, 10:06 PM #217 SezMe post-pre-born     Join Date: Dec 2003 Location: Santa Barbara, CA Posts: 16,369 Originally Posted by jt512 If someone deals themselves 15 royal flushes in a row, they're manipulating the cards. The probability of that occurring by chance is so minute that it is, for all practical purposes, physically not possible. It has never happened by chance in the history of poker, and it never will. Jay I know something equally amazing. Consider the last 15 games you've played. Now calculate the probability of that happening again. It's exactly the same as 15 royal flushes. And yet, it just did happen. Amazing, eh?
 23rd May 2012, 10:18 PM #218 jt512 Critical Thinker   Join Date: Sep 2011 Posts: 389 Originally Posted by marplots That's pretty good on the instinct and the hunch side, and even exceeds the "beyond a reasonable doubt" that a jury might use as a standard. But you know enough math to calculate the odds that it would happen. Is your claim that mathematically the odds are zero? No, just 1.6 × 1087 to 1. That's for being dealt 15 consecutive pat royal flushes in a 5-card game. For 5-card draw or holdem, I'd have to work a little harder to make the calculation; but I'd still shoot first, and pull out the pencil and paper later. Quote: I'm also interested in if you think you could make the same claim, should poker continue to be played regularly for the next billion or trillion or whatever years? Would there come a point in time where you would have to say, "Well, I guess by now it could have happened somewhere." Well, there is some length of time that if poker would continue to exist, that it will become likely that 15 consecutive royal flushes are dealt to some player by chance, but it would be a hell of a lot longer than a "mere" trillion years. We can be quite confident that the game of poker, along with the human race, will die out before any human being is randomly dealt 15 consecutive royal flushes. Quote: I don't mind the "practically impossible" or "I suspect it is extremely likely they are manipulating the cards" -- as long as we stay away from any kind of mathematical certainty and stick with human suspicion. Why? A probability on the order of 10–87 is essentially mathematical certainty of the complementary event. Jay
 23rd May 2012, 10:20 PM #219 jt512 Critical Thinker   Join Date: Sep 2011 Posts: 389 Originally Posted by OnlyTellsTruths All good until the highlighted part. You have to say "and it very probably never will". Or something like that. I'm quite comfortable saying that it never will. A probability on the order of 10–87 is essentially an impossibility. Jay
 23rd May 2012, 10:23 PM #220 jt512 Critical Thinker   Join Date: Sep 2011 Posts: 389 Originally Posted by SezMe I know something equally amazing. Consider the last 15 games you've played. Now calculate the probability of that happening again. It's exactly the same as 15 royal flushes. And yet, it just did happen. Amazing, eh? So what would your reaction to your opponent being dealt 15 royal flushes in a row? That it's just random, because, after all, it has the same probability as being dealt any 15 hands? If so, then it is your reaction that is "amazing." Jay
 23rd May 2012, 10:34 PM #221 jt512 Critical Thinker   Join Date: Sep 2011 Posts: 389 Originally Posted by marplots The reason the card cheat example is attractive is because we know that some people can cheat at cards. We don't, however, bring up astronomical probabilities in examples where we go in not knowing how cheating could be accomplished. I think we do sometimes, or at least we should. Even if we can't imagine how some unlikely event could have taken place by chance, if the event is unlikely enough, then the possibility that our imagination has failed us has to be seriously considered. Edit: I actually do think you're basically right, that we do and should take into account other information, like the plausibility of cheating, etc. Indeed, that is the whole point of Bayesian statistics. Jay Last edited by jt512; 23rd May 2012 at 10:39 PM.
 23rd May 2012, 10:46 PM #222 marplots Philosopher   Join Date: Feb 2006 Posts: 5,401 Originally Posted by jt512 Well, there is some length of time that if poker would continue to exist, that it will become likely that 15 consecutive royal flushes are dealt to some player by chance, but it would be a hell of a lot longer than a "mere" trillion years. We can be quite confident that the game of poker, along with the human race, will die out before any human being is randomly dealt 15 consecutive royal flushes. Alright, let me continue my thought experiment from here. We are starting at some theoretical point, any point at all, were we are justified in saying, "By now, somewhere, someone might have been dealt this unlikely sequence purely by chance and we shouldn't be surprised that it happened." Let us suppose that somewhere there's a race of poker playing aliens who have already been playing the game for a few billion years. And there are a lot of them playing -- vast planet-fulls, all playing poker. Does it make it more likely that such a sequence will or has already appeared somewhere? Would they be justified in making the statement? And if they are justified in making the statement, wouldn't we here on good old planet Earth be part of the pool of "somewhere, someone"? If the objection is that my aliens are fanciful and made up just to push a point, then we would have to investigate to find out if such a wonderfully blessed, poker-playing alien race actually exists. But then we are back to my statement about needing more information. Context matters, but one of the powerful things about math is that it is context free. That's what makes the math convincing. When it is dragged into the real world, things get messy. Edit to add: Jay, you are being gracious and so should I be. I would expect cheating. But then again, I do some card magic, so I have a bias. It's still a good conversation, and I want to get to ID. Last edited by marplots; 23rd May 2012 at 10:48 PM.
 23rd May 2012, 10:46 PM #223 OnlyTellsTruths     Join Date: Sep 2007 Posts: 5,797 Originally Posted by jt512 I'm quite comfortable saying that it never will. A probability on the order of 10–87 is essentially an impossibility. Jay Just because you are a sentient being willing to take a safe bet. That doesn't change what the word "never" means. You have to take the human brain out of your statements if you are talking about statistics and using words like "never". In fact, if poker got very popular, and we colonize a few thousand planets with billions of people each, and survive for millions of years, 15 royal flushes probably becomes very likely instead of very unlikely. __________________ ________________________
 23rd May 2012, 10:48 PM #224 jt512 Critical Thinker   Join Date: Sep 2011 Posts: 389 Originally Posted by OnlyTellsTruths In fact, if poker got very popular, and we colonize a few thousand planets with billions of people each, and survive for millions of years, 15 royal flushes probably becomes very likely instead of very unlikely. No it doesn't. Do the math. That's why I can confidently say "never." Jay
 23rd May 2012, 10:52 PM #225 marplots Philosopher   Join Date: Feb 2006 Posts: 5,401 ID segue: Before evolution was proposed, was it rational to believe that the design we saw was the result of God "cheating"? In other words, do the meaningful patterns we see actually embody a purposeful act as the default? I know this argument is brought by theists and they use whatever is currently known, but unexplained, like cosmic constants and so forth. Does their argument have weight?
 23rd May 2012, 11:12 PM #226 SezMe post-pre-born     Join Date: Dec 2003 Location: Santa Barbara, CA Posts: 16,369 Originally Posted by jt512 So what would your reaction to your opponent being dealt 15 royal flushes in a row? That it's just random, because, after all, it has the same probability as being dealt any 15 hands? If so, then it is your reaction that is "amazing." Any 15 hands specified ahead of time? Yep, just as amazing. But we've trod this ground so I'm going to drop it.
 23rd May 2012, 11:20 PM #227 OnlyTellsTruths     Join Date: Sep 2007 Posts: 5,797 Originally Posted by jt512 No it doesn't. Do the math. That's why I can confidently say "never." Jay Did I say colonize a few thousand planets? Make it a few million planets. 50 billion people per planet, 5 million planets, 5 thousand hands dealt per person per day for 50 million years Tell me that isn't plenty. If it isn't just assume I mean more planets. __________________ ________________________ Last edited by OnlyTellsTruths; 23rd May 2012 at 11:23 PM.
 23rd May 2012, 11:22 PM #228 jt512 Critical Thinker   Join Date: Sep 2011 Posts: 389 Originally Posted by marplots Alright, let me continue my thought experiment from here. We are starting at some theoretical point, any point at all, were we are justified in saying, "By now, somewhere, someone might have been dealt this unlikely sequence purely by chance and we shouldn't be surprised that it happened." Let us suppose that somewhere there's a race of poker playing aliens who have already been playing the game for a few billion years. And there are a lot of them playing -- vast planet-fulls, all playing poker. Does it make it more likely that such a sequence will or has already appeared somewhere? Would they be justified in making the statement? And if they are justified in making the statement, wouldn't we here on good old planet Earth be part of the pool of "somewhere, someone"? If the objection is that my aliens are fanciful and made up just to push a point, then we would have to investigate to find out if such a wonderfully blessed, poker-playing alien race actually exists. But then we are back to my statement about needing more information. Context matters, but one of the powerful things about math is that it is context free. That's what makes the math convincing. When it is dragged into the real world, things get messy. As I explained in this post. There have been on the order of 1026 nanoseconds (billionths of a second) since the Big Bang. If beings somewhere in the Universe played 1 billion hands of poker every single nanosecond since the Big Bang, then at this point in the history of the universe about 1035 hands of poker would have been played. But the probability of being dealt 15 consecutive royal flushes is on the order of 10–88, so it is still a virtual certainty that 15 consecutive royal flushes would ever have been randomly dealt to any player in this fictitious poker-dense history of the universe. To put this in another perspective, according to Wikipedia, there are about 1080 atoms in the observable universe. Say that if you were to correctly pick a particular one of these atoms that you'd win some lottery. The probability of you picking the correct atom is about 100 million times more likely than you being dealt 15 consecutive pat royal flushes. It is very easy to imagine and articulate events—like the innocent-sounding 15 consecutive royal flushes—that are astronomically improbable. We're great at imagining astronomically improbable events; intuiting the astronomicalness of their improbability, not so much. Jay Last edited by jt512; 23rd May 2012 at 11:36 PM.
 23rd May 2012, 11:23 PM #229 jt512 Critical Thinker   Join Date: Sep 2011 Posts: 389 Originally Posted by SezMe Any 15 hands specified ahead of time? Yep, just as amazing. But we've trod this ground so I'm going to drop it. Nice lowering of the goal post there. Last edited by jt512; 23rd May 2012 at 11:30 PM.
 23rd May 2012, 11:25 PM #230 OnlyTellsTruths     Join Date: Sep 2007 Posts: 5,797 That doesn't mean you get to use the word "never" without a qualifier. __________________ ________________________
 23rd May 2012, 11:26 PM #231 jt512 Critical Thinker   Join Date: Sep 2011 Posts: 389 Originally Posted by OnlyTellsTruths Did I say colonize a few thousand planets? Make it a few million planets. 50 billion people per planet, 5 million planets, 5 thousand hands dealt per person per day for 50 million years Tell me that isn't plenty. If it isn't just assume I mean more planets. You're not just "not in the ballpark." You're not in the universe that the ballpark is in. I've already explained that even if 1 billion poker hands were played every nanosecond since the Big Bang, it would still be overwhelmingly improbable that any player had ever been dealt 15 consecutive royal flushes. Weird, but true. Jay
 23rd May 2012, 11:28 PM #232 jt512 Critical Thinker   Join Date: Sep 2011 Posts: 389 Originally Posted by OnlyTellsTruths That doesn't mean you get to use the word "never" without a qualifier. Sure it does, because I understand (at least a little) what numbers like 10–80 imply. Jay
 23rd May 2012, 11:31 PM #233 OnlyTellsTruths     Join Date: Sep 2007 Posts: 5,797 Originally Posted by jt512 Sure it does, because I understand (at least a little) what numbers like 10–80 imply. Jay You obviously don't. Nothing about that number implies that I can't do it right now with 15 hands dealt. I can say that I have a chance of doing it. You, on the other hand, cannot say that it will never happen. That's just how the language of statistics works. The first sentence could be clarified with adding an "extremely small" before the word chance. The 2nd could be allowed with adding a "probably" before the word never. __________________ ________________________ Last edited by OnlyTellsTruths; 23rd May 2012 at 11:32 PM.
 23rd May 2012, 11:32 PM #234 Roboramma Philosopher     Join Date: Feb 2005 Location: Shanghai Posts: 7,096 Originally Posted by marplots ID segue: Before evolution was proposed, was it rational to believe that the design we saw was the result of God "cheating"? In other words, do the meaningful patterns we see actually embody a purposeful act as the default? I know this argument is brought by theists and they use whatever is currently known, but unexplained, like cosmic constants and so forth. Does their argument have weight? If the argument is that some process other than random chance was involved, then yes, it has weight. That doesn't tell us what that process is, of course, but it does tell us that the idea that, say, a) a tree just fell together from the constituent parts and b) there is no bias in the physics such that the tree was more likely than other configurations of those parts, is extremely likely to be false. Of course, the theory of evolution through natural selection can explain the order found in nature as a product of something other than random chance. Before we had the theory we may not have been able to say what that process was, but we could certainly say that there was some process involved, and while it's true that at the time "intelligent design" was one hypothesis, it is not the one that was born out by the facts*. *By this I mean that it hasn't been falsified, but so far nothing we've discovered has increased confidence in that idea, whereas the evidence for the theory of evolution has presented itself. __________________ "... when people thought the Earth was flat, they were wrong. When people thought the Earth was spherical they were wrong. But if you think that thinking the Earth is spherical is just as wrong as thinking the Earth is flat, then your view is wronger than both of them put together." Isaac Asimov
 23rd May 2012, 11:33 PM #235 jt512 Critical Thinker   Join Date: Sep 2011 Posts: 389 Originally Posted by OnlyTellsTruths You obviously don't. Nothing about that number implies that I can't do it right now with 15 hands dealt. So do it.
 23rd May 2012, 11:39 PM #236 Kevin_Lowe Penultimate Amazing     Join Date: Feb 2003 Location: Queensland Posts: 10,283 Originally Posted by marplots The reason the card cheat example is attractive is because we know that some people can cheat at cards. We don't, however, bring up astronomical probabilities in examples where we go in not knowing how cheating could be accomplished. So, for example, I am the product of the chances of a single sperm of millions fertilizing an egg. So was my dad, the guy who produced the semen (at least I hope so). Take that back a few generations and you get some pretty long odds. But I can't construct a "cheater" so I just assume it was all circumstance. If you believe in God, you have the ultimate cheat and might think differently. Sure, but if for example absolutely everybody born in 2013 was left-handed you'd think something was up. I think the essential stumbling block here is that people who only know frequentist statistics think it's impossible to say anything about the probability of an event after the fact. With Bayesian statistics there is in fact something to say. Case in point: Originally Posted by SezMe Any 15 hands specified ahead of time? Yep, just as amazing. But we've trod this ground so I'm going to drop it. Who said anything about the hands being specified ahead of time? SezMe is trying to redefine the scenario so he can apply frequentist maths, like someone trying to bash a round brick through a square hole. In a scenario were nobody specified anything ahead of time, but I still dealt myself fifteen royal flushes in a row, the kind of schoolboy probability theory that you might learn in Grade 11 or Grade 12 doesn't apply. You need Bayesian probability theory to explain in mathematical terms why your intuitive certainty that I'm a dirty cheatin' cheater is in fact mathematically sound. Originally Posted by marplots ID segue: Before evolution was proposed, was it rational to believe that the design we saw was the result of God "cheating"? In other words, do the meaningful patterns we see actually embody a purposeful act as the default? I know this argument is brought by theists and they use whatever is currently known, but unexplained, like cosmic constants and so forth. Does their argument have weight? In response to your first paragraph: Sure. It's perfectly possible for a perfect statistician to come to completely wrong conclusions if their data is faulty. It's perfectly possible for a perfect statistician to come to completely wrong results if they don't hit on the right hypothesis to test too. In response to your second paragraph: Nope. The issue there is that the existence of a cosmic constant isn't, as far as I can tell, any more consistent with a God-created universe than a non-God-created universe. It's possible I'm wrong about that and some argument could convince me otherwise but currently I just don't see the connection. If we saw on the dark side of the moon the words "Congratulations, you have completed Level One! Now colonise Mars! Signed, God!" in letters of supernatural fire, that would support the God hypothesis. Random stuff with no clear link to the Biblical God, not so much. __________________ Thinking is skilled work....People with untrained minds should no more expect to think clearly and logically than people who have never learned and never practiced can expect to find themselves good carpenters, golfers, bridge-players, or pianists. -- Alfred Mander
 23rd May 2012, 11:46 PM #237 Kevin_Lowe Penultimate Amazing     Join Date: Feb 2003 Location: Queensland Posts: 10,283 Originally Posted by OnlyTellsTruths You obviously don't. Nothing about that number implies that I can't do it right now with 15 hands dealt. I can say that I have a chance of doing it. You, on the other hand, cannot say that it will never happen. That's just how the language of statistics works. The first sentence could be clarified with adding an "extremely small" before the word chance. The 2nd could be allowed with adding a "probably" before the word never. Strictly speaking I'm not 100% certain nobody has psychic powers. Strictly speaking I'm not 100% certain that you are not in fact a monkey hitting keys at random and posting intelligible English by accident. Strictly speaking I'm not 100% certain that Superman, Batman and The Bionic Man aren't all real and having tea next door to me. However the probability I attach to those possibilities is for all intents and purposes indistinguishable from the probability of legitimately dealing myself fifteen royal flushes in a row - the human brain just isn't capable of intuitively handing probabilities that low. So if you are going to complain that you should qualify a claim like "fifteen legitimate royal flushes in a row will never happen" with a "probably" then you should also be demanding that I qualify a claim like "Superman is not at this very minute dancing the Frug with Sherlock Holmes in my bedroom" with a "probably". __________________ Thinking is skilled work....People with untrained minds should no more expect to think clearly and logically than people who have never learned and never practiced can expect to find themselves good carpenters, golfers, bridge-players, or pianists. -- Alfred Mander
 24th May 2012, 12:09 AM #238 xtifr Muse     Join Date: Apr 2012 Location: Sol III Posts: 563 Originally Posted by Kevin_Lowe So if you are going to complain that you should qualify a claim like "fifteen legitimate royal flushes in a row will never happen" with a "probably" then you should also be demanding that I qualify a claim like "Superman is not at this very minute dancing the Frug with Sherlock Holmes in my bedroom" with a "probably". Not the same. Superman isn't possible. Neither is getting five aces in a game without wild cards. 15 royal flushes in a row is technically possible, and if someone wants to be precise about such matters, it seems silly to try to correct them, even if we'd need to postulate uncountable numbers of universes to make the event plausible. Heck, there are people who like to try not to say that they saw a blue house unless they personally inspected all four sides, like one of Heinlein's "Fair Witnesses". It may be silly, but that doesn't make it wrong. There has to be a way to distinguish the truly impossible (like 5 aces) from the merely statistically unbelievable. __________________ "Those who learn from history are doomed to watch others repeat it." -- Anonymous Slashdot poster "The problem with defending the purity of the English language is that English is about as pure as a cribhouse whore." -- James Nicoll
 24th May 2012, 12:53 AM #239 Kevin_Lowe Penultimate Amazing     Join Date: Feb 2003 Location: Queensland Posts: 10,283 Originally Posted by xtifr Not the same. Superman isn't possible. How do you know absolutely for sure? Quote: Neither is getting five aces in a game without wild cards. Strictly speaking this is a different kind of claim, more like "2+2 can't equal five" or "you can't castle twice in chess", because of course you could get five aces if someone had accidentally shuffled in an ace from another deck but that's not what you meant. Quote: 15 royal flushes in a row is technically possible, and if someone wants to be precise about such matters, it seems silly to try to correct them, even if we'd need to postulate uncountable numbers of universes to make the event plausible. I wouldn't jump on someone for calling it "technically possible", no, but I wouldn't jump on someone for calling it "impossible" as layperson's shorthand either. Quote: Heck, there are people who like to try not to say that they saw a blue house unless they personally inspected all four sides, like one of Heinlein's "Fair Witnesses". It may be silly, but that doesn't make it wrong. I wouldn't even call it silly. It's the kind of thinking you apply when trying to solve a magic trick, for example. Quote: There has to be a way to distinguish the truly impossible (like 5 aces) from the merely statistically unbelievable. Sure, I'm just saying that when we're dealing with events so incredibly, staggeringly, incomprehensibly improbable as five pat royal flushes in a row, calling it impossible is quite reasonable. Put it this way - I currently believe it's impossible to go faster than light. However I don't know for sure it's impossible to go faster than light - it's possible it's possible, if you understand what I'm saying. I won't jump on someone for saying "it's impossible for you to have gone faster than light" but I won't jump on someone for saying "it's possible one day someone might go faster than light" either. __________________ Thinking is skilled work....People with untrained minds should no more expect to think clearly and logically than people who have never learned and never practiced can expect to find themselves good carpenters, golfers, bridge-players, or pianists. -- Alfred Mander
 24th May 2012, 01:43 AM #240 marplots Philosopher   Join Date: Feb 2006 Posts: 5,401 Originally Posted by Kevin_Lowe Who said anything about the hands being specified ahead of time? SezMe is trying to redefine the scenario so he can apply frequentist maths, like someone trying to bash a round brick through a square hole. I thought that's why we were talking about royal flushes in the first place, that someone had proposed that arrangement as improbable. Quote: In a scenario were nobody specified anything ahead of time, but I still dealt myself fifteen royal flushes in a row, the kind of schoolboy probability theory that you might learn in Grade 11 or Grade 12 doesn't apply. You need Bayesian probability theory to explain in mathematical terms why your intuitive certainty that I'm a dirty cheatin' cheater is in fact mathematically sound. I'd like to see why if you can explain this part. I really don't understand. Shouldn't you be just as surprised if you dealt 15 hands in a row, recorded them, and found a note in the mail listing just those hands, even though they appeared ordinary when you dealt them? Reading that note, are you justified in assuming trickery? And what if the note is destroyed and you never find out if it is correct, are you still justified in thinking cheating was involved, even though you still have the same cards as in the previous condition? Is it the recognizable pattern of the royal flushes that makes them special? Would it be just as likely to happen if someone who didn't know anything about poker dealt them in outer Mongolia? I don't understand how a pattern that has significance for the viewer somehow makes that pattern special for the cards themselves.

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