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 ISO: CardPlayer Article on card deck probability..., greg, 6. Aug 2003 15:31 | ||
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| a while ago i believe someone posted an article from cardplayer magazine about how a card deck will never repeat the same order of cards ever. unless artificially shuffled, the same order of cards will never exist. i search both the UPF and Cardplayer.com but couldn't find it. can anyone help me out? | ||
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| Re: ISO: CardPlayer Article on card deck probability..., Jav, 6. Aug 2003 15:41 | ||
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| I'm not sure where that article is, but I would have to disagree with the statement that it could never happen. Improbable, yes, but definately not impossible. | ||
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| Re: ISO: CardPlayer Article on card deck probability..., Allyc, 6. Aug 2003 15:48 | ||
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| there are 52x51x50x........2x1 permutations, that's approx an 8 with 67 zeros after it, so I woudn't hold my breath. | ||
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| Re: ISO: CardPlayer Article on card deck probability..., johnph77, 7. Aug 2003 11:11 | ||
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| Strange how that subject would come up more than once in a day. I posted a response to another thread (Online Poker), cranked up a calculator and arrived at the same number..... | ||
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| Re: ISO: CardPlayer Article on card deck probability..., greg, 6. Aug 2003 15:48 | ||
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| that's one of the reasons i want to re-read the article. the author states how many times he didn't believe the statement but semi-proves it later on. i'm realy interested in readnig it again. he compares the amount of possible combination of cards to stars in the universe. | ||
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| Re: ISO: CardPlayer Article on card deck probability..., Allyc, 6. Aug 2003 15:58 | ||
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| i think number of stars is estimated at approx 1 000,000,000,000,000,000,000 if you mutiply this by an 8 with 46 zeros after it you get approx the number of deck permutations. | ||
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| Re: ISO: CardPlayer Article on card deck probability..., Guru, 6. Aug 2003 16:03 | ||
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| It's on PkerPages.cpm. Here is the link to it: http://www.pokerpages.com/articles/archives/hench33.htm. It's called "conundrum" by David Hench. Just go to the site, click articles, and it's right there. | ||
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| Re: ISO: CardPlayer Article on card deck probability..., greg, 6. Aug 2003 16:23 | ||
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| thank you very much, good article | ||
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| Re: ISO: CardPlayer Article on card deck probability..., Snorbolus, 7. Aug 2003 07:29 | ||
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| Wow, I'm surprised that it's such a big number. I am not convinced that no 2 decks ever have or ever will be in the same sequence by chance alone though. That statement relies on essentially the same, flawed, logic as the "design" argument for the existence of God. Very improbable events can occur (by definition). If they do then they are just as real as anything else. Best not to count on one happening before you observe it though. Snorbolus | ||
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| Re: ISO: CardPlayer Article on card deck probability..., stdioh, 7. Aug 2003 09:37 | ||
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| Well the God argument works pretty well. If you were walking through a virgin forrest and came upon a nicely manicured rose garden with every blade of grass meticulously in place and you camped there for a long time, set traps, did everything in your power, but never saw a gardener - yet the garden stayed really nice - you would have to make a decision. Is there a magical invisible gardener who keeps things so perfect or is it just plain dumb random luck that this garden is here the way it is. As a fancier of chaos I'm a believer that a perfect system like the planet Earth is realistic to achieve through randomness, but impossible to maintain. The fact that life on this planet has survived 4 major extinctions alone is a slap in the face of chaos .... not to mention that if you take some universal constants and change them just a little, then simulate the world, life becomes impossible. Change the universal gravitational constant just a little and stars won't ignite properly. Mess with the strong atomic force just a little in either direction and protein chains cannot hold together. In essence, when things get just a little too perfect you are either paranoid or you're being set up. | ||
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| Re: ISO: CardPlayer Article on card deck probability..., Snorbolus, 7. Aug 2003 09:58 | ||
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| Please note that I am not saying anything about the existence of God. My opinion on that is not relevant here. I am just pointing out that the “design” argument is formally unsound. It comes down to: “There is only a small chance that something happened therefore that thing did not happen” This does not follow. Often, for pragmatic reasons, it is useful to discount the possibility of very unlikely events. However, when doing this, one should always be aware of the small chance that such an event has in fact occurred. Also, if there is no good reason to make a simplifying assumption such as this then why do so? Snorbolus | ||
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| Re: ISO: CardPlayer Article on card deck probability..., Snorbolus, 7. Aug 2003 10:43 | ||
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| By assigning a probability greater than 0 to an event you are accepting that it might occur. It is clearly absurd to argue that something can not happen precisely because it has a small chance of happening. Snorbolus | ||
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| Re: ISO: CardPlayer Article on card deck probability..., ezcheese, 7. Aug 2003 11:41 | ||
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| nobody is saying it is impossible... but the chance of it happening is soooo unlikely that it is nearly impossible... it's truly a test to think up something such as this that is ACTUALLY IMPOSSIBLE... anomalies occur and the exact same deck of cards could repeat itself 42 times in a row... likely? absolutely not... impossible? no | ||
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| Re: ISO: CardPlayer Article on card deck probability..., stdioh, 8. Aug 2003 15:39 | ||
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| But see that's the thing. Taking quantum physics into account it is literally possible you ricoculously unlikely for "ANYTHING" to happen. But I can still state something as so unlikely as to be negligeable in figuring probability. So we could look at the way the solar system is built and say what is the chance of life for a star system and how many star systems are there and come up with an EV for how many living systems there should be. If we get 1000 then everyhting works nicely. If we get 1 or less we lose perspective, since if there is one we are it. Essentially, once you've found the garden you can't know whether or not it is fair to call it the one. And hence the existing problems in the world. | ||
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| Re: ISO: CardPlayer Article on card deck probability..., Snorbolus, 9. Aug 2003 10:48 | ||
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| Stdioh, I droped you an e-mail about this to the hotmail address that you posted in TK's "spare a chip thread". I am interested in your opinion. Snorbolus | ||
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| Re: ISO: CardPlayer Article on card deck probability..., stdioh, 8. Aug 2003 15:36 | ||
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| oh oh. I think I opened a can of worms. It is fundamentally known that poker discussion begins to break down when people start arguing the existence of God and the merits of nonsmoking cardrooms. My sincerest appologies. | ||
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| Re: ISO: CardPlayer Article on card deck probability..., ezcheese, 7. Aug 2003 10:01 | ||
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| Think of how many things on our planet that are PERFECT for life, but if changed slightly become harmful or useless... One more Hydrogen atom in H20 and you no longer have water... increase earth's gravitational pull and there's a good chance we couldn't jump, maybe walk, or even live for that matter... Now think of all these variables and think of how many permutations there are for another planet to have the equivalents... such a huge number I can't even comprehend... But, then again, you never know how large the universe actually is so maybe it's large enough to make this randomness possible... (I'm speaking of human life out there, I realize different conditions could allow different lifeforms). | ||
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| Re: ISO: CardPlayer Article on card deck probability..., stdioh, 8. Aug 2003 15:44 | ||
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| I like the way you think, but I think you need to look deeper. Water is because hydrogen and oxygen work the way they do. They work the way they do because of the pattern of organization within their inner structures. The patterns within them form because there are laws which govern the forces between these tiny particles. When you break down these forces to their most primitive elements, there are only 4 of them - strong atomic, weak atomic, magnetic, and gravitational. Of course the first two are the very important ones. What gets interesting is the fact that if you changed either of these just a little, making water would be the least of your worries. By decreasing the weak atomic force only a small amount, just about everything would be massively radioactive and the universe would spiral very very quickly towards heat death. Make it just a little stronger and you'd make fusion possible in really small balls of gas - stuff the size of jupiter and smaller .. and then you woudl be unable to make a stable solar system in the first place. We live in a *very* carefully tweaked simulation of physics that we call physics and things work out so nicely only because everything was initialized just so. | ||
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| Re: ISO: CardPlayer Article on card deck probability..., ezcheese, 11. Aug 2003 13:15 | ||
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| I agree with you that everything is in a *perfect* balance to allow our universe to exist... I think just analyzing how coincidental everything seems to be is the main reason people believe in god... they feel that a higher power must have put this stuff together because random luck wouldn't. | ||
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| Re: ISO: CardPlayer Article on card deck probability..., stdioh, 6. Aug 2003 16:38 | ||
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| There are exactly 52! possible deck configurations. If I put a 1 with a bunch of zeros after it I don't think it would sink in as to what an increadibly large number this is. Instead I'm going to give the start of a table and you can see the factorial growth curve (which by the way is just friggin huge compared to exponential curves). 1!=1 2!=2 3!=6 4!=24 5!=120 6!=720 7!=5,040 8!=40,320 9!=362,880 10!=3,628,800 So I'm sure that you can see that 1/52! is really really really really really uncommon. The ability for a given deck to be repeated in another given deck becomes so rare that it is less likely that some ghastly quantum events. Richard Fenyman worked out a bunch of these in one of his books, including the chance of a full can of beer falling over sideways all by itelf and including a given person spontaneously dematerializing and rematerializing on the surface of the planet Mars (possible, but extremely unlikely). While we're not at that stage yet, I'd say that there's a greater chance that some quantum effects change a couple of cells in your brain and cause you to think that the same deck appeared twice than for it actually to happen. | ||
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| Re: ISO: CardPlayer Article on card deck probability..., ezcheese, 7. Aug 2003 09:53 | ||
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| What are the chances of being struck by lightning?? If I recall, it's much greater than the chance of two decks every repeating... If, then, you can go outside when it is raining, unafraid of being struck by lightning because the odds are against it... why would anyone then believe that two decks will repeat themselves, when the odds are much more strongly against it.... I'm thinking that if a deck of cards ever ends up in the same order as a previous deck, it will spark some immensly strange ripple in time and the universe will be thrown into chaos. | ||
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| Re: ISO: CardPlayer Article on card deck probability..., pt_Gatsby, 8. Aug 2003 13:13 | ||
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| Hi Stdioh, Hopefully this one hasn't been pushed off your radar. I'm no math expert (ie: not even close to), but I have a passing knowledge of statistics (well, as it relates to option models, anyway - binomial primarily). Something didn't ring true about this probability question, so today at work I pulled out my notepad and came up with this (which is probably the worst possible way of calculating it, but anyway). n = number of attempted deck configurations (ie: number of decks shuffled) d = potential deck configurations, or 52! = number of potential standard deck configurations Then, the chances of shuffling a deck and getting two decks exactly the same is; 1- [(d-1)/d], or 1- [(52!-1)/52!], or 0 for any rational person! However, this leads to the expanded formula of Q(n,d) = [ (d-1)(d-2) ... ((d-(n-1)) ] / d^(n-1) Or, factorials (not matched): Q(n,d) = d! / [(d-n)!d^n Am I not correct in saying that: 1 - { (52!)! / [(52!-n)! * 52!^n } would be the that for over n shuffles the chances of having a deck in the same combination at least once would not occur? I'm afraid I can't go beyond that though. I don't know how to reduce: (52!)! / (52!-n)! ... I don't know how to compare it to the growth in 52!^n. But anyway... Maybe I got lost on the way instead. It seems to me, however, to be likely considering the rapid growth of n... or rather, there should be a point of convergence (I would love to know at what point n would have to be to have a 50% chance of it having happened. ) | ||
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| Re: ISO: CardPlayer Article on card deck probability..., LJH, 8. Aug 2003 13:21 | ||
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| PT_GATSBY AND ALL OTHERS, READ LOU KREIGER'S ARTICLE IN TH AUG.15TH ISSUE OF CARD PLAYER MAGAZINE, ABOUT RANDOMNESS, AND THEN YOU CAN ALL GET A BETTER UNDERSTANDING OF THE SUBJECT. LJH | ||
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| Re: ISO: CardPlayer Article on card deck probability..., stdioh, 8. Aug 2003 15:48 | ||
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| You're falling into a statistical "fancy play" trap here. The probability is easy to work out and you don't need to create a random distribution to do it. Simply put, there are 52! possible deck configurations. You will thorougly shuffle 2 decks. One of them, without loss of generality we'll say the blue deck, will come up with some particular configuration. What is the chance that the other deck is also in this configuration? Well, quite simply, the shuffling of the second deck was an independant event, so the status of one deck does not affect the status of the other. The result is that you have 52! equally likely configurations for the deck and one of them matches. Thus your 1/52! chance. | ||
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| Re: ISO: CardPlayer Article on card deck probability..., ezcheese, 11. Aug 2003 13:23 | ||
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| you would almost have to say 1/52!-n though (with n = previous shuffles)... because if the deck ends up as any previous shuffle (n), the theory is disproved... I want somebody to do this... Find out how many times a deck of cards is shuffled at any ONE particular poker table in a casino on one 24 hour period... just estimate the number of card tables there are IN THE WORLD... now double that for the amount of people in the world who are playing cards at home or even just practicing shuffling a deck at dealer school and what not... take that number and multiply it by 365... you now have how many times a deck is shuffled a year ( a good guess )... now multiply this times 50 for 50 years... cards have been around for a lot longer but not as abundant so I'm just using 50... You now have the # of shuffles in the past 50 years... LARGE NUMBER... If you wanted to talk about the # of shuffles in the history of cards, how about you double the # that you currently have... ok... now you have 1/52!-n (n = the number you just got)... it's a lot more likely now... double n again to equal how many shuffles will have occured in 10 years from now... I think that its unlikely that a deck has repeated a permutation, but definately becoming a lot closer in possibility. | ||
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| Re: ISO: CardPlayer Article on card deck probability..., stdioh, 12. Aug 2003 10:41 | ||
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| Read my later post on innumeracy and you'll see that any amount of shuffles that would be technically possible is too tiny compared to 52! to be significant. 1/52!-n is still itsy bitsy. | ||
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| Re: ISO: CardPlayer Article on card deck probability..., Murry Martin, 6. Aug 2003 19:39 | ||
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| The article is on Pokerpages.com. I found it to be very astonishing. | ||
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| Re: ISO: CardPlayer Article on card deck probability..., WilliamS, 8. Aug 2003 06:18 | ||
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| This is kind of a moot point and I may be misunderstanding the thread, but here is my take. (Man, I feel like I'm still in my college philosophy class). I agree if you take a certain shuffling of cards the odds of that particular sequence repeating itself is infinitesimal, but if the question is, are there ever 2 sequences the exact same I would have to say, that even though we can't prove it, definitely so. I compare this to the Amarillo Slim birthday hustle. In a room with 30 or so folks the odds of anyone having the same birthday are pretty good because you aren't looking for someone with an exact birthday (the odds are long against that) but looking for any people with the same birthday (drastically improving the odds of the occurrence). I may be way off but with the amount of decks being shuffled I would say there would be "twin decks". | ||
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| NO NO NO! INNUMERATE!, stdioh, 8. Aug 2003 16:10 | ||
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| no no no no no. It seems that you're falling victim to a classic piece of innumeracy here. Not understanding how really damn hell big some gigantic numbers are. There are 365 (really 366) birthdays and 30 people. The chance of them sharing a birthday is obviously within the bounds of understanding for most smart people. Now lets look at how many poker hands there have ever been, but I'm going to really stretch things for you. Lets assume that there are an average of 100,000 poker tables in operation on planet Earth, all of them playing around the clock. Lets say that they each deal an increadible 50 hands per hour so you're getting in 5 million hands per hour worldwide. Then you get 120 million hands per day or about 43.8 billion hands per year. Lets say that they play for 1000 years (much longer than we've had cards at all) then you get 43.8 trillion poker hands dealt and one fresh shuffle for each deal. Sounds like a lot, huh? I'll bet that you could definitely have repetition in your 52! with that many, right? 43.8 trillion is much less than 17! ... it is massively dwarfed by a number so giant as 52! What if they played for a million years? They would still play much less than 19! hands. Better yet, lets take 6 billion people (more than there are on earth) and have them shuffling for 1 million years each at 10 shuffles per minute. You get 5,256,000 shuffles per person per year, so you get 31.536 quentillion hands dealt. How much is that really? Very much less than 24! Pretty soon we're going to need to enlist genetically modified super ants to shuffle for us. 24! is so tiny compared to 52! that it is as insignificant as a gnat flying around the arse of a cow standing by the highway that you drive by at 120 km/h ten years from now. For the sake of humour, the universe is about 9 billion years old. If you took your 6 billion continuous shufflers and they had been going since the beginning of time, until last Tuesday, you would have still less than 26! total shuffles. So the long and short of it is that it is very different from Slim's husstle. It is so unlikely that there were ever two decks shuffled into the same position (assuming reasonable and fair shuffling of course) that there is a greater likelyhood that our sun has already exploded and that its light will stop hitting us within the next 9 minutes or so. | ||
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| Re: NO NO NO! INNUMERATE!, WilliamS, 8. Aug 2003 19:01 | ||
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| I stand corrected............thanks for the reply will | ||
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| Re: NO NO NO! INNUMERATE!, stdioh, 8. Aug 2003 19:09 | ||
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| GRIN. I hope I wasn't too brash there. Sometimes I just get a little flustered ... comes from spending too much of my time in university around arts majors who had numerical knowledge that extended to 'one, two and many'. :) | ||
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| Re: NO NO NO! INNUMERATE!, ezcheese, 11. Aug 2003 13:26 | ||
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| stdioh that was really a terrific explanation of 52!... you made my previous post look retarded, but i still believe it's going to be happening eventually. | ||
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| Re: NO NO NO! INNUMERATE!, stdioh, 12. Aug 2003 10:43 | ||
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| Even if you could get in 51! shuffles, 1/(52!-51!) is pretty close to 1/51! :) | ||
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| Re: ISO: CardPlayer Article on card deck probability..., Allyc, 8. Aug 2003 19:35 | ||
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| Should have more important things to do, but i think this is correct. Mankind been's around for about 2.5exp6 years (yes,here we go), that's 2,500,000. We have about 31.5exp6 seconds in 1 year ( I don't like where this is going) So we've been around for approx 8exp12 seconds. That's 8 with 12 zeros after it. If we started shuffling decks way back then, at a rate of 1000 billion decks per second, we would have completed about 1exp12 x 8 exp 12 shuffles. That's about 8exp24 shuffles, give or take the odd shuffle or two. That's still an order of magnitude of 1exp 43 less than the number of possible deck permutations. Zager Evans would be quite correct. 'Your arms are hanging limp at your side'. And we'd still have quite a way to go. Allyc. | ||
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| Re: ISO: CardPlayer Article on card deck probability..., CMass, 9. Aug 2003 17:41 | ||
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| Just because the odds say that it is 1/52! does not mean that it won't, or hasn't happened in the history of humankind. If you were a betting man (which most of us probably are), it would be in your best interest to bet against the fact that it has happened. However, everyone is putting out these statistics of "so many people shuffling every second for so many years and they still would have only shuffled [a number much less than 52!] times" As if on the 52!th shuffle, the same combination would appear, and then they could suffle 52! more times, and there it is again. I could go shuffle four decks right now, and all four of them could come up the same, and this doesn't fly in the face of the 1/52! propability of two decks being the same. 1/52! only refers to the expected value as the number of trials approaces infiinity (and yes, infinity if much bigger than 52!). It says almost nothing about the short term outcomes. So the potential that during the lifespan of humans that the same order of cards has appeared is there. That just means that somewhere along the line of an infinite number of trials, the phenomenon will occur less likely than expected and will balance out the more than expected occuranced. My money is of course on the theory that it hasn't happened. But for the author to plain flat out claim that it hasn't happened, and won't happen is certainly a brazen statement. | ||
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| Re: ISO: CardPlayer Article on card deck probability..., Allyc, 9. Aug 2003 18:07 | ||
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| on 9. Aug 2003 17:41 CMass wrote: > Just because the odds say that it is 1/52! does not mean that it won't, or hasn't happened > in the history of humankind. If you were a betting man (which most of us probably are), > it would be in your best interest to bet against the fact that it has happened. However, > everyone is putting out these statistics of "so many people shuffling every second for so > many years and they still would have only shuffled [a number much less than 52!] times" > As if on the 52!th shuffle, the same combination would appear, and then they could suffle > 52! more times, and there it is again. > > I could go shuffle four decks right now, and all four of them could come up the same, and > this doesn't fly in the face of the 1/52! propability of two decks being the same. 1/52! > only refers to the expected value as the number of trials approaces infiinity (and yes, > infinity if much bigger than 52!). It says almost nothing about the short term outcomes. > > > So the potential that during the lifespan of humans that the same order of cards has > appeared is there. That just means that somewhere along the line of an infinite number of > trials, the phenomenon will occur less likely than expected and will balance out the more > than expected occuranced. > > My money is of course on the theory that it hasn't happened. But for the author to plain > flat out claim that it hasn't happened, and won't happen is certainly a brazen statement. Hi, don't want to sound like a smart ass, but if you let the number of trials tend to infinity, the number of repeated shuffles will tend to infintity also. It has too. No upper bound on the number of trials, will eventually make 52! look infinitesimal. You're right, it's not impossible to get a repeated shuffle, but it is highly improbable. | ||
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| Re: ISO: CardPlayer Article on card deck probability..., CMass, 9. Aug 2003 18:32 | ||
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| Yes, the number of repeated same decks will approach infinity as well. I wasn't commenting on that. I said that as the number of trails approaches infinity, the frequency of the occurances will approach the expected value of 1/52!. Or at least thats what I meant to say. Looking back, I said a few things which are mathematically innacurate, if they are taken literally. Hopefullly everyone sees what I intended them to mean. | ||
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| Re: ISO: CardPlayer Article on card deck probability..., Allyc, 9. Aug 2003 18:40 | ||
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| sorry, didn't read you properly. | ||
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| Re: ISO: CardPlayer Article on card deck probability..., stdioh, 12. Aug 2003 10:47 | ||
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| Of course you can force a repetition, since there are a finite number of deck positions you just need to use the pigeon hole principle. If you shuffle 52!+1 decks then you are bound to have a repetition. The only problem is that if you went from the start of the universe until the time that it reaches heat death and had every human that has ever existed and will ever exist shuffling continuously for that entire time you won't get enough to force it. So the chance that it happened naturally is so small it isn't worth worrying about as existant at all. Just like it is possible that our sun exploded 1 minute ago, but why worry about that? It is more likely that our sun has already exploded than it is that 2 decks have been matched. | ||
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