iPod classic on shuffle 
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cyberpainter 5940 posts 
wracket wrote: cyberpainter wrote: Hmm, I'm no mathematician, but wouldn't the odds change with each flip? Each flip has a 50% chance of being odd or even. But the chances of all being even in a row gets statistically lower each flip. Is that right? Well, even if you've already had 7 straight heads, the 8th flip is clearly still a 50/50 scenario. Of course, the odds are pretty low that you would get 10 straight heads (hhhhhhhhhh), but are the exact same as that of any other single combination (hththththt, hhhhhttttt, hhtththttt, etc.) Not sure if that's what you're asking about. Yeah, however you say the odds are "low", but I don't delve deep enough to understand what that means. Seems like the odds would go down to get all heads repeatedly over time because as each is 50/50, you have 50% chance each time of breaking the streak. Also, since over time you'd probably break even, it feels like there should be some other kind of statistical factors in play (that are like some kind of magic hocus pocus to the likes of me). 
Jul 10, 2011, 08:24

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wracket 1427 posts 
cyberpainter wrote: Yeah, however you say the odds are "low", but I don't delve deep enough to understand what that means. Seems like the odds would go down to get all heads repeatedly over time because as each is 50/50, you have 50% chance each time of breaking the streak. Yes, the odds of getting 6 heads in a row are half of the odds of getting 5 heads in a row and so on. cyberpainter wrote: Also, since over time you'd probably break even, it feels like there should be some other kind of statistical factors in play (that are like some kind of magic hocus pocus to the likes of me). Here's where the essential misunderstanding for most people comes in. Of course, taken from point 0 (before the first flip) you can say that the single most likely scenario is that, 10 flips from now, you will find yourself with a distribution of 5 heads and 5 tails. But let's assume that you've already flipped 4 straight heads and you're now at point 4, with six flips remaining. Would you then expect that over time, starting from this point on, the most likely scenario will be with you ending (after 10 flips, 100 flips, whatever) at an even distribution of heads and tails for the set taken as a whole (from point 0 until the end)? The answer to this is a resounding "no"...since you already have four heads "in the bag", the odds calculated at point 4 are that, once you have finished flipping, you are more likely to have more heads than tails. There is no "mean reversion" here because each flip is independent of those that came before it. No hocus pocus here!
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In reply to: Re: iPod classic on shuffle (cyberpainter) 
Jul 10, 2011, 10:38

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Harold Bissonette 2062 posts 
wracket wrote: Harold Bissonette wrote: I don't do the Lottery, but read someone saying that there is a way of at least narrowing down your chances of winning by understanding the way random 'patterns' can work. In theory if you chose 123456 you are as likely to win as by choosing any other set of numbers. But in reality there is nearly always a mixture of a fairly even spread and clusters. So, you actually have more chance to win if you put say three numbers in the twenties (or any other row) and then a rough spread in your other numbers. Something like that. There is no way of narrowing down your odds in a true* lottery scenario. To imply that any single number near the mean would have a higher rate of occurrence would of course only apply to a classic "bell curve" population, but in a lottery there is one example (in the form of a ball) of each number and no correlation between any of the balls in the population. So therefore the theory that "1 2 3 4 5 6" is as likely a combination as any other single combination of numbers. *as opposed to a "rigged" lottery, in which the best way to narrow down your odds is to be in on the scam My point was that although in theory a sequence like 123456 is as likely as any other, in practice it is less likely to happen than a semipattern such as the one as I suggested (say three closely grouped numbers and three more evenly spread out). A look at any previous results would confirm this. So, I think it is possible to at least narrow down your odds of winning, even though your chances would still be extremely unlikely  just less so. I would imagine that there is a mathematical theory that would at least in part explain this, but am certainly no expert. 
Jul 10, 2011, 11:30

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wracket 1427 posts 
Harold Bissonette wrote: My point was that although in theory a sequence like 123456 is as likely as any other, in practice it is less likely to happen than a semipattern such as the one as I suggested (say three closely grouped numbers and three more evenly spread out). A look at any previous results would confirm this. So, I think it is possible to at least narrow down your odds of winning, even though your chances would still be extremely unlikely  just less so. I would imagine that there is a mathematical theory that would at least in part explain this, but am certainly no expert. Not to be antagonistic, but are you basing your "look at any previous results" on an actual study? Because I've never come across anything which would confirm or even hint at that. Perhaps an easier way of understanding the probabilities is to remove the numbers painted on those balls entirely, as their sole purpose is to distinguish one ball from the next and possess no sequential/factorial/etc. correlation to each other. So if, over the numbers, we randomly assigned painted each ball with the representation of an animal, (1 = grizzly bear, 2 = squid, 3 = porpoise ... 23 = salmon, 24 = raccoon, 25 = flamingo... 38 = dung beetle, 39 = fruit bat, 40 = salamander, etc.), you probably wouldn't expect there to be any such "semipatterns" you spoke of before, would you? Your brain might, however, start to suggest to you that patterns exist where in fact they do not. Maybe you would notice that never does anyone ever win with exclusively land creature balls and deduce that you could increase your chances of winning by ensuring that each combination has at least one bird or fish. This would merely be your brain trying to find a logical pattern where one does not exist...any combination of six land creatures, six nonvertebrates, etc. would have exactly the same chance of winning as any randomly chosen combination. Hopefully that nonnumeric perspective helps make sense of why the statistical theory must hold true in practice. And even if not, at least now you can least be somewhat amused at the thought of a lottery player leaning forward towards the TV, stub in sweaty hand, desperately pleading "come on porpoise!"
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In reply to: Re: iPod classic on shuffle (Harold Bissonette) ............................................... Re: iPod classic on shuffle (Harold Bissonette) 
Jul 10, 2011, 13:14

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hito 1745 posts 
Now I tried the same thing with Winamp and had first thought it was more random. However, when I looked closely at the list (I wasn't listening as intently), I saw that it also repeatedly played REM (thrice), Fantomas (3 times in 18 songs), DJ Krush (3 times within 6 songs including two from the same album), Aus twice in 14 songs (and I only have one 8 song album), Sentridoh twice from the same album within three songs. All this and more within 80 tracks. Now I have 77 fantomas tracks (why?), 192 REM, 254 DJ Krush and 21494 overall. So there is a good chance of hitting Krush etc. I did get one Stereolab out of 277 and one Buttholes out of 274 but no Residents out of 213, no PJ Harvey out of 154. The other kooky thing that happened was that I listened to my iPod on the same list and had more repeats (including two Crystal Stilts when I only have one album) but the the funny thing was The Prophet Song by Queen played and it ends all acoustic like, it was then followed by an acousticy Lou Barlow track (that I thought was Nick Drake) and then followed up with a Nick Drake song. A DJ couldn't have done better. The iPod has done this before. Perhaps you are right, Booklover. Maybe I am just looking for patterns 
Jul 10, 2011, 13:24

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Harold Bissonette 2062 posts 
Not to be antagonistic, but are you basing your "look at any previous results" on an actual study? Because I've never come across anything which would confirm or even hint at that. Perhaps an easier way of understanding the probabilities is to remove the numbers painted on those balls entirely, as their sole purpose is to distinguish one ball from the next and possess no sequential/factorial/etc. correlation to each other. So if, over the numbers, we randomly assigned painted each ball with the representation of an animal, (1 = grizzly bear, 2 = squid, 3 = porpoise ... 23 = salmon, 24 = raccoon, 25 = flamingo... 38 = dung beetle, 39 = fruit bat, 40 = salamander, etc.), you probably wouldn't expect there to be any such "semipatterns" you spoke of before, would you? Your brain might, however, start to suggest to you that patterns exist where in fact they do not. Maybe you would notice that never does anyone ever win with exclusively land creature balls and deduce that you could increase your chances of winning by ensuring that each combination has at least one bird or fish. This would merely be your brain trying to find a logical pattern where one does not exist...any combination of six land creatures, six nonvertebrates, etc. would have exactly the same chance of winning as any randomly chosen combination. Hopefully that nonnumeric perspective helps make sense of why the statistical theory must hold true in practice. And even if not, at least now you can least be somewhat amused at the thought of a lottery player leaning forward towards the TV, stub in sweaty hand, desperately pleading "come on porpoise!" [/quote] No antagonism felt or meant  hopefully just an interesting bit of debate. I understand what you are saying, but even you must see that certain 'patterns', or maybe 'rules' can be applied to winning numbers. If not in a hard and fast way, at least in a vague general way that can narrow down probabilities. Even in your animal version, I think it would be more likely in practice for a cluster of similar animals plus a random spread to come up rather than either a set all from the same type or a set where all are different or indeed, say, a set of animals with consecutive alphabetical names. Here are the last 50odd winning numbers. http://www.nationallottery.co.uk/player/p/drawHistory.do I think this is a fairly typical sample, that could be replicated again and again. My theory of 3fromonerow plus 3spread out only works in about half of these answers, but I think even if it only works half the time, that would at least  if only fractionally  narrow the odds. Certainly nothing even approaching 6inarow  and presumably nothing like that has ever come up. Not sure that I can put it better than that. 
Jul 10, 2011, 14:20

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wracket 1427 posts 
Harold Bissonette wrote: My theory of 3fromonerow plus 3spread out only works in about half of these answers, but I think even if it only works half the time, that would at least  if only fractionally  narrow the odds. Certainly nothing even approaching 6inarow  and presumably nothing like that has ever come up. Whether we're talking about numbers or animals, there are no rows, no groupings. It's all purely artificial, hence the ability to substitute animals for numbers. There are x numbers of balls in pot and at the first go any of those balls has a 1/x chance of being selected, at the second drawing 1/(x1), etc. The fact that they use numbers tends to draw your attention into grouping them into rows or multiples of three or whatever, though my point with the animals is that one could regroup the animalspaintedovernumbers balls into rows of, say, mammals, fish, reptiles, birds...and then probably try to find patterns of the winning combinations based upon these new row groupings. But if you scratched off the animals, you might find yourself with one "row" of balls 2,7,18,19,24,38,43,45. So which "row" actually applies to the varied probability of these balls being selected, the animal one or the number one? The answer is clearly that it is neither of them.
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In reply to: Re: iPod classic on shuffle (Harold Bissonette) ............................................... Re: iPod classic on shuffle (Harold Bissonette) 
Jul 10, 2011, 15:04

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cyberpainter 5940 posts 
wracket wrote: cyberpainter wrote: Yeah, however you say the odds are "low", but I don't delve deep enough to understand what that means. Seems like the odds would go down to get all heads repeatedly over time because as each is 50/50, you have 50% chance each time of breaking the streak. Yes, the odds of getting 6 heads in a row are half of the odds of getting 5 heads in a row and so on. cyberpainter wrote: Also, since over time you'd probably break even, it feels like there should be some other kind of statistical factors in play (that are like some kind of magic hocus pocus to the likes of me). Here's where the essential misunderstanding for most people comes in. Of course, taken from point 0 (before the first flip) you can say that the single most likely scenario is that, 10 flips from now, you will find yourself with a distribution of 5 heads and 5 tails. But let's assume that you've already flipped 4 straight heads and you're now at point 4, with six flips remaining. Would you then expect that over time, starting from this point on, the most likely scenario will be with you ending (after 10 flips, 100 flips, whatever) at an even distribution of heads and tails for the set taken as a whole (from point 0 until the end)? The answer to this is a resounding "no"...since you already have four heads "in the bag", the odds calculated at point 4 are that, once you have finished flipping, you are more likely to have more heads than tails. There is no "mean reversion" here because each flip is independent of those that came before it. No hocus pocus here! Interesting, thanks wracket. But even though each flip is independent, can't you look at odds over a longer span? Let's say you did 100 flips. The first 4 were even. You've already "beaten" the odds. But I thought maybe the odds would get greater as time went on, that it would indeed get close to 50 odd and 50 even. I'm thinking there might be some magic number that would bring the odds back to 50/50? :) 
Jul 10, 2011, 17:23

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Harold Bissonette 2062 posts 
wracket wrote: Harold Bissonette wrote: My theory of 3fromonerow plus 3spread out only works in about half of these answers, but I think even if it only works half the time, that would at least  if only fractionally  narrow the odds. Certainly nothing even approaching 6inarow  and presumably nothing like that has ever come up. Whether we're talking about numbers or animals, there are no rows, no groupings. It's all purely artificial, hence the ability to substitute animals for numbers. There are x numbers of balls in pot and at the first go any of those balls has a 1/x chance of being selected, at the second drawing 1/(x1), etc. The fact that they use numbers tends to draw your attention into grouping them into rows or multiples of three or whatever, though my point with the animals is that one could regroup the animalspaintedovernumbers balls into rows of, say, mammals, fish, reptiles, birds...and then probably try to find patterns of the winning combinations based upon these new row groupings. But if you scratched off the animals, you might find yourself with one "row" of balls 2,7,18,19,24,38,43,45. So which "row" actually applies to the varied probability of these balls being selected, the animal one or the number one? The answer is clearly that it is neither of them. (I hope we're not boring people too much with this) I think the difference between our arguments is that you are arguing for what should happen mathematically/logically, whereas I am arguing for what tends to happen in practice. I think it would be possible to take a set of results  similar to those I linked to and make certain conclusions. For instance: the average gap between the 6 numbers that come up is so much the average variation within those gaps is so much the average odd/even numbers are so much and so on and from that come up with rules relating to these. Then choose your set of 6 numbers that roughly following these rules  wouldn't that lower the odds of winning? 
Jul 10, 2011, 17:24

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cyberpainter 5940 posts 
cyberpainter wrote: wracket wrote: cyberpainter wrote: Yeah, however you say the odds are "low", but I don't delve deep enough to understand what that means. Seems like the odds would go down to get all heads repeatedly over time because as each is 50/50, you have 50% chance each time of breaking the streak. Yes, the odds of getting 6 heads in a row are half of the odds of getting 5 heads in a row and so on. cyberpainter wrote: Also, since over time you'd probably break even, it feels like there should be some other kind of statistical factors in play (that are like some kind of magic hocus pocus to the likes of me). Here's where the essential misunderstanding for most people comes in. Of course, taken from point 0 (before the first flip) you can say that the single most likely scenario is that, 10 flips from now, you will find yourself with a distribution of 5 heads and 5 tails. But let's assume that you've already flipped 4 straight heads and you're now at point 4, with six flips remaining. Would you then expect that over time, starting from this point on, the most likely scenario will be with you ending (after 10 flips, 100 flips, whatever) at an even distribution of heads and tails for the set taken as a whole (from point 0 until the end)? The answer to this is a resounding "no"...since you already have four heads "in the bag", the odds calculated at point 4 are that, once you have finished flipping, you are more likely to have more heads than tails. There is no "mean reversion" here because each flip is independent of those that came before it. No hocus pocus here! Interesting, thanks wracket. But even though each flip is independent, can't you look at odds over a longer span? Let's say you did 100 flips. The first 4 were even. You've already "beaten" the odds. But I thought maybe the odds would get greater as time went on, that it would indeed get close to 50 odd and 50 even. I'm thinking there might be some magic number that would bring the odds back to 50/50? :) Scratch that last bit, magic number that would make the results split evenly, is what I meant
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In reply to: Re: iPod classic on shuffle (cyberpainter) 
Jul 10, 2011, 17:25

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