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16th September 2009, 11:28 PM | #41 |
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The OP specifically rules out spinning coins by saying that the coin is caught. The (flawed) argument in the OP is not based on the coin being biased.
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17th September 2009, 03:15 AM | #42 |
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No worries
I think you've misunderstood me. I'm saying that every coin is biased to some degree. But I'm also saying that it makes absolutely no difference to the likely outcome of a fair toss. Yes, I think we've digressed unnecessarily, and don't really hold any significant difference in views. |
17th September 2009, 07:22 AM | #43 |
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Back to the actual paper, I think it's quite an interesting result and a very simple analysis - I wish I'd thought of it!
It would be fun to figure out how to flip coins to increase the bias. It doesn't sound very hard to do and should be almost impossible to detect by eye. |
17th September 2009, 08:18 AM | #44 |
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The argument in the paper seems a lot more complicated than I had realized from the OP.
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17th September 2009, 08:36 AM | #45 |
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17th September 2009, 10:20 AM | #46 |
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Wow, totally different to the OP.
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17th September 2009, 12:02 PM | #47 |
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The paper is very different to the OP (which most of us were responding to).
They put together quite a nice detailed physical model of the coin toss - which seems impressive - but then somewhat ruin it by making pretty crude assumptions about the probability distributions of the inputs to this model. I say this because the output distributions will merely be a function of the input distributions, and the subtle effects they are looking for could be swayed by these assumptions. I was also surprised that 1 in 25 of their "vigorous" flips did not flip the coin once. This brings me back to an earlier point about the statistics being a function of the flipper. I don't think this would be anything like (for example) if I were the one flipping the coin! It is an interesting paper, as far as the assumptions go. I think I would need rather more convincing evidence of those assumptions before buying into the predictions made by their model. |
17th September 2009, 12:10 PM | #48 |
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I'd be interested in seeing the results of a large number of real world coin tosses. Do they show any bias?
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17th September 2009, 01:58 PM | #49 |
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The paper itself quotes a study in which they praise someone for their perseverance in completing 10,000 coin tosses. Unfortunately, the sampling error is too great, and not accurate enough to detect the effect they describe. (The study found no statistically significant bias in the results)
The paper estimated that a total of 250,000 tosses would be needed to confidently identify a bias of the magnitude they describe. They appear unwilling to embark on such a study! They need to make an event of it - go for a world record |
17th September 2009, 02:06 PM | #50 |
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They're mathematicians.
Quote:
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17th September 2009, 02:15 PM | #51 |
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Have I missed something here? I'm not sure what you're getting at.
No, that certainly does not follow. Just because we know the values at point A and B - say f(A) and f(B) - does not automatically imply that f(C) will lie between f(A) and f(B) just because C lies between A and B. And, indeed, the paper makes no such broad-brush claim either. |
17th September 2009, 06:55 PM | #52 |
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When you say "OP", I assume that you're not really referring to my original post, you're referring to the article by James Devlin, which I quoted in the OP. Remember, I warned you that "James Devlin says this, parts of which may or may not be supported by the paper."
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17th September 2009, 08:10 PM | #53 |
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Just that mathematicians aren't necessarily the best people to be doing experiments.
Quote:
Quote:
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18th September 2009, 01:34 AM | #54 |
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18th September 2009, 02:06 AM | #55 |
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18th September 2009, 02:55 AM | #56 |
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The argument is really simple. Flip a coin that starts heads up and it spends more of its time in the air heads up, unless you flipped it exactly right (angular momentum perfectly parallel to the coin), in which case it's 50-50 heads-tails. It's impossible to flip it exactly right.
So, which assumption do you think might be invalid? |
18th September 2009, 03:02 AM | #57 |
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Simple thought experiment for you. What do you think happens when there is a non-zero angular difference between the angle at which the coin is tossed and the angle at which it is caught?
Do you think that the angular difference will always be *exactly* zero, i.e. the catching angle will be exactly identical to the initial toss? |
18th September 2009, 03:16 AM | #58 |
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Quote:
Starting at 1 and ending at 18 would yield equal odd and even numbers. If you were to do an infinite amount of coin tosses, there would be no way to determine if there's more odds and evens, and it would be 50/50. |
18th September 2009, 03:35 AM | #59 |
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That's one of the things that might matter, yes. Air resistance is another, as is catching time/time of flight. They comment on a list of such assumptions.
So, will you answer my question? Which of those do you think is important? The one you raised doesn't sound it, because so long as the angle is less than 90 degrees their argument still works. |
18th September 2009, 04:10 AM | #60 |
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I'd never trust a coin flip to be fair, unless I do it myself, in which case I know it's not fair.
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18th September 2009, 04:25 AM | #61 |
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The quote in the OP seems to be based on a misreading of the paper in a blog post. The argument in the paper is not based on the coin being heads up more times than not due to a simple counting argument, it's about it being heads up for longer than not due to angular momentum.
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18th September 2009, 04:27 AM | #62 |
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Doesn't the findings of the real world tossing experiments indicate that their model, or their assumptions are flawed? A 2% bias shouldn't require 250,000 tosses to demonstrate should it?
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18th September 2009, 04:46 AM | #63 |
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18th September 2009, 05:38 AM | #64 |
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Right. Which is why I said they were right for their assumptions, but I'm not convinced their assumptions are right.
? I've already answered this, the catch angle will not be the same as the toss angle, and the distributions they have assumed for this (I think) are unrealistic. This doesn't make them wrong, it just doesn't mean they've made their case. Wrong, and they even acknowledge this in the paper. The bias can be reversed with angles of much less than 90 degrees. Think about the percentage of time the normal of the coin projected on to the great circle spends above the equator. |
18th September 2009, 05:40 AM | #65 |
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18th September 2009, 07:41 AM | #66 |
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Where do they acknowledge it? I missed that.
Quote:
Basically, what I'm saying is that the coin flip is inherently asymmetric, and so to compensate for that perfectly you have to do something very special. A generic flip and catch sequence won't do that. |
18th September 2009, 08:47 AM | #67 |
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First para, page 14 of the preprint linked in the OP. Here they discuss a generalisation in which they attempt to account for the difference in flipping and catching angles, and note that there is an angle at which the bias reverses. I wish they had chosen a different terminology for "same side" and "different side", but they refer to this as heads and tails respectively, so where they refer to a bias towards tails, they mean the bias switches to the other side of the coin.
They way they get around it in the paper is (IMHO) a bit tricky. They assume orthogonal, normally distributed components when consider a flip angle different to the catch angle. This results in an unbiased distribution of flips about the nominal catch angle. I'm not convinced by this. I suspect the vast majority of coin flippers would have a bias in the angle between flip and catch. Just because you flip and catch naturally and the most natural position is unlikely to be centred on a zero angle. Because the angle can result in a bias in the opposite sense (i.e. opposite side rather than same side), you can no longer conclude a consistent bias to one side between the two extremes. It might be the case that there is, but it doesn't automatically follow. |
18th September 2009, 10:20 AM | #68 |
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"Anyway, why is a finely-engineered machine of wire and silicon less likely to be conscious than two pounds of warm meat?" Pixy Misa "We live in a world of more and more information and less and less meaning" Jean Baudrillard http://bokashiworld.wordpress.com/ |
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18th September 2009, 10:25 AM | #69 |
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"Anyway, why is a finely-engineered machine of wire and silicon less likely to be conscious than two pounds of warm meat?" Pixy Misa "We live in a world of more and more information and less and less meaning" Jean Baudrillard http://bokashiworld.wordpress.com/ |
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18th September 2009, 11:38 AM | #70 |
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Uh... it kinda does have a memory.
Namely, each time the coin undergoes a mechanical process of turning over, it has to 'remember' what side it was on on the last time it turned over. This seems plausible, as it is handing you a piece of information about a random process, which gives you more information about the process. Or, classically: A couple has two kids. If one is a boy, what are the odds the other one is a girl? Information about a random process... |
18th September 2009, 05:14 PM | #71 |
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19th September 2009, 01:58 AM | #72 |
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It is certainly possible. But since a bias in the angle can cause the bias to reverse (to a bias of the reverse side), and since any spread in the distribution will encapsulate cases where the bias is both one side or the other, I suspect they have over estimated the bias, and it could be less than they expect.
That said, this is all conjecture, until the maths are worked through... I think step one would be to conduct an experiment to get a feel of the typical catch / toss angle bias and distribution. Do we have any experienced tossers on this forum? |
19th September 2009, 06:54 AM | #73 |
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Except that it's utter nonsense, unless balrog has simply decided to ignore my challenge rather than seeking to validate his claim: And if we ever get beyond conjecture what then? This is all academic, given that there are absolutely no conceivable scenarios in which any bias would have a real and practical effect. |
19th September 2009, 12:23 PM | #74 |
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Well... I can't see any immediate use of this research. But that doesn't mean it isn't an interesting puzzle to solve; not all puzzles need a reason for solving them.
That said, gaming statistics can be worth a lot of money. As it happens, I can't think of any casinos that use coin flipping as a standard game. But loading a game by as little as 1% in a casino can be worth a lot of money to somebody... |
19th September 2009, 12:43 PM | #75 |
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19th September 2009, 01:28 PM | #76 |
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In principle a similar argument could work for dice, although the dynamics when they hit the table are much more complicated. Still, that's interesting.
But bear in mind that reversing the advantage of the casino is actually not enough to be able to earn money. The casino has much more money than you do (I assume), which means the situation is asymmetric and you'd need to place many of small bets to leverage your advantage. With a 1% edge you'd need lots of time playing craps to earn anything (same reason why this coin bias requires so many flips to test). |
19th September 2009, 07:13 PM | #78 |
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19th September 2009, 11:55 PM | #79 |
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Seems you're alluding to the stereotypical professional gambler here!
Ditto, but remember that a very large bankroll will soon come up against the house limits, and in any event a clearly winning strategy will very quickly result in the casino manager politely showing you the exit sign, via the restaurant, of course! |
20th September 2009, 07:24 AM | #80 |
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There's a lot of misunderstanding about positive expectation gambling here. Maybe we should get a thread going about the subject.
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