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Double Headed Coins and skepticism

Let's say it turns up THHTHTTHHHTTHTTTTHTHTHHTHTTHHHTTHTTTTHTHHTHHTHTTHHHTTHTTHTTHHHTHHTHTTHHHTTHTTTTHHHTHHTHHTTHHHTTHTTHTHH.

My understanding is it could have just as easily been all heads as it could have been in that order. But if it turned up in that order, it wouldn't look suspicious. Even though the chance of it happening is the same.

It can turn up in that above combination, just like any of them (including all one or the other, or perfectly alternating, or anything).
 
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Alan said:
Let's say it turns up THHTHTTHHHTTHTTTTHTHTHHTHTTHHHTTHTTTTHTHHTHHTHTTHHHTTHTTHTTHHHTHHTHTTHHHTTHTTTTHHHTHHTHHTTHHHTTHTTHTHH.

My understanding is it could have just as easily been all heads as it could have been in that order. But if it turned up in that order, it wouldn't be suspicious.

It can turn up in that above combination, just like any of them (including all one or the other, or perfectly alternating, or anything).
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Pretty sad definition of "can", in a world where we observe that fair coins don't actually have runs of anywhere near 100, nor do we expect them to.

What you're doing is abandoning your actual experience of the world in favor of abstractions and idealizations that don't appear to describe the universe we really live in.

Bad strategy, that.

And btw, in real-world terms, our brains turn out to be not bad statisticians. Even infants somehow understand that something's wrong when events occur that are way outside expected probabilities.
 
Very unlikely things happen all the time. Things equally as unlikely as a run of 100 heads. Like any one other combination after 100 coin tosses.


We are terrible statisticians. For example, are you aware of the Monty Hall problem? Or the question of how many people need to be in a room for there to be a greater than 50% chance of two of them sharing the same birthday (not including the year)?
 
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Alan said:
Very unlikely things happen all the time. Things equally as unlikely as a run of 100 heads. Like any one other combination after 100 coin tosses.


We are terrible statisticians. For example, are you aware of the Monty Hall problem? Or the question of how many people need to be in a room for there to be a greater than 50% chance of two of them sharing the same birthday (not including the year)?
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We're not very good statisticians when it comes to artificial situations or unimportant business such as the number of folks in a room sharing a birthday. But for everyday work, our brains are Johnny on the spot.

I've seen some wild coincidences. But nothing approaching 100 consecutive heads on a fair coin.

And there's no doubt in my mind that you would back off a bet if you saw a coin exhibit such behavior. I sure would. And if you wouldn't, you're more gullible than I'd care to admit.

That's because we know how coins really behave. We know they're well enough balanced that they're not actually going to land on one side or another 100 times in a row if there's no manipulation going on.

Drawing Ts and Hs on paper doesn't change that, of course, because we don't live in a world of Ts and Hs and white plains and mathematical abstractions.

We live in a world of metal and air, and experience that lets us know when things are out of whack.

Our instincts do not let us down in this case.

We may not understand precisely why, but we're not wrong when we conclude that a coin flipped to 100 consecutive heads is fixed. And no number of Ts and Hs on a sheet of paper changes that. Evolution serves us better.
 
Alan said:
Very unlikely things happen all the time. Things equally as unlikely as a run of 100 heads. Like any one other combination after 100 coin tosses.
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As Sol pointed out we are talking about significant events, not "any combination".

Odds of 100 heads is (somewhere around) 1 in 1,270,000,000,000,000,000,000,000,000,000. Even if all 7,000,000,000 people on the planet flipped all day for years it still probably wouldn't happen.

ETA: ...and before the thread goes on the same derail that a similar thread did months ago: Yes, the odds get better if you start counting again after every miss (tails) instead of starting the count again after every 100 flips. It's still very unlikely though.
 
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I'm not saying that it is impossible that a person can cheat. I am saying that it is possible that the person is not cheating.

I, for one, was talking about any combinations.

What's the chance of any other combination after 100 coin tosses? It's low, therefore that combination probably wouldn't happen either.
 
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Well if you change "possible" to "very, very, very small possibility" then, yes, I agree.

Obviously the smaller the possibility becomes, the closer it gets to impossible.

This is a very similar discussion to the .999... repeating = 1 thread.
 
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OnlyTellsTruths said:
I'm fairly certain that the total number of significant interest events would still be a drop in a bucket. At least in this scenario.

Like in your example, changing the number that appears 10 times in a row. That would be any of the 100 numbers.

100 in 100,000,000,000,000,000,000 is, relatively speaking, nearly the same as 1 in 100,000,000,000,000,000,000.

Add in 900 more "significant events" (which you would think would cover them all); like consecutives (rolling a 1 then a 2 then 3.... up to 10), and it would still be 1000 in 100,000,000,000,000,000,000.
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Yes, so probably any of those anomalies would be very unlikely to happen to any given individual. But if none had happened to sadhatter, s/he wouldn't be posting about them - but someone else might. And if none of them had happened to anyone that could post here, some other - equally unlikely, but different - anomaly might have happened to someone. Etc.

Ex post facto statistics is a very, very tricky business.
 
It's a good thing sadhatter kept his story believable. If he had said he rolled 39 17 55 80 48 51 96 23 52 88 31, I would have called him out on it, because that's even less likely.
 
The word "possible" covers things that are very unlikely to happen so I'm perfectly satisfied with the word. I don't think somebody could read what I wrote and think that I was saying that it wasn't very unlikely. Just that other possible strings of the same length are equally unlikely to occur.
 
Yashichi said:
It's a good thing sadhatter kept his story believable. If he had said he rolled 39 17 55 80 48 51 96 23 52 88 31, I would have called him out on it, because that's even less likely.
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Well, he'd either have to be writing them down or have a very good memory!

Again, we all understand that any and all sets have the same odds of occurring. We are talking about significant sets. For instance if he had predicted those 11 (from Yashichi's post) beforehand it would then become significant.

10 numbers in a row has to happen (unless the die breaks!). Any specific 10 in a row is very unlikely.
 
As far as varying levels of "possible" go, I'm going to steal Modified's great example from the
Impossible or just unlikely thread:


Someone wins the big weekly one in a billion lotto.

Now compare that to the same person winning it every single week of their life.

The first is nearly impossible. The second is so close to impossible that it basically equals impossible.

Again, this brings to mind the .999... repeating = 1 thread.
 
OnlyTellsTruths said:
As far as varying levels of "possible" go, I'm going to steal Modified's great example from the
Impossible or just unlikely thread:


Someone wins the big weekly one in a billion lotto.

Now compare that to the same person winning it every single week of their life.

The first is nearly impossible. The second is so close to impossible that it basically equals impossible.

Again, this brings to mind the .999... repeating = 1 thread.
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Considering that things just as unlikely happen regularly, I wouldn't feel comfortable putting it in the 'nearly impossible' category.
 
sol invictus said:
Yes, so probably any of those anomalies would be very unlikely to happen to any given individual. But if none had happened to sadhatter, s/he wouldn't be posting about them - but someone else might. And if none of them had happened to anyone that could post here, some other - equally unlikely, but different - anomaly might have happened to someone. Etc.

Ex post facto statistics is a very, very tricky business.
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I accept that, clearly if there are six billion people on this planet, and some fraction of them are rolling dice regularly, some of those people will see some pretty strange rolls come up, and those are the ones that we'd expect to post on forums. But I still don't believe it, and the reason for that, and I think yours too, has to do with the crazy probabilities involved.

I did fail to include the possibility that it just happened to be an unfair die, though. It's possible for that to be the case and for the players not to know about it.
 
Alan said:
Considering that things just as unlikely happen regularly, I wouldn't feel comfortable putting it in the 'nearly impossible' category.
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You think that things just as unlikely as the same person hitting the one in a billion lottery every single week of their entire life happen "regularly"?

We're talking about one single person hitting one in a billion, hundreds of times in a row.

ETA: I see you are talking about the first part, apologies. Still, I would personally call one in a billion 'nearly impossible'.
 
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There is another thread at the moment on the topic of whether something is impossible or just unlikely.
http://www.internationalskeptics.com/forums/showthread.php?t=200580

I think that there are examples in that thread of things that I would call "almost impossible". One in a billion doesn't come close to that. But this is a subjective matter of what to call things and it isn't important.
 
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Post deleted -- I made the same error as OTT. Sorry.
 
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Btw, I don't think this is actually a problem of pure probabilities. It's a problem of probabilities plus real physics.
 
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