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Intelligent Design

Fudbucker said:
Uh huh. And if you flipped a coin 50 times and got heads each time, you would conclude the coin is fair, right? After all, 50 heads is just as likely as any other combination. A fair coin could do that, right?

This is why I "lol" so much on these kinds of threads.
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You are mixing up your probabilities.
 
Oh Jesus.

Any variation of 50 coin tosses (we'll assume a well balanced coin and leave off stuff like a coin landing on its side and use the traditional metaphorical use of the term to mean a 50/50 chance of outcome) is as equal as any other.

This is technically correct (the best kind of correct and the only kind the internet cares about) but misses the point being made.

None of this has anything to do with what is being discussed however.
 
Fudbucker said:
Uh huh. And if you flipped a coin 50 times and got heads each time, you would conclude the coin is fair, right? After all, 50 heads is just as likely as any other combination. A fair coin could do that, right?

This is why I "lol" so much on these kinds of threads.
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MikeG said:
50 heads is NOT as likely as any other combination. That's a ridiculous claim.
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Fast Eddie B said:
No, it’s exactly true.
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The correct term for what it would be as likely as would be permutation, rather than combination. 50 heads in a row is as likely as any other permutation. It's one of the two least likely combinations, though.

Either way, 50 heads in a row would likely be well past the point where it's worth examining the coin and the surroundings for factors that could be messing with the actual odds, but would not be valid reason to conclude that the coin is not "fair," on its own, and that seems to be Fudbucker's big stumbling point.
 
Fast Eddie B said:
No, it’s exactly true.
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I wouldn’t bet on that. That 50 heads will come up is 1 in 1125899906842624. That any other particular combination will come up is also 1 in 1125899906842624. That “any other combination” will come up however is 1125899906842623 for to 1 against.
 
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MikeG said:
Which wasn't the claim.
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The claim:

“50 heads is NOT as likely as any other combination.”

Yes it is. Unless I’m misunderstanding your claim.

I had to argue why buying a lottery ticket with 1-2-3-4-5-6 was a bad bet.

The assertion was that it was because it was so unlikely. The fact is it’s exactly as likely as any other combination.

It’s a bad bet because if it does hit, you will be sharing the prize with thousands of people, not because it’s less likely to hit.

Please correct me if you’re saying something else with your claim or if I’m parsing it incorrectly.
 
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50 heads is half as likely a combination as 49 heads and 1 tail, which is half as likely a combination as 48 heads and 2 tails, and so on.
 
MikeG said:
50 heads is half as likely a combination as 49 heads and 1 tail, which is half as likely a combination as 48 heads and 2 tails, and so on.
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Given each of the 50 tosses is equally likely to be a tail, 49 heads and 1 tail is more than "half as likely" than 50 heads.
 
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Yes, it was a bit simplistic, but a useful illustration, I thought. YMMV.
 
Fudbucker said:
Having a sample size of one doesn't necessarily mean anything. If I design a new lottery, and run it for the first time, and the winning numbers are 3141592653, I'm going to conclude a lot, just from that one run. I don't need to run it again to know it's not a fair lottery.
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What is it about one of the possible results turning up that tells you it isn't fair?
 
I'm with Fudbucker I think - that is if I understand what is being suggested.

If the numbers 3141592653 were to come up in a supposedly random exercise, it would be significant because that number is a very special number, being the ratio between the diameter and circumference of a circle by one million. If the number 1618033989 were to come up, that would be significant also - being the value of Phi by one million.

If numbers like these were to occur, in a situation where a completely random number was expected, it would suggest some intelligent controlling influence was at work. This is the thinking behind those who suggest the proportions of our bodies and those of other creatures, show the value of Phi all over the place. The examples given are not impressive however - in fact some are laughable.
 
Thor 2 said:
I'm with Fudbucker I think - that is if I understand what is being suggested..........
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Are you with him on this, too?

50 heads is just as likely as any other combination.
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There is only one way of tossing a coin 50 times and getting 50 heads. There are 50 ways of getting 49 heads and one tail. There are 50 x 49 ways of getting 48 heads and 2 tails. There are 50 x 49 x 48 ways of getting 47 heads and 3 tails. And so on. There is a vastly greater chance of getting 25 heads and 25 tails than there is of getting 50 heads. So 50 heads is not as likely a combination as any other combination.

If Fudbucker had meant 50 heads has the same probability as any other sequence, then perhaps he should have said that.
 
I, too, assumed we were talking about a sequence of coin tosses, not a distribution.

I think that was the misunderstanding, and I see Fudbucker used the word “combination”, which left room for interpretation.
 
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Fast Eddie B said:
I, too, assumed we were talking about a sequence of coin tosses, not a distribution.

I think that was the misunderstanding, and I see Fudbucker used the word “combination”, which left room for interpretation.
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Yes I agree and perhaps it is not a good analogy to the Pi appearing randomly.

If you were to predict an outcome of:

1 Head ... 2 Tails ... 3 H .... 1 T ... and so on for 50 tosses the likelihood would be similar to that of 50 heads in a row. If the coin was precisely made perfectly symmetrical and the flipping perfectly random - both of these impossible really.
 
Like I said earlier I think we can assume the metaphorical "Thought Experiment Coin" and safely ignore stuff like uneven coins (IIRC there are coins in common circulation that are off centered enough to be as bad as a 45/55 heads/tails distribution over multiple tosses) or a coin landing on its side or quantum tunneling through the table.

Everyone should get that "Coin toss" is a layman's phrase for "50/50 Odds."
 
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