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RE: Unfair Coin Flip
September 29, 2017 at 12:15 pm
(This post was last modified: September 29, 2017 at 12:19 pm by Edwardo Piet.)
(September 29, 2017 at 11:57 am)Tiberius Wrote: Suppose you have a coin, and you suspect it is unfair (i.e. it lands on one side more often than the other). You don't know which side it lands on more, and for sake of argument assume you can't find out.
How can you simulate a fair coin flip using this coin only? By "fair" I mean that you should get a "heads" result exactly 50% of the time, and a "tails" result exactly 50% of the time.
Oh fill in all the indentations with cement and then write "tails" on one end and "heads" on the other should work.
(September 29, 2017 at 12:15 pm)Tiberius Wrote: Increasing the sample size gets you closer to the actual value but you never touch it.
Oh so we'd have to be 100% accurate too.
If it truly is an unfair coin and you have to use that coin and one side is not 50% and there is no way you're allowed to modify the coin and you have to flip it the normal way and it's not a trick question... then it's not possible.
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RE: Unfair Coin Flip
September 29, 2017 at 12:19 pm
(This post was last modified: September 29, 2017 at 12:23 pm by The Grand Nudger.)
All you have to do to find which side it is, and the distribution of probability, is determine how many flips it takes you to reach a distribution wherein P(h1)*P(h2)=.5
Or, if you prefer, wherein, after the first flip of any two consecutive flips, the probability of getting heads or tails again..the next flip, is 50/50.
-or am I missing something?
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RE: Unfair Coin Flip
September 29, 2017 at 12:19 pm
(September 29, 2017 at 12:15 pm)Hammy Wrote: If it truly is an unfair coin and you have to use that coin and one side is not 50% and there is no way you're allowed to modify the coin and you have to flip it the normal way and it's not a trick question... then it's not possible.
But it is. 
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RE: Unfair Coin Flip
September 29, 2017 at 12:20 pm
Must be a trick question 
Am I allowed to modify the coin?
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RE: Unfair Coin Flip
September 29, 2017 at 12:20 pm
(September 29, 2017 at 12:19 pm)Khemikal Wrote: All you have to do to find which side it is, and the distribution of probability, is determine how many flips it takes you to reach a distribution wherein P(h1)*P(h2)=.5
Sure, but how do you do that with 100% certainty. You can't unless you flip it an infinite number of times.
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RE: Unfair Coin Flip
September 29, 2017 at 12:20 pm
(September 29, 2017 at 12:20 pm)Hammy Wrote: Must be a trick question
Am I allowed to modify the coin?
No.
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RE: Unfair Coin Flip
September 29, 2017 at 12:21 pm
If I'm being told I have to flip a coin the normal way that is completely unfair for coin flipping the normal way by definition and end with a result that isn't completely unfair.... that sounds to me like being told to make a square circle.
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RE: Unfair Coin Flip
September 29, 2017 at 12:21 pm
(This post was last modified: September 29, 2017 at 12:22 pm by Foxaèr.)
It is possible, but the chances are not precisely in your favor. It could literally take years of flipping, or any amount of time really, but eventually the 50-50 would happen naturally.
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RE: Unfair Coin Flip
September 29, 2017 at 12:22 pm
(September 29, 2017 at 12:14 pm)RoadRunner79 Wrote: (September 29, 2017 at 11:57 am)Tiberius Wrote: Suppose you have a coin, and you suspect it is unfair (i.e. it lands on one side more often than the other). You don't know which side it lands on more, and for sake of argument assume you can't find out.
How can you simulate a fair coin flip using this coin only? By "fair" I mean that you should get a "heads" result exactly 50% of the time, and a "tails" result exactly 50% of the time.
Assuming only 1 flip of the coin, then if I don't know which side the coin lands on more, then it would be a fair coin flip, if I call it. (since I have a 50/50 chance of getting the dominant side).
That's actually a pretty clever way of doing it, but not the method I was looking for. It also breaks down when you have someone who chooses "heads" every single time, since they should (with a fair coin flip) win 50% of the time, but they won't.
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RE: Unfair Coin Flip
September 29, 2017 at 12:23 pm
(September 29, 2017 at 12:21 pm)Lutrinae Wrote: It is possible, but the chances are not precisely in your favor. It could literally take years of flipping, or any amount of time really, but eventually the 50-50 would happen naturally.
What if I told you you could perform a fair coin flip relatively simply in a small number of flips, certainly not taking "years".
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