RE: Unfair Coin Flip
September 30, 2017 at 1:21 am
(This post was last modified: September 30, 2017 at 3:03 am by Tiberius.)
(September 29, 2017 at 5:11 pm)Alex K 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.
Invert the result of every other flip?
Probably too easy - it depends on what you want to accomplish. It'll give you exactly 50:50, but with strong correlation between subsequent flips if the coin is unfair.
Can you show the math on that, I'm not seeing how inverting every other flip means you get a 50:50 result regardless of the unfairness of the coin. If anything, doesn't it make the coin slightly more biased towards the less likely result?
Also your method can't be used to generate a single fair coin flip, because the first flip you get will always be un-inverted and will therefore have the probability of the unfair coin, so you've achieved nothing. Note my question said to "simulate a fair coin flip", not requiring multiple flips to average out 50/50. The first simulated flip (and therefore all subsequent simulated flips) should have a 50/50 chance of being heads or tails.
