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I feel like this question is quite paradoxical: the only reasonable way we have of deciding whether a coin is fair is by flipping it repeatedly. So has anyone

by ronaldx 13y ago

I feel like this question is quite paradoxical: the only reasonable way we have of deciding whether a coin is fair is by flipping it repeatedly. So has anyone ever flipped heads 76 times in a row on a fair coin? No. Because we would judge that coin to be unfair. In reality, an individual's the flipping method is likely to be more deterministic than random and show bias - it's not the coin that is fair or not, but the method of flipping it.

aristus 13y ago
It's quite simple to implement a fair coin from a coin of unknown fairness. So simple, I put it in a children's book. http://carlos.bueno.org/2011/10/fair-coin.html http://carlos.bueno.org/2011/10/fair-coin.html
- martijn_himself 13y ago
  Very nicely presented. How would you define 'simple'? While I can see the heuristic process is simple (i.e. flip twice and choose the first result in case of HT or TH) to follow, and you could arrive at the conclusion that this gets rid of bias through experiment, I don't find this intuitively simple at all. EDIT: I've also noticed that if I choose 'Suppose Heads comes up 50% of the time.' it says 'You'll need an average of 3.00 flips to get a fair coin.' If heads comes up 50% of the time then I have a fair coin, so shouldn't that be 1.00 flip?
  - aristus 13y ago
    Re-deriving from scratch it is hard. No question about that. Magnetism doesn't make a ton of sense either, but it's simple to demonstrate. Intuitive and simple are not always the same thing. If your coin happens to be absolutely fair, it will require on average 3 flips to generate a fair flip via this method. The point is you don't know a priori whether a given coin is fair.
    - martijn_himself 13y ago
      Great reply, thanks, that makes a lot of sense. Very impressive work too on the book.
tel 13y ago
If you were to be walking down the street and for no particular reason walk into a probability lab and watch two scientists immediately flip 76 heads in a row then, based on observed evidence, you'd be inclined to believe an unfair coin. But that's very unlikely to happen if you've got a fair coin. Almost certainly you'll flip ungodly zillions of failing sequences first before hitting any particular pre-ordained target. So with a fair coin the story is that you peep in on a probability lab and then wait there until just before the heat death of the universe and suddenly observe 76 heads. So honestly, in any fair coin situation your Bayesian probabilistic update going on will actually be predicated on very different evidence.

by ronaldx 13y ago

aristus 13y ago

It's quite simple to implement a fair coin from a coin of unknown fairness. So simple, I put it in a children's book. http://carlos.bueno.org/2011/10/fair-coin.html http://carlos.bueno.org/2011/10/fair-coin.html

martijn_himself 13y ago
Very nicely presented. How would you define 'simple'? While I can see the heuristic process is simple (i.e. flip twice and choose the first result in case of HT or TH) to follow, and you could arrive at the conclusion that this gets rid of bias through experiment, I don't find this intuitively simple at all. EDIT: I've also noticed that if I choose 'Suppose Heads comes up 50% of the time.' it says 'You'll need an average of 3.00 flips to get a fair coin.' If heads comes up 50% of the time then I have a fair coin, so shouldn't that be 1.00 flip?
- aristus 13y ago
  Re-deriving from scratch it is hard. No question about that. Magnetism doesn't make a ton of sense either, but it's simple to demonstrate. Intuitive and simple are not always the same thing. If your coin happens to be absolutely fair, it will require on average 3 flips to generate a fair flip via this method. The point is you don't know a priori whether a given coin is fair.
  - martijn_himself 13y ago
    Great reply, thanks, that makes a lot of sense. Very impressive work too on the book.

tel 13y ago

If you were to be walking down the street and for no particular reason walk into a probability lab and watch two scientists immediately flip 76 heads in a row then, based on observed evidence, you'd be inclined to believe an unfair coin. But that's very unlikely to happen if you've got a fair coin. Almost certainly you'll flip ungodly zillions of failing sequences first before hitting any particular pre-ordained target. So with a fair coin the story is that you peep in on a probability lab and then wait there until just before the heat death of the universe and suddenly observe 76 heads. So honestly, in any fair coin situation your Bayesian probabilistic update going on will actually be predicated on very different evidence.