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How to create an unfair coin and prove it with math (2011) (izbicki.me)
48 points by homarp on June 27, 2021 | hide | past | favorite | 10 comments


A play on the fact you can't load a coin?

You can load a die but you can’t bias a coin - https://www.stat.berkeley.edu/~nolan/Papers/dice.pdf


...if you toss the coin by catching it mid air and then slapping it onto a flat surface, that is.

if you let the biased coin bounce and flop around, e.g. by throwing it onto a table or into the ground, it will show biased results.

thats what I read in your quoted report.


> Amazingly, it takes some pretty big bends to make a biased coin. It’s not until coin 3, which has an almost 90 degree bend that we can say with any confidence that the coin is biased at all.

Is this a parody of statistical driven thinking?

The coins are clearly biased from the first bent coin on. It just takes a more extreme bias for the statistics to "prove" the bias assuming no other information using only 100 flips.

But we have other information: you know you bent the coins...

The statistics are not useful for confirming the bias. Rather they are useful for finding "how much cheating" you can push before the statistics alone are enough to get you beat up.


Ironically your being biased when you think that just because you can see a coin it bent that it must then be based. It’s perfectly possible that a coin even with an extremely visible bend is still unbiased, and the only way to prove it’s biased is to conduct the experiment.


They implicitly mean 'practical' or 'observable' bias. A coin with a .0001 bias isn't very interesting.


Just because you can easely see the bias in the example doesn't mean you can in other area's. There are magicians that can reliably flip coins.

I mean, what were you expecting? He flipped a coin 600 times. his findings aren't going to be groundbreaking if he did it 6.000 times.


The point is that stats isn't useful for demonstrating the existence of bias since we know already the bias exists given the deliberate introduction of bias. We know the population function is biased and sample data from that function isn't going to change that.

The stats in the post is mostly a commentary on the phenomenon of statistical power. It may also be a commentary on how the angle of the bend is non-linearly related to coin flip bias. I did find that bit to be unexpected. Although given the wide sampling distribution due to the low N, this could easily be variance.


Seems unintended parody, the best kind of parody.

Because 3rd coin flipped 41 out of 100, at level 0.95 the confidence interval still contains 0.50


boublepop is right -- you know you bent the coins. So what? You don't know that bending the coins causes them to be biased.


Lol, I thought this was going to be about crypto currency. Lovely article!




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