
You can load a die but you can't bias a coin (2002) [pdf] - krmtl
http://www.stat.columbia.edu/~gelman/research/published/diceRev2.pdf
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kens
If you go beyond the title and read the paper carefully, what it states is if
you spin a coin rapidly in the air with a horizontal spinning axis and catch
it in the air, then weighting the coin doesn't bias it. If you throw a coin in
other ways (e.g. let it land on a surface), then you can of course bias a
coin.

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brownbat
That's why cypherpunks each bring their own coin and XOR the heads. Or flip a
biased coin twice. If you get HH or TT, discard and start over. If you get HT
or TH, take the first flip of the pair.

More to the paper, I liked the point about using unexpected results to drive
student engagement. In one of the early episodes of Very Bad Wizards, they
described some aspects of teaching as like a magic show. I think it's a good
analogy.

[http://verybadwizards.com/](http://verybadwizards.com/)

~~~
bmm6o
"Or flip a biased coin twice" \- TFA argues that there is no such thing.

> _That 's why cypherpunks each bring their own coin and XOR the heads_

I'm not sure what part of the article you are referring to here, but this is
more about the XOR being decorrelated from either of the inputs than about
anything to do with the efficacy/existence of a biased coin, right?

~~~
brownbat
> a biased coin ... TFA argues that there is no such thing.

The article repeatedly admits biased coins exist, it just adds a flipping
protocol that can mitigate this bias, a protocol that can only be verified by
a nonflipper who can accurately measure the angle of spin and number of
rotations with the naked eye in under a second.

You can instead generate unbiased "flips" through math, rather than physics
and trusting someone else's thumb.

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jmount
I still think you manufacture a (slightly) unfair coin: [http://www.win-
vector.com/blog/2015/04/i-still-think-you-can...](http://www.win-
vector.com/blog/2015/04/i-still-think-you-can-manufacture-an-unfair-coin/)

( The post got truncated by a bad character in my blockquote paste (sorry!).
It should be legible now (and include two figures). )

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shalmanese
This is only with solid coins. I'm pretty sure with a liquid centered coin,
with sufficient tinkering, it would be possible to design a biased coin using
the changing weight distribution to keep the flip biased to certain positions.

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thret
It's already biased towards the face that is facing up to start. With practice
or by accident, you can toss it so that it wobbles but doesn't actually flip
over. A casual observer cannot tell the difference.

Explained in [http://www.amazon.com/Heads-Or-Tails-Gary-
Kosnitzky/dp/B00FM...](http://www.amazon.com/Heads-Or-Tails-Gary-
Kosnitzky/dp/B00FM0IALE)

~~~
fennecfoxen
TODO: Build a robot with precise enough control that it can flip a coin
(properly flipping, not just wobbling) and then catch it in a desired state
(either heads or tails) with substantial accuracy.

~~~
Crito
That reminds me of the rock-paper-scissors robot from a while ago that always
"wins" by watching the human hand to see what sign they are throwing, then
throwing the countersign faster. It is so fast that unless you are watching it
on high-speed film, you can't tell that it is cheating.

[https://www.youtube.com/watch?v=3nxjjztQKtY](https://www.youtube.com/watch?v=3nxjjztQKtY)

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TimPC
This needs a 2002 in the title.

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j2kun
> The biased coin has long been part of statistical folklore, but it does not
> exist in the form in which it is imagined.

Sure it does, just abstractly. You can simulate a coin if any bias using a
fair coin.

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GFK_of_xmaspast
Got a lot of respect for Andrew Gelman, but it's too bad he didn't cite Persi
Diaconis:
[http://statweb.stanford.edu/~susan/papers/headswithJ.pdf](http://statweb.stanford.edu/~susan/papers/headswithJ.pdf)

~~~
madcaptenor
The Gelman-Nolan paper is from 2002; the Diaconis et al. paper is from 2007,
and cites Gelman-Nolan. Gelman and Nolan are pretty smart, but they don't have
a time machine.

~~~
jmount
Indeed Diaconis et al. cites Gelman-Nolan.

~~~
mturmon
The nut of the citation is worth reading:

"In light of all the variations, it is natural to ask if inhomogeneity in the
mass distribution of the coin can change the outcome. [Lindley, 1981] followed
by [Gelman & Nolan, 2002] give informal arguments suggesting that
inhomogeneity doesn’t matter for flipped coins caught in the hand. Jaynes
reports that 100 flips of a jar lid showed no evidence of bias. We had coins
made with lead on one side and balsa wood on the other. Again no bias showed
up. All of this changes drastically if inhomogenious coins are spun on the
table (they tend to land heavy side up). As explained above, some of this bias
persists for coins flipped onto a table or floor."

You have to love Persi Diaconis. Having coins made up with lead on one side
and balsa wood on the other.

