You can load a die but you can't bias a coin (2002) [pdf]

kens 11 years ago |

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.

brownbat 11 years ago |

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/

bmm6o 11 years ago | |

"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 11 years ago | | |

> 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.

jmount 11 years ago |

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

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

shalmanese 11 years ago |

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.

thret 11 years ago |

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...

fennecfoxen 11 years ago | |

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 11 years ago | | |

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

dubya 11 years ago | | |

Not a robot, but Persi Diaconis (mathematician and magician) built a coin-flipping machine.

http://www.npr.org/templates/story/story.php?storyId=1697475

neya 11 years ago | | |

That's a pretty cool idea! Let me know how it goes :) I think it's totally possible.

For your viewing pleasure:

https://www.youtube.com/watch?v=tIIJME8-au8

Cheers.

TimPC 11 years ago |

This needs a 2002 in the title.

j2kun 11 years ago |

> 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.

GFK_of_xmaspast 11 years ago |

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

madcaptenor 11 years ago | |

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 11 years ago | | |

Indeed Diaconis et al. cites Gelman-Nolan.

mturmon 11 years ago | | |

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.