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It is very easy to bias a coin. Ask any stage magician. You can bend them, you can taper the outer edge, you can cover one side in a thin layer of something b

It is very easy to bias a coin. Ask any stage magician. You can bend them, you can taper the outer edge, you can cover one side in a thin layer of something bounce-deadening (like rubber cement), et cetera. There's a big difference between "you can't bias a coin using weight" and "you can't bias a coin." https://izbicki.me/blog/how-to-create-an-unfair-coin-and-prove-it-with-math.html https://izbicki.me/blog/how-to-create-an-unfair-coin-and-pro...

kybernetikos 11y ago
The article says that the flip should be caught and not allowed to bounce or spin on the ground. It still seems to me possible to bias it with weight, based on angular momentum. I think a cavity internally that went from the center of the coin towards one side, with a small weight that moved up and down freely would cause one part of the spin to go faster (when the weight was in the center) than the other part, and would cause a bias if the spin were slow enough not to keep the weight locked at the outside (maybe a spring would be needed? Turns out I don't have a good intuition for what happens when you mix gravity with fast rotation)
- GFK_of_xmaspast 11y ago
  Persi Diaconis, 2004: http://statweb.stanford.edu/~susan/papers/headswithJ.pdf http://statweb.stanford.edu/~susan/papers/headswithJ.pdf and http://news.stanford.edu/pr/2004/diaconis-69.html http://news.stanford.edu/pr/2004/diaconis-69.html
  - kybernetikos 11y ago
    Thanks for those links, really interesting. Summary for anyone who hasn't read them: Diaconis did detailed analysis and ran experiments and found that coins are biased to land the way they start, but it's a small bias in normal use (51%). The article also claims that he has trained himself to reliably flip coins so they land the same every time. Interesting that it seems to contradict the article linked here.
  - ziyao_w 11y ago
    And some more magic by Persi: https://youtu.be/ZdA7TeoZD_g?t=2m10s https://youtu.be/ZdA7TeoZD_g?t=2m10s
    - davidb_ 11y ago
      That's a neat trick. Based on the article and rewatching the video, he's not actually flipping the coin. > In Section Three we prove that the angle ψ between M and the normal to the coin stays constant. If this angle is less than 45 ◦ , the coin never turns over. It wobbles around and always comes up the way it started. Magicians and gamblers can carry out such controlled flips which appear visually indistinguishable from normal flips.
      - steve19 11y ago
        He refers to it at the end of that video clip as tossing. looking closely that's pretty much what he is doing. it looks like he might be flipping it once during the toss for effect. Such a slow rotation allows him to easily catch it at the right moment.
mrestko 11y ago
Your concern is addressed within the first three sentences of the article.

kybernetikos 11y ago

The article says that the flip should be caught and not allowed to bounce or spin on the ground. It still seems to me possible to bias it with weight, based on angular momentum. I think a cavity internally that went from the center of the coin towards one side, with a small weight that moved up and down freely would cause one part of the spin to go faster (when the weight was in the center) than the other part, and would cause a bias if the spin were slow enough not to keep the weight locked at the outside (maybe a spring would be needed? Turns out I don't have a good intuition for what happens when you mix gravity with fast rotation)

GFK_of_xmaspast 11y ago
Persi Diaconis, 2004: http://statweb.stanford.edu/~susan/papers/headswithJ.pdf http://statweb.stanford.edu/~susan/papers/headswithJ.pdf and http://news.stanford.edu/pr/2004/diaconis-69.html http://news.stanford.edu/pr/2004/diaconis-69.html
- kybernetikos 11y ago
  Thanks for those links, really interesting. Summary for anyone who hasn't read them: Diaconis did detailed analysis and ran experiments and found that coins are biased to land the way they start, but it's a small bias in normal use (51%). The article also claims that he has trained himself to reliably flip coins so they land the same every time. Interesting that it seems to contradict the article linked here.
- ziyao_w 11y ago
  And some more magic by Persi: https://youtu.be/ZdA7TeoZD_g?t=2m10s https://youtu.be/ZdA7TeoZD_g?t=2m10s
  - davidb_ 11y ago
    That's a neat trick. Based on the article and rewatching the video, he's not actually flipping the coin. > In Section Three we prove that the angle ψ between M and the normal to the coin stays constant. If this angle is less than 45 ◦ , the coin never turns over. It wobbles around and always comes up the way it started. Magicians and gamblers can carry out such controlled flips which appear visually indistinguishable from normal flips.
    - steve19 11y ago
      He refers to it at the end of that video clip as tossing. looking closely that's pretty much what he is doing. it looks like he might be flipping it once during the toss for effect. Such a slow rotation allows him to easily catch it at the right moment.

mrestko 11y ago

Your concern is addressed within the first three sentences of the article.