Is there such a coin – or cylinder – in which there is an equal chance of getting heads, tails or landing on its side? I am guessing that it is a ratio between the radius and height of the coin, but what are the numbers?

  • $\begingroup$ There was a youtube video that actually tested this a while ago. They calculated the height two different ways and got two different answers, and experimentally determined that the correct height was somewhere between the two they had calculated. I don't think it's a trival calculation, since surface area and inertia interact... $\endgroup$ – Selvek Mar 28 '18 at 16:37
  • 2
    $\begingroup$ I suspect there is a certain amount of chaos involved in the bouncing and such like making it extremely hard to predict how a given shaped object will bounce. With symmetric objects it doesn't really matter how it bounces but if you are talking about a cylinder then a small change to the angle and speed with which it hits a surface can probably make a big difference to the following motion, thus making it hard to predict when a bounce will end with it being on an end or the side... $\endgroup$ – Chris Mar 28 '18 at 16:54
  • 1
    $\begingroup$ This is the video Selvek might have been mentioning. youtu.be/-qqPKKOU-yY $\endgroup$ – Austin Weaver Mar 28 '18 at 17:12
  • 1
    $\begingroup$ It seems to me that you are trying to reinvent the dice. $\endgroup$ – rhsquared Mar 29 '18 at 7:28
  • 3
    $\begingroup$ I don't think this is on topic here; it isn't really anything to do with creating or solving puzzles. It's more topical for perhaps Physics.SE, or slightly more relevantly, for Mathematics.SE where it has already been asked: What should be the proportions of a three sided coin? $\endgroup$ – Rubio Mar 30 '18 at 19:40