Persis Diaconis and many stage magicians can flip a coin and catch it so as to always get heads. Brent Meeker On 9/21/2012 10:25 AM, Charles Greathouse wrote:
I wonder what is known about the fairness of dice -- and even more, of flipping coins -- in practice. Supposing good practices are used (no spinning, lots of flips, etc.), how fair is an American penny? A 1€ coin? Etc. I've "noticed" some biases in my experience but I don't know that those would stand up to statistical scrutiny.
Charles Greathouse Analyst/Programmer Case Western Reserve University
On Fri, Sep 21, 2012 at 12:57 PM, Fred lunnon<fred.lunnon@gmail.com> wrote:
There was a discussion of questions related to polyhedral stability by Conway and others on math-fun in June 1997, under subject headings including ' Thoughts about "fair dice" ', ' oddohedrons ', ' Odd dice ' .
I have a file of it available if anyone wants to take a look; though it should be easy to locate in the archive.
Fred Lunnon
On 9/21/12, Allan Wechsler<acwacw@gmail.com> wrote:
If you make a longish pentagonal prism, and cap the ends with pentagonal pyramids, the resulting 15-faced die has 0 probability of landing on one of the triangular faces, and 1/5 of landing on each of the rectangular faces. All this is by symmetry, and doesn't depend on the physical model except that we expect the die to topple off an unstable face. This of course is not a solution to the D5 problem Warren proposed.
I wonder if there is a pentahedron that is fair regardless of physical model. My intuition is "no", but I don't see any way to prove that.
Andy, I haven't frequented casinos. Don't they require you to throw dice from a cup?
On Fri, Sep 21, 2012 at 9:59 AM, Andy Latto<andy.latto@pobox.com> wrote:
On Fri, Sep 21, 2012 at 9:13 AM, Veit Elser<ve10@cornell.edu> wrote:
I bet if one "rolled" a cubic dice more like the standard coin toss one could strongly bias the outcome (against the faces intersected by the rotation axis).
Provided you don't think this bias is almost completely undone by requiring the die to bounce against an irregularly-shaped surface before it lands, there are any number of casinos willing to take your bet. You don't even need a strong bias; a bias of 5% or so on the individual dice should be big enough to get the 2% bias you need on the total to make money at the craps table.
Andy andy.latto@pobox.com
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