🚀 go-pugleaf

In article <1992Dec15.233405.2306@muddcs.claremont.edu>
jhoste@kuju.claremont.edu (Jim Hoste) writes:
 
>
>Next semester I will be teaching an elementary probability class
>structured around the theme of games and gambling. I want to include some
>material on loaded dice. Surely someone has worked out the physics of
>rolling a die (in the shape of a cube) whose center of mass is not in the
>center of the die. What are the probablities of landing on the various
>faces as a function of the location of the center of mass? The same
>question can be asked for dice in the shape of other polyhedron,
>homogenious or not.
>	I am also interested in the following related question:
>Can one create a die having n faces where the probability of landing on
>each of the faces is given in advance?  This is certainly true if *die* is
>interpreted fairly loosely. Somebody must have worked this out already.
>	Can anyone recommend any good articles on these topics?
>	I will summarize the replies that I receive.
>	Thanks, Jim Hoste
>
>ps I am also posting to:
>	rec.gambling
>	sci.math
>	sci.physics
See Letter to Editor re Kemp & Kemp, The American Statistician, August
1992, Vol. 46, No 3, pp. 239-240.  Says  spots on most dice are
countersunk, which throws the center of gravity off.  Also, since
6 is opposite to 1, 5 to 2, etc., there is a predictable bias.
                       Phil Emerson
                       Cleveland State University
 

In article <168BFB8E5.R0264@vmcms.csuohio.edu> R0264@vmcms.csuohio.edu writes:

#See Letter to Editor re Kemp & Kemp, The American Statistician, August
#1992, Vol. 46, No 3, pp. 239-240.  Says  spots on most dice are
#countersunk, which throws the center of gravity off.  Also, since
#6 is opposite to 1, 5 to 2, etc., there is a predictable bias.

See also

  P.F. Fougere, "Maximum entropy calculations on a discrete 
  probability space," in G.J. Erickson and C.R. Smith, Eds.,
  _Maximum-Entropy and Bayesian Methods in Science and
  Engineering_, Vol. 1, 205-234 (1988). Dordrecht: Kluwer
  Academic Publishers.

  P.F. Fougere, "Maximum entropy calculations on a discrete 
  probability space: Predictions confirmed" in J. Skilling, Ed.,
  _Maximum-Entropy and Bayesian Methods_, 303-308 (1989).
  Dordrecht: Kluwer Academic Publishers.

This discusses an analysis of a long series of throws with
a (handmade in 19th century) set of dice by the Swiss
astronomer Wolf (of Wolf Sunspot Number fame). The tallies
were recorded and analyzed, an hypotheses about the shape
and irregularities of the dice suggested (in the first paper).
Later the actual dice were located and some of the predictions
confirmed. 

I don't know how good modern dice are, but the dice Wolf used
did show the spot effect, as well as two others.

Bill