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CarlPierce wrote:i've been trying to derive the equations for the probability of a cuboid dice landing on its six faces if the X,Y,Z lengths are not equal.
I don't think it is so simple as being proportional to the area of the face.
Pulsar wrote:The probabilities will depend on the position of the center of mass.
Pulsar wrote:CarlPierce wrote:i've been trying to derive the equations for the probability of a cuboid dice landing on its six faces if the X,Y,Z lengths are not equal.
I don't think it is so simple as being proportional to the area of the face.
Interesting question. The probabilities will depend on the position of the center of mass. The dice is more likely to land on the side for which the center of mass is closest to the ground. I don't know how to calculate the odds, though.
EDIT: I found a discussion about this: http://physics.stackexchange.com/questions/41297/how-to-determine-the-probabilities-for-a-cuboid-die
Microfarad wrote:Using magnetic properties, would be possible to make a unequal-faces fair dice?
tuco wrote:To be isohedral, each face must have the same relationship with all other faces, and each face must have the same relationship with the center of gravity. - http://www.mathpuzzle.com/Fairdice.htm
This makes sense, and can, in limited fashion, be observed when playing with toys as a kid. So how many possible there are?
lpetrich wrote:As to coins and dice, coins can be interpreted as d2 dice.
A sequence of all distinct for d(n)? The probability that any one sequence will have all distinct will be 1*(1-1/n)*(1-2/n)*...*(1/n) = n!/(nn) ~ e-n*sqrt(2*pi*n).
Number of faces, probability of an all-faces sequence:
2 0.5
3 0.222222
4 0.09375
5 0.0384
6 0.0154321
7 0.0061199
8 0.00240326
9 0.000936657
10 0.00036288
11 0.000139906
12 0.0000537232
So this method quickly becomes impractical.
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