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Impact of weight of the dice

If you throw a 6-sided die there is a probability of 1/6 to throw any specific value.

However, this assumes that dice are exactly symmetrical, and we all know that they are not. Let's assume that the sides with more eyes weigh less, because the eyes are carved in the surface of the dice.

Would that mean that the probability of throwing a 6 becomes bigger? At first sight, that seems to make sense, because the heavier side of the dice is impacted more by gravity.

On the other hand, while the die makes a circular movement through the air, the heavier side is more likely to hit ground first. Assuming that a dice always roles after hitting the ground, that again makes it just a little less likely to actually finish in the position that it landed at.

So, do you think that weight increases/decreases the probability?

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  • $\begingroup$ One would really need to experiment, or build a (quite complicated) physical model one can simulate. $\endgroup$ – kjetil b halvorsen Feb 26 '17 at 10:56
  • $\begingroup$ See rpg.stackexchange.com/questions/65206/… for some real testing $\endgroup$ – Henry Feb 26 '17 at 10:57
  • $\begingroup$ On good-quality dice, the "carvings" on the different faces remove the same amount of weight from each face. Notice, for example, that the "ONE" hole is much larger than the smaller holes on the other faces. Some dice just have the numbers imprinted on the faces and then you need to consider only the difference in the weight of the ink of the imprint. $\endgroup$ – Dilip Sarwate Feb 26 '17 at 14:10
  • $\begingroup$ Always remember that even with a symmetric die, you can always force a bias on the outcome by "clever" tossing (cheating, essentially). $\endgroup$ – Deep Feb 27 '17 at 14:12

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