bigjeff5 comments on Probability is in the Mind - Less Wrong
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Case in point:
There are dice designed with very sharp corners in order to improve their randomness.
If randomness were an inherent property of dice, simply refining the shape shouldn't change the randomness, they are still plain balanced dice, after all.
But when you think of a "random" throw of the dice as a combination of the position of the dice in the hand, the angle of the throw, the speed and angle of the dice as they hit the table, the relative friction between the dice and the table, and the sharpness of the corners as they tumble to a stop, you realize that if you have all the relevant information you can predict the roll of the dice with high certainty.
It's only because we don't have the relevant information that we say the probabilities are 1/6.