Probability Distribution of Rolls
A test published in White Dwarf magazine concluded that the frequency distribution of the Zocchihedron was substantially uneven. Jason Mills performed 5,164 rolls and found that results more than 93 or less than 8 are significantly rarer than middling results. Mills attributed this to the placement of the extreme numbers near the poles of the zocchihedron, where they are closer together. Numbers near the equator are more widely spaced.
Note: A statistical analysis conducted by Ph.D. students at the University of Melbourne found that 5164 rolls is inadequate to base statistical conclusions on. With such an insufficient sample, the statement that the die does not return fairly weighted results cannot be founded and should be regarded with skepticism. An evenly weighted die should demonstrate variance of up to 20-40% from the expected value when so few rolls are made, masking any physical error present. An adequate statistical sample would require a minimum of 100,000 rolls in order to drop statistical variance below 5%. In conclusion, the performance of the die cannot be determined to be poor until a more comprehensive sample is developed.
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