MATHEMATICAL MODEL OF AN UNBIASED AND RANDOM ARRANGEMENT OF ELEMENTS IN AN INHERENTLY BIASED DIE

摘要

Systems and methods are disclosed herein to a die comprising a plurality of faces (N); and a plurality of elements (n), including an unbiased set of elements and a biased set of elements, that are labeled on the plurality of faces, wherein each face is labeled with one of the plurality of elements, at least one element is labeled on more faces than the other elements, and all the faces are labeled in an unbiased manner such that the faces are labeled by placing an element from the unbiased set of elements after every (N−n)/n occurrences of an element from the set of biased elements, when a count (ci) of each unique element in the unbiased set is equal to 1.

主权项

1. A die comprising:
a plurality of faces (N); and a plurality of elements (n), including an unbiased set of elements and a biased set of elements, that are labeled on the plurality of faces, wherein each face is labeled with one of the plurality of elements, at least one element is labeled on more faces than the other elements, and all the faces are labeled in an unbiased manner such that the faces are labeled by placing an element from the unbiased set of elements after every (N−n)/n occurrences of an element from the set of biased elements, when a count (ci) of each unique element in the unbiased set is equal to 1.