Dice hand; they are thus a crude form of hardware random number generator. Perhaps to mitigate concerns that the pips on the faces of certain styles of dice cause a small bias, casinos use precision dice with flush markings. Common dice are small cubes most commonly across, whose faces are numbered from one to six, usually by patterns of round dots called pips. (While the use of Arabic numerals is occasionally seen, such dice are less common.) Opposite sides of a modern die traditionally add up to seven, implying that the 1, 2 and 3 faces share a vertex. The faces
Nontransitive dice B", A wins in 9 out of 16 cases. In "B versus C", B wins in 9 out of 16 cases. In "C versus A", C wins in 9 out of 16 cases. P(A > B) = P(B > C) = , P(C > A) = 9/16 In analogy to the nontransitive six-sided dice, there are also dodecahedra which serve as nontransitive twelve-sided dice. The points on each of the dice result in the sum of 114. There are no repetitive numbers on each of the dodecahedra. Miwin’s dodecahedra (set 1) win cyclically against each other in a ratio of