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 of . Efron's dice are a set of four nontransitive dice invented by Bradley Efron. The four dice A, B, C, D have the following numbers on their six faces: Each die is beaten by the previous die in the list, with a probability of : B's value is constant; A beats it on rolls because four of its six faces are higher. Similarly, B beats C with a probability because only two of C's faces are higher. P(C>D) can be calculated by summing conditional probabilities for two events: The total probability of win for C is therefore With a