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 stronger property that, for each die in the set, there is another die that rolls a higher number than it more than half the time. Now, consider the following game, which is played with a set of dice. If this game is played with a transitive set of dice, it is either fair or biased in favor of the first player, because the first player can always find a die that will not be beaten by any other dice more than half the time. If it is played with the set of dice described above, however, the game is biased