While the terms ace, deuce, trey, cater, cinque and sice are generally obsolete, with the names of the numbers preferred, they are still used by some professional gamblers to designate different sides of the dice. Ace is from the Latin as, meaning "a unit"; [23] the others are 2 to 6 in Old French. [24] Many board games use dice to randomize how far pieces move or to settle conflicts. Typically, this has meant that rolling higher numbers is better. Some games, such as Axis & Allies, have inverted this system by making the lower values more potent. In the modern age, [ when?] a few games and game designers have approached dice in a different way by making each side of the die similarly valuable. In Castles of Burgundy, players spend their dice to take actions based on the die's value. In this game, a six is not better than a one, or vice versa. In Quarriors (and its descendant, Dicemasters), different sides of the dice can offer completely different abilities. Several sides often give resources while others grant the player useful actions. [36] This 12 sided dice template printable, has another name, it’s also known as the Dodecahedron. Each face of the dice is a regular pentagon.

Although the image shows some of the more common die shapes, there are many other polyhedral dice, or dice of other shapes. There are also non-numeric dice, dice that do not follow a counting sequence that begins at one, and spherical dice. How random is a dice? There are a number of companies that manufacture dice, and some more rigorous tests (than the one described above) have been performed on dice manufactured by different companies in an effort to determine how truly random the dice (mostly d20 dice) are. These studies confirmed that even dice manufactured within the same company under the same conditions could vary significantly from each other, and are not truly random. Some companies produced dice that were more random than others, but even then, they were not found to be truly random.

Phi and 3-dimensional geometry

If you have played Tetris then you will know that there are 5 shapes of 4 square tiles ( tetrominoes) as shown here. H S M Coxeter's Regular Polytopes, (Third Ed) 1973, Dover, is a very popular book at an amazingly low price - well worth getting! An Icosahedron in an Octahedron Using the same three golden rectangles at right-angles to each other, we can also make an octahedron. Uniform fair dice" are dice where all faces have equal probability of outcome due to the symmetry of the die as it is face-transitive. In addition to the Platonic solids, these theoretically include:

Guthrie, Kenneth (1988). The Pythagorean sourcebook and library: an anthology of ancient writings which relate to Pythagoras and Pythagorean philosophy. Grand Rapids, MI: Phanes Press. ISBN 978-0-933999-50-3. OCLC 255212063. Each of the 5 cubes has 12 edges, totalling 60 in the dodecahedron and so each of the 12 faces of the dodecahedron will have 5 of the edges in it. In fact, 5 distinct cubes can be fitted into the dodecahedron, with the verticesof the cubes meeting at the vertices of the dodecahedron as shown in the pictures below. The two solids are similar to a cube but the faces are golden rhombs. The first shape is made by attaching three golden rhombs at their shorter angles in the same way as three squares meet at a corner of a cube. A duplicate is made and the two fit together to make a six-sided shape like a slanted cube. This is called a prolate rhombohedron.It includes all our 5 Platonic solids, and,since it also includes those where not every edge is the same length, it includes the bi-pyramids too. Every face is identical toevery other face, so all the faces have exactly the same polygonal shape, but some edges have different lengths to others. There are others apart fromthe Platonic solids and the bi-pyramids and are some pretty weird too! The probability of rolling all the values equal to or lower than y – this option is almost the same as the previous one, but this time we are interested only in numbers that are equal to or lower than our target. If we take identical conditions ( s=6, y=3) and apply them in this example, we can see that the values 1, 2, & 3 satisfy the rules, and the probability is: P = (3 · 1/6) n = (1/2) n. When we think of a die, a small cubic object comes to mind which, when dropped on a flat surface, shows one of its possible faces. A traditional die has six faces, and on each of its faces, numbers from 1 to 6. Rolling the die implies that chance will show a whole number from one to six, and that the odds of each of those numbers coming up are the same, due to the geometric shape, as long as the die is perfect.