US20190282890A1

US20190282890A1 - Gaming Die with Incongruent Sides and More Sides than Outcomes

Info

Publication number: US20190282890A1
Application number: US16/283,408
Authority: US
Inventors: James Kelly
Original assignee: Individual
Current assignee: Individual
Priority date: 2018-03-19
Filing date: 2019-02-22
Publication date: 2019-09-19

Abstract

This invention is a gaming die that use a combination of incongruent sides and a number of sides that is greater than the number of outcomes in order to produce practically fair results.

Description

BACKGROUND

The present disclosure is generally directed to gaming dice, and more particularly to a gaming die that use a combination of incongruent sides and a number of sides that is greater than the number of outcomes in order to produce practically fair results.
Dice have been created that have incongruent sides and are practically fair, such as the 400 year old juryeonggu die from Korea. This is a fourteen-sided, fourteen-outcome die used in a traditional drinking game. Additionally, there are a few examples of dice with incongruent sides in gaming, such as the Zocchi five-sided die described in U.S. Pat. No. 6,926,275.
Dice have also been created that have more sides than outcomes, such as the four-outcome (d4), eight-sided (octahedron) die, or the ten-outcome (d10) twenty-sided die. The eight-sided d4 is of particular note because it is designed for the purpose of being more aesthetically pleasing than the traditional tetrahedron d4.
It would be useful to have dice that were aesthetically pleasing and fair, as well as simple and cheap to manufacture.

SUMMARY

In one example of a die with incongruent sides and more sides than outcomes according to this invention, the die is a “truncated octahedron” having fourteen sides. An octahedron is used as the base shape, then the “points” are removed to create a shape with six square faces and six hexagonal faces. Outcomes are then assigned to the sides such that there are more sides than outcomes.
In another example of a die with incongruent sides and more sides than outcomes according to this invention, the die is a “chamfered cube” having eighteen sides. A cube is used as the base shape, then the intersections of edges are chamfered, or shaved down, to create a shape with six square faces and twelve hexagonal faces. Outcomes are then assigned to the sides such that there are more sides than outcomes.
These as well as other aspects, advantages, and alternatives, will become apparent to those of ordinary skill in the art by reading the following detailed description, with reference where appropriate to the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an isometric view of an example embodiment showing a truncated octahedron shape.

FIG. 2 is an isometric view of an example embodiment showing a truncated octahedron shape where the edge length of hexagonal sides differs from that of FIG. 1.

FIG. 3 is an isometric view of an example embodiment showing a chamfered cube shape.

FIG. 4 is an isometric view of an example embodiment showing a chamfered cube shape where the edge length of hexagonal sides differs from that of FIG. 3.

FIG. 5 is an orthogonal view of an example embodiment showing a truncated octahedron shape labeled with six outcomes.

FIG. 6 is an orthogonal view of an example embodiment showing a truncated octahedron shape labeled with four outcomes.

FIG. 7 is an orthogonal view of an example embodiment showing a truncated octahedron shape labeled with eight outcomes.

FIG. 8 is an orthogonal view of an example embodiment showing a truncated octahedron shape labeled with ten outcomes.

FIG. 9 is an orthogonal view of an example embodiment showing a chamfered cube shape labeled with twelve outcomes.

FIG. 10 is an orthogonal view of an example embodiment showing a chamfered cube shape labeled with ten outcomes.

FIG. 11 is an orthogonal view of an example embodiment showing a chamfered cube shape labeled with two outcomes.

DETAILED DESCRIPTION

In the particular embodiment illustrated in FIG. 1, hexacube die 50 includes a die body 100, square sides 110, and hexagonal sides 120. The die body 100 is composed of plastic or another suitable material that is substantially rigid and lightweight. Die body 100 can be shaped in its final form and manufactured through a 3-D printing, plastic molding, or other suitable process. Die body 100 can also be shaped in an intermediate base form, such as a cube or octahedron, and reduced into its final form by removing excess portions of material from the points.
Square sides 110 are substantially flat and substantially square shaped. The surface of square sides 110 can be imprinted with numbers, pips representative of numerical values, or other images as appropriate for the intended use of hexacube die 50.
Hexagonal sides 120 are substantially flat and substantially hexagon shaped. As illustrated in FIG. 1, hexagonal sides 120 are shaped as irregular hexagons. The surface of hexagonal sides 120 can be imprinted with numbers, pips representative of numerical values, or other images as appropriate for the intended use of hexacube die 50.
The term ‘incongruent sides’ refers to the fact that square sides 110 have different surface areas and/or shapes than hexagonal sides 120. Due to differences in surface area, shape, and edge length, square sides 110 have a different probability of landing face down (and thus the corresponding opposite side being face up) than hexagonal sides 120.
The term hexacube die′ as used in this document refers to a die that has both square and hexagonal sides. It should be noted that this invention does not contemplate only hexacube dice with square and hexagonal sides, as other shapes may be constructed according to the principles discussed, such as a chamfered octahedron which results in a die having twenty sides in the shape of triangles and hexagons.
To aid in determining fairness of a die, the hex to square ratio is calculated as the length of an edge that is shared by hexagonal sides 120 divided by the length of an edge of a square side 110. The Best Mode hexacube illustrated in FIG. 1 has a hex to square ratio of 0.4044. In the labeled hexacube illustrated in FIG. 5, half of the square sides 110 are assigned to an outcome of 1, half of the square sides 110 are assigned to an outcome of 6, and hexagonal sides 120 are distributed evenly among outcomes 2, 3, 4, and 5. For the Best Mode hexacube illustrated in FIGS. 1 and 5, empirical testing has shown the probability of any of square sides 110 landing face up on a given roll to be approximately 5.56%, while the probability of any of hexagonal sides 120 landing face up on a given roll is approximately 8.33%. The odds of any of outcomes 1-6 landing face up on any given roll is approximately 16.66%.
FIG. 2 illustrates a hexacube die 50 where the length of hexagonal sides 120 is set such that hexagonal sides 120 appear nearly as triangles.
The shape of the die illustrated in FIG. 3 is a chamfered cube 60. This can also be referred to as a tetratruncated rhombic dodecahedron, or (inaccurately) as a truncated rhombic dodecahedron. The base shape of this die is a cube, and the final shape as illustrated can be reached by removing material at the intersections of edges (a process known as chamfering in woodworking or related arts). As with hexacube 50, the sides of chamfered cube 60 in its final shape are hexagonal or square shaped. Chamfered cube 60 as illustrated in FIG. 3 has six square sides 110 and twelve hexagonal sides 120. The hex to square ratio of chamfered cube 60 illustrated in FIG. 3, as calculated by the formula described above, is 0.5738. Chamfered cube 60 can be used as an approximately fair twelve-sided die, or “d12”, by assigning each square side 110 a different outcome from 1-12, and then assigning each of the remaining outcomes to two hexagonal sides 120, as illustrated in FIG. 9.
FIG. 4 illustrates a chamfered cube 60 where the length of hexagonal sides 120 differs from that of the chamfered cube 60 illustrated in FIG. 3.
FIGS. 8 and 10 illustrate dice where the number of assigned outcomes totals ten. In many tabletop dice games, it is common to use a pair of “d10” or ten-outcome dice to generate a random number from 1-100 (a “percentile” roll), by assigning the result of one die to the “tens” digit of the final result and assigning the result of the second die to the “ones” digit (and treating two tens or zeroes as a result of 100). The dice illustrated in FIGS. 8 and 10 are each labeled with ten outcomes and are intended to be usable as a “d10” or “percentile” pair.
While various aspects and embodiments have been disclosed herein, other aspects and embodiments will be apparent to those skilled in the art. The various aspects and embodiments disclosed herein are for purposes of illustration and are not intended to be limiting, with the true scope and spirit being indicated by the following claims. Other embodiments may be utilized, and other changes may be made, without departing from the spirit or scope of the subject matter presented herein, for example, die body 100 can have a different shape, or a different number of outcomes may be assigned to the dice shapes previously described, such as the four outcomes for a hexacube die shown in FIG. 6, eight outcomes shown in FIG. 7, or ten outcomes shown in FIG. 8. Also, additional variations are contemplated such as the alternate labeling of ten outcomes for a chamfered cube die with eighteen sides shown in FIG. 10, or the two-outcome labeling for a chamfered cube die with eighteen sides shown in FIG. 11. It will be readily understood that the aspects of the present disclosure, as generally described herein and illustrated in the figures, can be arranged, substituted, combined, separated, and designed in a wide variety of different configurations, all of which are contemplated herein.

Claims

What is claimed is:

1. A gaming die comprising:

a die body;

a first side having a first outcome;

a second side having a second outcome;

a third side having a third outcome;

a fourth side having the first outcome;

where the shape of at least one of the first, second, or third sides is different from the shape of at least one of the first, second, or third sides.

2. The gaming die of claim one wherein the die body has the shape of a truncated tetrahedron.

3. The gaming die of claim two wherein the die body has the shape of a tetratruncated rhombic dodecahedron.