DICE WITH CURVED, BUT NON-SPHERICAL SURFACES, CERTAIN OF WHICH FEATURE NONUNIFORM DISPLAY PROBABILITIES
The current document is directed to gaming dice, including physical dice and virtual dice represented on an electronic display or viewing screen. Certain of the currently disclosed gaming dice have approximately ovoid, prolate spheroid, or ellipsoid shapes that are modified to include planar surfaces. Other of the disclosed gaming dice have angular shapes, including cubes, tetrahedrons, octahedrons, and other regular shapes that are modified to provide nonuniform probabilities of position landings.
This application claims the benefit of Provisional Application No. 62/388,414, filed Jan. 30, 2016.
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TECHNICAL FIELDThe present invention relates to the fields of entertainment and gaming and, in particular, to multifaceted dice that, after thrown or rolled, land on at least two different planar surfaces with two different probabilities.
BACKGROUNDMultifaceted dice with indices on at least one surface have been used for games and gambling for thousands of years. The shape most familiar is a cube with the faces having indices on the surfaces such as numbering with the numerals 1 through 6 or with dots representing those numbers. The dice faces have also been decorated with special marks or indicia which distinguish the different surfaces of the die, including images, colors, and various icons, shapes and symbols. In more recent years, non-cubic dice with numbered or specially marked faces have found favor with people interested in role playing games where expanded probabilities are desirable. Platonic solids having 4 to 20 regular faces of triangles, squares and pentagons are commonly used in these games. Such types of dice typically have planar faces of equal size and shape and the surfaces are generally provided with marks or indicia. Non-polyhedral shapes have been used also. For example, a spherical die has been developed. The spherical die has the numbers 1-6, or other markings, located equidistant from one another on spherical surface. To make the die land stably, the die is provided with a hollow interior formed in the shape of a regular octahedron, which has 6 equidistant vertices, and an internal metal ball bearing to assure that one of the rounded surfaces with a mark or number will face upward when the die comes to rest.
While most die are designed with sharp edges, it is possible to round the corners and edges, either by a manufacturing process or by tumbling the dice in an abrasive media following manufacture. Examples of the above-mentioned types of dice are illustrated in
The current document is directed to gaming dice, including physical dice and virtual dice represented on an electronic display or viewing screen. Certain of the currently disclosed gaming dice have approximately ovoid, prolate spheroid, or ellipsoid shapes that are modified to include planar surfaces. Other of the disclosed gaming dice have angular shapes, including cubes, tetrahedrons, octahedrons, and other regular shapes that are modified to provide nonuniform probabilities of position landings.
In this discussion, a landing position is the position of a die when it has come to rest, after being thrown or rolled. A die in a landing position is generally resting on a planar portion of the die's surface, referred to as the “landing surface,” with one marking or indicia on a complementary, generally opposite surface presented as the highest marking or indicia that represents a result of outcome of the throw or roll. In standard, hexahedral dice, the result or outcome is printed or inscribed on the top, horizontal surface opposite from the landing surface. However, in certain of the dice to which the current document is directed, markings or other indicia that represent the result or outcome may be printed on, or inscribed in, a curved surface or on a planar surface that is not horizontally oriented in the resting position of the dice. In general, however, the markings or indicia representing the result or outcome are located in a most prominent position when the dice are in resting position, so that the result or outcome is unambiguous.
There is a probability associated with each result or outcome. For a well-manufactured standard cubic die, the probability that any particular number of the numbers 1-6 results from a roll is 1/6. The probability of a particular result is the probability of the die coming to rest in a stable landing position on the opposite, complementary face or planar surface, so that the markings or indicia representing the result or outcome are visible in a most prominent location, generally the highest position with respect to the surface on which the die rests. For a Platonic solid with n faces, in which the faces have identical shapes and sizes, and in which the same number of faces include each vertex point, the probability that die lands on a particular face after being thrown or rolled is referred to as “the probability associated with the face” or “the probability of the face,” which is also the probability that the result of the throw or roll is the marking or indicia on the, opposite, complementary side. Similarly, in dice, discussed below, the probability that a die lands on a particular planar surface is referred to as “the probability associated with the surface” or “the probability of the surface,” which is also the probability that the result of the throw or roll is the marking or indicia in the opposite, complementary position, the most visually prominent position on the resting die.
In certain of the implementations, discussed below, a die has a die body with a non-spherical, curved surface and two or more planar landing surfaces. In these implementations, a result indication is associated with each planar landing surface, each result indication prominently displayed when the die rests in a stable position on the planar landing surface with which the result indication is associated. In certain of the implementations, discussed below, the non-spherical, curved surface of the die body comprises a portion of the surface of one of an ovoid-shaped solid, a prolate-spheroid-shaped solid, and an ellipsoid-shaped solid. In certain of the implementations, the result indication associated with a planar landing surface is located at a position at the intersection of the surface of the die body and a line normal to the planar landing surface that passes through the center of the planar landing surface and continues through the die body to the position of the result indication. In certain of the implementations, discussed below, each result indication comprises a numeral, marking, or indicia that is inscribed in, molded onto, printed on, painted on, and/or affixed to the surface of the die in a neighborhood surface about the result-indication position. In certain of the implementations, discussed below, the landing surfaces are symmetrically disposed about a rotation symmetry axis of a solid, with which the curved surface of the die body is coincident. In certain of the implementations, discussed below, the landing surfaces have a common shape and size and are associated with equal landing-surface probabilities. In certain of the implementations, discussed below, a first set of two or more of the landing surfaces are symmetrically disposed about a rotation symmetry axis of a solid, with which the curved surface of the die body is coincident and a second set of two of the landing surfaces are normal to the rotation symmetry axis of the a solid, with which the curved surface of the die body is coincident. In certain of the implementations, discussed below, the landing surfaces include a first set of two or more landing surfaces that have a common first shape and first size and are associated with equal first landing-surface probabilities and a second set of two or more landing surfaces that have a common second shape and second size and are associated with equal second landing-surface probabilities that differ from the first landing-surface probabilities.
One of the smaller two surfaces 605, shown in
In rolling experiments with prototype die, it was observed that die of the approximate shape illustrated in
The used of truncated tetrahedron is instructional only. It will be obvious to the mindful observer than the modification of other polyhedrons can result in similar variations, including a cube where in reducing on of the 3 equal widths of the die, rendering it a rectangular solid, will change the odds of it landing on any surface.
While various embodiments have been described above, it should be understood that they have been presented by way of example only, and that the breadth and scope of the invention should not be limited by any of the above described exemplary embodiments. As one example, the sizes, dimensions, and angles between the surfaces and faces of the described die may be altered and modified to render different probabilities to the surfaces and shapes. Ellipsoids with different ratios between major and minor axes of symmetry may be employed. Any suitable material can be used to form the die. However, plastics which can be molded by injection, compression or casting are easiest for production. To design and form a gaming die based on an ellipsoid, the basic shape is provided with at least one planar surface (i.e., a circular solid segment of the ellipsoid removed) either on one of its tapered ends or along its length. The planar surface (nominally round in shape when viewed perpendicular to the surface) provides a stable landing position for the die in order for the user to determine more exactly the resulting object, mark or indicia at the end of a roll of die of the base shape.
The planar surfaces may be machined or otherwise formed following casting or molding of the die or may be molded or otherwise formed during manufacture. For example, the ellipsoid shape could be employed without having any planar surface but instead having a construction similar to that described earlier for the round gaming die, including a hollow core and ball bearing which assures the die lands in a definitive position. For example, if the desired response is 1, 2, 3, the interior can be shaped as a triangular pyramid assuring the ball bearing drops into one the vertices. If the desired response is 1,2,3,4 the interior can be shapes as a square based pyramid or, in the case of 1 through 5, the interior can be shaped as a hexagonal pyramid. This specification should be read and considered in accordance with the following claims and their equivalents. The specification and drawings are, accordingly, to be regarded in an illustrative for teaching the concept rather than a restrictive sense.
Claims
1. A die comprising:
- a die body with a non-spherical, curved surface and two or more planar landing surfaces; and
- a result indication associated with each planar landing surface, each result indication prominently displayed when the die rests in a stable position on the planar landing surface with which the result indication is associated.
2. The die of claim 1 wherein the non-spherical, curved surface of the die body comprises a portion of the surface of one of:
- an ovoid-shaped solid;
- a prolate-spheroid-shaped solid; and
- an ellipsoid-shaped solid.
3. The die of claim 1 wherein the result indication associated with a planar landing surface is located at a position at the intersection of the surface of the die body and a line normal to the planar landing surface that passes through the center of the planar landing surface and continues through the die body to the position of the result indication.
4. The die of claim 1 wherein each result indication comprises a numeral, marking, or indicia that is inscribed in, molded onto, printed on, painted on, and/or affixed to the surface of the die in a neighborhood surface about the result-indication position.
5. The die of claim 1 wherein the landing surfaces are symmetrically disposed about a rotation symmetry axis of a solid, with which the curved surface of the die body is coincident.
6. The die of claim 5 wherein the landing surfaces have a common shape and size and are associated with equal landing-surface probabilities.
7. The die of claim 5 including a number landing surfaces equal to one of:
- 2;
- 3;
- 4;
- 5; and
- 6.
8. The die of claim 1
- wherein a first set of two or more of the landing surfaces are symmetrically disposed about a rotation symmetry axis of a solid, with which the curved surface of the die body is coincident; and
- wherein a second set of two of the landing surfaces are normal to the rotation symmetry axis of the a solid, with which the curved surface of the die body is coincident.
9. The die of claim 8 wherein the landing surfaces include:
- a first set of two or more landing surfaces that have a common first shape and first size and are associated with equal first landing-surface probabilities; and
- a second set of two or more landing surfaces that have a common second shape and second size and are associated with equal second landing-surface probabilities that differ from the first landing-surface probabilities.
10. The die of claim 8
- wherein the second set of landing surfaces includes 2 landing surfaces; and
- wherein the first set of landing surfaces includes a number landing surfaces equal to one of:
- 2;
- 3;
- 4;
- 5; and
- 6.
10. A die comprising:
- a polyhedral die body two or more planar landing faces of a first common size and shape and two or more additional planar landing surfaces of a second, common size and shape; and
- a result indication associated with each planar landing surface and planar landing face, each result indication prominently displayed when the die rests in a stable position on the planar landing surface with which the result indication is associated.
11. The die of claim 10 wherein the two or more planar landing faces correspond to faces of one of a tetrahedron, cube, octahedron, dodecahedron, and icosahedron.
12. The die of claim 1 wherein the result indication associated with a planar landing face is located on an opposite, complementary planar landing face.
13. The die of claim 1 wherein the result indication associated with a planar landing surface is located on an opposite, complementary planar landing surface.
14. A virtual die that is displayed on a display device, the virtual die comprising:
- a die body with a non-spherical, curved surface and two or more planar landing surfaces; and
- a result indication associated with each planar landing surface, each result indication prominently displayed when the die rests in a stable position on the planar landing surface with which the result indication is associated.
15. The virtual die of claim 14 wherein the non-spherical, curved surface of the die body comprises a portion of the surface of one of:
- an ovoid-shaped solid;
- a prolate-spheroid-shaped solid; and
- an ellipsoid-shaped solid.
16. The virtual die of claim 14 wherein the result indication associated with a planar landing surface is located at a position at the intersection of the surface of the die body and a line normal to the planar landing surface that passes through the center of the planar landing surface and continues through the die body to the position of the result indication.
17. The virtual die of claim 14 wherein the landing surfaces are symmetrically disposed about a rotation symmetry axis of a solid, with which the curved surface of the die body is coincident.
18. The virtual die of claim 17
- wherein the landing surfaces have a common shape and size and are associated with equal landing-surface probabilities; and
- wherein the virtual die includes a number landing surfaces equal to one of:
- 2;
- 3;
- 4;
- 5; and
- 6.
19. The virtual die of claim 14
- wherein a first set of two or more of the landing surfaces are symmetrically disposed about a rotation symmetry axis of a solid, with which the curved surface of the die body is coincident; and
- wherein a second set of two of the landing surfaces are normal to the rotation symmetry axis of the a solid, with which the curved surface of the die body is coincident.
20. The virtual die of claim 8
- wherein the landing surfaces include a first set of two or more landing surfaces that have a common first shape and first size and are associated with equal first landing-surface probabilities; and a second set of two or more landing surfaces that have a common second shape and second size and are associated with equal second landing-surface probabilities that differ from the first landing-surface probabilities;
- wherein the second set of landing surfaces includes 2 landing surfaces; and
- wherein the first set of landing surfaces includes a number landing surfaces equal to one of:
- 2;
- 3;
- 4;
- 5; and
- 6.
Type: Application
Filed: Jan 30, 2017
Publication Date: Nov 23, 2017
Inventor: Joseph Charles Fjelstad (North Bend, WA)
Application Number: 15/419,927