U.S. patent application number 15/419927 was filed with the patent office on 2017-11-23 for dice with curved, but non-spherical surfaces, certain of which feature nonuniform display probabilities.
The applicant listed for this patent is Joseph Charles Fjelstad. Invention is credited to Joseph Charles Fjelstad.
Application Number | 20170333782 15/419927 |
Document ID | / |
Family ID | 60329829 |
Filed Date | 2017-11-23 |
United States Patent
Application |
20170333782 |
Kind Code |
A1 |
Fjelstad; Joseph Charles |
November 23, 2017 |
DICE WITH CURVED, BUT NON-SPHERICAL SURFACES, CERTAIN OF WHICH
FEATURE NONUNIFORM DISPLAY PROBABILITIES
Abstract
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.
Inventors: |
Fjelstad; Joseph Charles;
(North Bend, WA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Fjelstad; Joseph Charles |
North Bend |
WA |
US |
|
|
Family ID: |
60329829 |
Appl. No.: |
15/419927 |
Filed: |
January 30, 2017 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
62388414 |
Jan 30, 2016 |
|
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|
Current U.S.
Class: |
1/1 |
Current CPC
Class: |
A63F 2009/0446 20130101;
A63F 2009/0431 20130101; A63F 2007/4012 20130101; A63F 9/0415
20130101; A63F 2009/0437 20130101; A63F 2250/063 20130101; A63F
2009/0422 20130101; A63F 9/0468 20130101 |
International
Class: |
A63F 9/04 20060101
A63F009/04 |
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.
Description
CROSS-REFERENCE TO RELATED APPLICATION
[0001] This application claims the benefit of Provisional
Application No. 62/388,414, filed Jan. 30, 2016.
COPYRIGHT NOTICE AND PERMISSION
[0002] This document contains some material which is subject to
copyright protection. The copyright owner has no objection to the
reproduction with proper attribution of authorship and ownership
and without alteration by anyone of this material as it appears in
the files or records of the Patent and Trademark Office, but
otherwise reserves all rights whatsoever.
TECHNICAL FIELD
[0003] The 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.
BACKGROUND
[0004] Multifaceted 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.
[0005] 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
FIG. 1. While not known to be normally used as gaming dice,
Archimedean solids, which are generally derived from Platonic
solids but have different shapes on their surfaces, such as, for
example, more than one type of regular triangle, square or polygon
surface, can also be used for gaming and entertainment. However,
because of their greater complexity and their lower predictability
in terms of results, solid Archimedean polygons are unlikely to be
useful in most gaming applications, but may find use in gaming
applications where nonuniform probabilities among the possible
landing or resting positions of an Archimedean-polygon die are
acceptable or desirable. Examples of solid Archimedean polygons are
shown in FIG. 2
BRIEF SUMMARY
[0006] 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.
BRIEF DESCRIPTION OF THE DRAWINGS
[0007] FIGS. 1A-G provide examples of currently available gaming
dice.
[0008] FIG. 2A-M provides examples of Archimedean-polygon dice.
[0009] FIGS. 3A-C show a die with 3 primary and equally probable
landing surfaces.
[0010] FIGS. 4A-C show a die with 4 primary and equally probable
landing surfaces.
[0011] FIGS. 5A-C show a die with 5 primary and equally probable
landing surfaces.
[0012] FIGS. 6A-E show a die with 3 primary and equally probable
landing surfaces and 2 additional surfaces having at least one
lower probability.
[0013] FIGS. 7A-E show a die with 4 primary and equally probable
landing surfaces and 2 additional surfaces having at least one
lower probability.
[0014] FIGS. 8A-E shows a die with 5 primary and equally probable
landing surfaces and 2 additional surfaces having at least one
lower probability.
[0015] FIGS. 9A-B shows a polyhedron die with 4 primary and equally
probable landing surfaces and 4 additional surfaces having at least
one lower probability.
DETAILED DESCRIPTION
[0016] FIGS. 1A-G provide examples of currently available gaming
dice and shapes of dice. FIG. 1A shows a tetrahedral die shape
having four sides. FIG. 1B shows a hexahedral, or cubic, die shape
having six sides. FIG. 1C shows an octahedral die shape having
eight sides. FIG. 1D shows a dodecahedral die shape having 12
sides. FIG. 1E shows an icosahedral die shape having 20 sides. The
shapes shown in FIGS. 1A-E are referred to as the "Platonic
solids." FIG. 1F shows an example of a round die having six
numbered locations on the surface, the six locations corresponding
to the 6 vertices of an octahedral cavity in the interior of the
sphere. A weight, such as a ball bearing, provides a mechanism for
holding the die in a stable position when the die comes to rest
after being rolled or thrown. FIG. 1G shows another example of a
die with rounded edges and corners.
[0017] FIG. 2A-M provides examples of Archimedean-polygon dice. As
discussed above, these types of dice may be used in applications in
which is it desirable for two or more landing positions of the die
associated with different probabilities are desired.
[0018] 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.
[0019] 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.
[0020] 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.
[0021] FIGS. 3A-C show a die with 3 primary and equally probable
landing surfaces. FIG. 3A provides a side view of an
ellipsoid-based gaming die 300 with three identically sized and
shaped planar surfaces 301 designed to provide three different but
equally possible outcomes indicated by a numeral, markings, or
other indicia 302 on the curved surfaces opposite the planar
surfaces, such as the curved surface 303 opposite the planar
surface 301'. The elongation of the die along the axis of symmetry
of the ellipsoid and the resulting slightly pointed ends helps
better ensure that die comes to rest on one of the planar surfaces,
just as it is very difficult to balance an egg or football on end
without support.
[0022] FIG. 3B provides a perspective view of the die 300 in a
landed position. FIG. 3C provides an end view of the die with one
of the three planar surfaces 301' in a landed position.
[0023] FIGS. 4A-C show a die with 4 primary and equally probable
landing surfaces. FIG. 4A provides a side view of an
ellipsoid-based gaming die 400 with four identically shaped and
sized planar surfaces 401 and 401' designed to provide four
different but equally possible outcomes. Each planar surface
includes numbers, markings, or indicia 402. The elongation of the
die and the resulting slightly pointed ends, such as end 403, helps
to better ensure that die comes to rest on one of the four planar
surfaces. As stated earlier, it is very difficult to balance an egg
or football on end without support.
[0024] FIG. 4B provides a perspective view of the die 400 in a
landed position and FIG. 4C provides and end view of the gaming die
400 with one of the four planar surfaces 401' in a landed position.
The four planar surfaces are visible, on end. One of the most
curved, or pointed, surfaces is pointing upward, out of the plane
of the page. Ellipsoid surfaces 404 connect the planar surfaces
where, on a cubic die, the planar surfaces would meet at angles of
90.degree..
[0025] FIGS. 5A-C show a die with 5 primary and equally probable
landing surfaces. FIG. 5A provides a side view of an
ellipsoid-based gaming die 500 with five identically shaped and
sized planar surfaces 501 designed to provide five different but
equally possible outcomes. An outcome is indicated by the number,
marking, or other indicia 502 on the curved side 503 of the
ellipsoid and opposite the planar surface 501' shown in a landing
position. The elongation of the die and the resulting slightly
pointed end helps to better ensure that die comes to rest on one of
the five planar surfaces.
[0026] FIG. 5B provides a perspective view of the die 500 in a
landed position. FIG. 5C provides an end view of the ellipsoid
gaming die 500.
[0027] FIGS. 6A-E show a die with 3 primary and equally probable
landing surfaces and 2 additional surfaces having at least one
lower probability. FIG. 6A provides a top view of an
ellipsoid-based gaming die 600 having planar surfaces 602 with a
roll-result indicium 603 facing upward. In FIG. 6A, the indicium
comprises two dots representing the number 2. FIG. 6A also shows
that the ends of die 600 have been truncated to generate two
additional planar surfaces, including planar surface 604, at the
pointed ends of the ellipsoid. These additional planar surfaces are
also landing surfaces, but the additional two landing surfaces are
associated with smaller probabilities than those associated with
the three larger planar surfaces 602. The remnant taper 601 near
these two additional surfaces is more highly curved than the
main-body curved surfaces of the die, which, combined with the
smaller areas of these two additional planar surfaces in comparison
to the three larger planar surfaces 602, reduce the probability of
the die landing on one of these two additional surfaces. In rolling
experiments with prototype die, it was observed that die of the
approximate shape illustrated in FIG. 6A land on one of the larger
three surfaces 90% of the time with approximately equal
probability. The die lands on one of the smaller two planar
surfaces approximately 10% of the time.
[0028] FIG. 6B provides an end view of die 600 and the three larger
planar surfaces 602 and 602' designed to provide three different
but equally probably outcomes. Surface 602' is the landing surface,
in this illustration. Numbers, dots, markings, or other indicia 603
are provided on the curved surface 604 opposite the three planar
surfaces.
[0029] One of the smaller two surfaces 605, shown in FIG. 6B,
includes an additional indicium or indicia which indicates an
outcome when the die comes to rest on the opposite, complementary
smaller surface.
[0030] FIG. 6C provides a perspective view of the die 600 in a
landed position. FIG. 6D provides a view of the gaming die 600
having landed on one of its smaller end surfaces 605. The diameters
of the ends are shown as both being equal and having the value D1.
In contrast, FIG. 6E show a derivative die 607, also landed on one
of the end surfaces 605", in which the two end surfaces 605 and
605" have two different diameters D1 and D2, respectively. This
results in die 607 having three equally probable primary landing
positions and two different landing positions of unequal
probabilities both smaller than those of the primary landing
positions.
[0031] FIGS. 7A-E show a die with 4 primary and equally probable
landing surfaces and 2 additional surfaces having at least one
lower probability. FIG. 7A provides a top or side view of an
ellipsoid-based gaming die 700 having four larger planar surfaces
702. FIG. 7A also shows that the ends of die 700 have been
truncated to form smaller planar surfaces on the ends 704 that
together comprise two additional landing positions. The remnant
taper 701 on the ends is more highly curved than the main-body
curved surfaces. This greater curvature, combined with the smaller
areas of the two additional surfaces, combine to reduce the
probability of the die landing on one of these two additional
surfaces. Numbers, markings, or other Indicia 703 are provided on
the planar surfaces 702.
[0032] In rolling experiments with prototype die, it was observed
that die of the approximate shape illustrated in FIG. 7A landed on
one of the four larger surfaces approximately 90% of the time with
approximately equal probabilities. The die landed on one of the two
smaller, additional surface approximately 10% of the time.
[0033] FIG. 7B provides an end view of die 700 and the four
identically shaped and sized planar surfaces 702 designed to
provide four different but equally possible outcomes. The die 700
in FIG. 7B is shown with an additional indicium or indicia on one
of the smaller two surfaces.
[0034] FIG. 7C provides a perspective view of the die 700 in a high
probability landed position and FIG. 7D provides a view of the
gaming die 700 having landed in one of two lower but equal
probability surfaces. The diameters of the end surfaces are shown
as both being equal and both having the diameter D1. In contrast,
FIG. 7E shows a derivative die 706 with end surfaces having two
different diameters D1 and D2 end surfaces 704 and 704'. This
results in die 707 having four equally probable primary landing
positions and two different additional landing positions of lower
and unequal probability.
[0035] FIGS. 8A-E shows a die with 5 primary and equally probable
landing surfaces and 2 additional surfaces having at least one
lower probability. FIG. 8A provides a top view of an
ellipsoid-based gaming die 800 having five planar surfaces 803
(only three planar surfaces are evident in this view) with a
number, marking, or other indicia 801 indicating a roll result
placed or inscribed on curved surface 801. FIG. 8A also shows that
the ends of die 800 have been truncated to generate end planar
surfaces 805 that comprise two additional landing positions. The
remnant taper 801 on the ends is more highly curved than that on
the main-body surface of the die. The greater curvature and smaller
surface area of the end surfaces combine to reduce the probability
of the die landing on one of these two additional surfaces. In
rolling experiments with prototype die, it was observed that die of
the approximate shape illustrated in FIG. 8A land on one of the
larger, five planar surfaces approximately 90% of the time with
approximately equal probability. The die landed on one of the two
end surfaces approximately 10% of the time.
[0036] FIG. 8B provides an end view of die 800 and the five
identically sized and shaped planar surfaces 803 designed to
provide five different but equally probable outcomes. Indicia 804
are provided on the curved surfaces 801. The die 800 is shown with
ends truncated to generate two additional planar end surfaces 805
which may include additional indicia, such as indicium 806. FIG. 8C
provides a perspective view of the die 800 in a higher probability
landed position.
[0037] FIG. 8D provides a view of the gaming die 800 having landed
on one of its end surfaces 805. The diameters of the ends are both
D1. In contrast, FIG. 8E show a derivative die with end surfaces
805' and 805'' having two different diameters D.sup.x and D.sup.y,
respectively
[0038] FIG. 8B provides an end view of die 800 and the five
identically shaped and sized planar surfaces 803 designed to
provide three different but equally possible outcomes. A number,
marking, or other indicia on the curved side of the die 801
opposite the face down planar surface 802' indicates the outcome in
the illustrate orientation. The die 800 is shown with truncated
ends that generate two additional planar end surfaces 805
associated with smaller probabilities. They may also include
numbers, markings, or other indicia. FIG. 8C provides a perspective
view of the die 800 in a higher probability landed position.
[0039] FIG. 8D provides a view of the gaming die 800 having landed
on one of its end surfaces 805. The diameters of the ends are shown
as both D1. In contrast, FIG. 6E shows a derivative die 806
similarly oriented but with end surfaces 605 and 605 having two
different values D1 and D2. This results in die 806 having five
equally probable primary landing positions and two different
landing positions with lower and unequal probabilities.
[0040] FIGS. 9A-B shows a polyhedron die with 4 primary and equally
probable landing surfaces and 4 additional surfaces having at least
one lower probability. FIG. 9A provides a perspective view of a
polyhedron, 900, more specifically a truncated tetrahedron, having
eight faces that include four faces having equilateral-triangular
shapes 902a and 902b (the other two faces are not shown in FIG. 9A)
and four faces having equilateral-hexagonal shapes 903a and 903b.
The die 900 has two types of stable landing positions, landing
either on one of the hexagonal faces, as shown, or alternatively
landing on one of the smaller triangular faces. In empirical
studies of the die, it was determined that the die lands on one of
the smaller triangular faces approximately 4% of the time and on
one of the larger hexagonal faces approximately 96% of the time,
two different types of outcomes with different probabilities for
the same die.
[0041] FIG. 9B provides a perspective view of a polyhedral die. The
polyhedral 901 die is again a truncated tetrahedron, having eight
faces that include four faces having equilateral triangular shapes
904a and 904b and four faces having hexagonal shapes 905a and 905b.
A difference between die 901 and die 900 is that one of the
triangular faces, 904a, is larger than the other three triangular
faces. In addition, only one of the hexagonal faces is equilateral,
shown in FIG. 9B as the landing surface. The other three hexagonal
faces are irregular hexagons. As with die 900, die 901 has more
than one probable stable landing positions, landing on the regular
hexagonal base as shown or alternatively landing on any one of the
other three irregular hexagonal faces. Die 901 can also land on any
one of the equilateral triangular faces, however, a logical
observer would conclude that the larger area triangle surface would
be landed on with greatest frequency.
[0042] 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.
[0043] 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.
[0044] 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.
* * * * *