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In role-playing games (and occasionally in other tabletop games), multiple shapes of dice are often used to generate random numbers in specific ranges. By convention, these are referred to as d''n'' according to their number of faces. A traditional six-faced die would be a d6, and many popular pen-and-paper role-playing games use dice ranging between d4 and d20. While there are larger dice used in tabletop games (most commonly d100), these are usually split into multiple smaller ones. For example, a d100 is often two d10s rolled together, with one die providing the first digit and the other die giving the second digit β the total number of possible combinations (100) is the product of the number of faces of the two dice (10 * 10). While "real" {{w|Zocchihedron|d100s}} and other large-numbered dice do exist, most people consider them to be impractical: they need to be either impractically large or have very small faces (resulting in small print for the numbers), they're close enough to being spheres that it's difficult to get them into a stable resting position, and even if they are stationary, determining which face is "on top" is difficult to do by eye. The Zocchihedron (d100) die is also difficult to ensure as unbiased because of geometry requiring dissimilar faces and therefore a different mixture of 'stopping factors' for each face it could land upon. The largest unbiased die is a [https://en.wikipedia.org/wiki/Disdyakis_triacontahedron d120] (excluding the bipyramids and trapezohedra, which can theoretically be made with arbitrarily many sides), so it is very likely that [[Cueball|Cueball's]] d65536 die is also biased. | In role-playing games (and occasionally in other tabletop games), multiple shapes of dice are often used to generate random numbers in specific ranges. By convention, these are referred to as d''n'' according to their number of faces. A traditional six-faced die would be a d6, and many popular pen-and-paper role-playing games use dice ranging between d4 and d20. While there are larger dice used in tabletop games (most commonly d100), these are usually split into multiple smaller ones. For example, a d100 is often two d10s rolled together, with one die providing the first digit and the other die giving the second digit β the total number of possible combinations (100) is the product of the number of faces of the two dice (10 * 10). While "real" {{w|Zocchihedron|d100s}} and other large-numbered dice do exist, most people consider them to be impractical: they need to be either impractically large or have very small faces (resulting in small print for the numbers), they're close enough to being spheres that it's difficult to get them into a stable resting position, and even if they are stationary, determining which face is "on top" is difficult to do by eye. The Zocchihedron (d100) die is also difficult to ensure as unbiased because of geometry requiring dissimilar faces and therefore a different mixture of 'stopping factors' for each face it could land upon. The largest unbiased die is a [https://en.wikipedia.org/wiki/Disdyakis_triacontahedron d120] (excluding the bipyramids and trapezohedra, which can theoretically be made with arbitrarily many sides), so it is very likely that [[Cueball|Cueball's]] d65536 die is also biased. | ||
| β | Here, Cueball has constructed a d65536 for generating random 16 bit numbers. It may have solved the problem of generating large random numbers with fewer die rolls, but it magnifies all of the problems with large-numbered dice to ludicrous extremes. In order for the faces to be readable, the die is ridiculously huge, dwarfing the human standing next to it. Rolling such a die is not only physically challenging, but it would also need a huge space in which to roll if the result is to be random, and that space would need to have an extremely flat and rigid surface in order for the die to come to rest. And even if those problems were solved, simply getting to a vantage point to see the top of the die would be a major challenge, and determining which number was truly on top would be near impossible to do by eye. If one really wished to use dice, it would be much easier to simply use multiple dice rolls. For instance, one could roll eight d4 dice (or use 16 coin flips), and convert the result into binary. This has the same randomness as a single die roll{{fact}}, but can take much longer, so people do purchase d16s to simplify it and speed it up. | + | Here, Cueball has constructed a d65536 for generating random 16 bit numbers. It may have solved the problem of generating large random numbers with fewer die rolls, but it magnifies all of the problems with large-numbered dice to ludicrous extremes. In order for the faces to be readable, the die is ridiculously huge, dwarfing the human standing next to it. Rolling such a die is not only physically challenging, but it would also need a huge space in which to roll if the result is to be random, and that space would need to have an extremely flat and rigid surface in order for the die to come to rest. And even if those problems were solved, simply getting to a vantage point to see the top of the die would be a major challenge, and determining which number was truly on top would be near impossible to do by eye. If one really wished to use dice, it would be much easier to simply use multiple dice rolls. For instance, one could roll eight d4 dice (or use 16 coin flips), and convert the result into binary. This has the same randomness as a single die roll{{fact}}?, but can take much longer, so people do purchase d16s to simplify it and speed it up. |
The closest regular shape similar to the depicted in the comic could be a {{w|Goldberg polyhedron}}. However, no such polyhedron exists with exactly 65536 hexagonal faces. The closest Goldberg Polyhedron has a mixture of 65520 hexagons and 12 pentagons, totaling 65532 faces. It is possible to construct a fair die without a matching regular shape by limiting the sides which it could land on and designing those sides to be fair (for instance, a prism with rectangular facets that extend its entire length, and rounded ends to ensure it doesn't balance on end). | The closest regular shape similar to the depicted in the comic could be a {{w|Goldberg polyhedron}}. However, no such polyhedron exists with exactly 65536 hexagonal faces. The closest Goldberg Polyhedron has a mixture of 65520 hexagons and 12 pentagons, totaling 65532 faces. It is possible to construct a fair die without a matching regular shape by limiting the sides which it could land on and designing those sides to be fair (for instance, a prism with rectangular facets that extend its entire length, and rounded ends to ensure it doesn't balance on end). | ||
