# 2626: d65536

d65536 |

Title text: They're robust against quantum attacks because it's hard to make a quantum system that large. |

## Explanation[edit]

In binary computing, 16 bit unsigned numbers range from 0 to 65535, for a total of 65536 unique numbers, a number which is hence well-known to software engineers. Generating large numbers in a manner that is truly random is a recurring problem in cryptography, required to send private messages to another party. People today still use dierolls to generate private random numbers.

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 — the total number of possible combinations (100) is the product of the number of faces of the two dice (10 * 10). While "real" 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 d120 (excluding the bipyramids and trapezohedra, which can theoretically be made with arbitrarily many sides), so it is very likely that Cueball's d65536 die is also biased.

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^{[citation needed]}, 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 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 title text references how cryptographic systems (especially RSA and other factoring-is-hard based systems) are vulnerable to quantum attacks as quantum computing technology develops. The title text is essentially punning on the idea of a "large" quantum system. "Large" in the quantum computing sense would be on the order of 64 qubits each of which would be an atom or two at most. This would still be microscopic and will never be as large as the giant die the comic is centered on; but for a well-observed environment and human rolling without sufficient entropy (consider somebody obsessed with a certain number dropping the die on something soft), a conventional computer could predict some rolls. See also 538 for non-mathematical paths of cryptography.

Since 65536 is 2^16, if for some reason you must simulate a D65536 using nothing but D&D dice, the most efficient method is to roll a D8 4 times and roll a D4 twice (2^(3×4) · 2^(2×2)), or roll a D8 5 times and toss a coin (2^(3×5) × 2).

## Transcript[edit]

- [A large sphere with a several lines, and in some places grids, are shown. Cueball, standing next to it, is dwarfed by its size, as it is at least seven times as tall as he is. The sphere has many lines following various great circles or parallel lesser circles around the curve of the sphere, and some patches of cross hatching to suggest further texturing along these lines hovering just below the degree of most of the illustrative detailing. The lines and grids cover the sphere in three layers of parallel axes, angled sixty degrees from each other, implying a huge mesh of equilateral triangles or hexagons. In the top right part of the ball is a black circle. An arrow points to this circle, and the end of the arrow goes to a larger circle that partly obscures the rightmost part of the sphere. The circle shows a zoom in on the surface in the black circle on the sphere. The zoom shows a small portion of the sphere's surface, showing that the grid comes along because the sphere is divided into elongated hexagonal faces with numbers up to at least five-digits. Seven numbers can be fully seen, but there are nine other faces partly shown, five of these with part of their numbers visible, one of these clearly only have four digits. One of the empty faces must also have a number with only 1-3 digits, as no numbers are visible although a significant part of the face is visible.]

- [Here follows the numbers in the zoomed in part of the sphere, with "..." represents numbers being cut off. The numbers are read in lines left to right, even though the numbers are tilted from down towards the right, which could have suggested a different reading order.]
- 30827
- 16[bottom part of a cut-off line][small cut-off circle]
- ...38
- 11875
- 25444
- ...[top part of a cut-off line]5
- 12082
- 28525
- 3 [left part of a cut-off line]...
- 13359
- 13874
- [Two cut-off lines, likely the start of the number 2]...

- [Caption below the image:]
- The hardest part of securely generating random 16-bit numbers is rolling the d65536.

## Trivia[edit]

- If a real d65536 were constructed with each number having an equal area and each printed in 12 point font, the resulting die would be about 5 feet (1.5 meters) in diameter, which isn't several times the size of a person as the comic suggests, but is still large enough to be hilariously inconvenient. If it were made out of standard acrylic, and not hollow, it would weigh about 2 tons (1700kg).
- This die would have a 0.00001526 chance of rolling a natural one (or any other number).
- There are seven 16-bit numbers fully visible in the picture: 30827, 25444, 11875, 28525, 12082, 13874 and 13359. They conceal a message. If these numbers are split big-endian into two 8-bit ASCII characters each, the result is
`xkcd.com/2624/`

. For example, converting the first number 30,827 to hexadecimal (in which a four digit number covers exactly 65,536 different values) converts to a hex value of 786B. Splitting this into 78 and 6B, these are the hex ASCII codes for "x" and "k" respectively.

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# Discussion

I wonder: can we even make a fair polyhedron with 65536 faces? In Randal's illustration, the faces seem to be irregular hexagons. 172.70.130.105 21:37, 30 May 2022 (UTC)

- This is better than my question, which was simply if you could tile a sphere with these. 172.70.211.36 23:01, 30 May 2022 (UTC)
- Definitely possible, just create two identical right pyramids with a 32768-gon base and glue the bases together. Clam (talk) 23:53, 30 May 2022 (UTC)
- Would this design be fair? Consider a set of 256 lines of latitude overlapping another set, with the second set's polar axis at the equator of the first. Cut flat quadrangles between the intersection points of the lines of latitude. Doesn't use hexagons like the comic does though. 172.70.110.121 09:41, 31 May 2022 (UTC)
- Fairness is a given for pyramids (if that's what you're asking). As long as there's enough 'rolling energy' to get either of the pyramids 'facing up', any N-agon base to the pyramids should have enough indeterminate impetous to then finally roll around a bit to end up with any of those exposed faces on top.
- (Interesting to note that for odd-numbered N-agonal bases, like that in a D10, you need to offset the bases and instead of sticking to the triangular faces base-to-base you now have kite-shapes that interlock in a serration that is no longer strictly planar along the axis's perpendiculars.)
- That might need a selection of the pyramidal slope. A very wide pair of bases with very little tip-'elevation' (to fit tightly within an oblate spheroid) should transition very well between same-pyramid faces, like a bulgy button, but one with highly acute tip-angle (prolate, likewise) might find the dominant behaviour to be tip-to-tip tipping, more like a toggle-fastener. OTOH, for odd-numbered end-agons it would probably ratchett to subsequent sides as it tips back and forth so long as it has enough energy to it.
- If you're asking about lines of latitude intersecting, consider that near the poles of either latitudinal reference the division of the other reference-system is going to be spliced more irregularly and thus give varying degrees of stability to rest upon.
- (Also, do you have a latitudinal line that crosses
*both*pairs of poles, or are you deliberately moving them by half a phase (1/512th of the relevent circumference) so that you at least don't have them entirely coincident.) - I believe the suggested scheme would be to take a dodecahedron or icosohedron (either of the two duals can be used to start with) and then subdivide each face in such a manner that equally-sized (but differently distorted) hexagons – and 12 little regular pentagons of identical area fitting in at the old dodecahedron centre/the old icosahedron vertex – emerge from the required segmentation/vertex-truncation and readjustment the radiality of all new mid-edge vertices (or maybe the newer-edges' centres or the newer-faces' centres) to touch the unit sphere. If done symmetrically, it should be entirely fair.
- The face-count might be troublesome, though. The twelve necessary pentagonal faces leaves 65524 hexagons, to split evenly between* either 12 or 20 zones, and it should be obvious that neither is possible**, in whole numbers, given the starting point of 2
^{n}faces...- (* - you can, and probably will in this design, have some that cross between two of the top-level polygons, but you can fully 'donate' as many as you then fully
*get*donated from the next face around, so it might as well be just counted as a group of whole tiles on an a set of Escher-like interlocking 'rough' polygons.) - (** - If you're using 12 zones, that's 3x4x(however many in the zone + one corner each) and there's no factor of 3 in
*any*value that is 2^{n}. Arranging into 20 symmetrical zones (5x4), you will find that 65524 isn't divisible by 5, either...)

- (* - you can, and probably will in this design, have some that cross between two of the top-level polygons, but you can fully 'donate' as many as you then fully
- You could probably arrange an N-ahedron with the number of faces being 12+(12a) or 12+(20b), for some higher value (a bit of mental arithmatic suggests 65592 might be that value) and mark all the 'excess' faces (56?) with "Roll Again!". Or perhaps some pithy motivational slogans that also convey roughly the same meaning... :P 172.70.162.5 11:32, 31 May 2022 (UTC)
- Postcript: Ok, so this is my idea for face-placing. Take a D8 (octahedron) and divide each of its 8 originally triangular faces into 8192 smaller faces (alternatively, start with a cube and progressively truncate its corners towards the same end). This is not a divisible by three number (neither can you put one in the centre, the rest are divisble by three and can surround it symmetrically), but you don't need strict rotational symmetry in any way. The opposing side can reflect/copy the non-symmetry as required to create any useful symmetry across the whole of the structure (and make floored-base/upmost-face pairings, amongst other things).
- As long as you make the faces equally likely to land on
*and stay on*(could be hyperstellated as a slightly flat irregular 8192agon-based right-pyramid with the pyramid-faces of adjacent sides matching or meshing edges with those of each other, or a complicated mostly-hexagonal mesh, or a triangular one that's a limited fragment of a fine geodesic-like bulged pattern) by some suitable scheme governing area, aspect ratio and inter-face angle of incidence (probably normalising features to touch the unit sphere, for a start) then it should do it fairly and with*exactly*65536 faces. I leave the fine-tweaking up to someone else. 172.70.162.5 12:59, 31 May 2022 (UTC)

I don't know why it's so big? Seems like it should have a diameter of approx. 1 meter. 172.70.130.105 21:37, 30 May 2022 (UTC)

- Cueball is 50 pixels high. The ball is 340 px high. Assuming Cueball is an average-height male (1.7m), and is standing the same distance from the viewer as the center of the ball, roughly how large is each face of the polygon? Area of a sphere is 4.pi.r.r, r=0.85, so 9.08 m^2 or 9080000 mm^2, divide by number of faces, get 277 mm^2, so we get 1.6cm to a side. If I did that right, then you're right: those are fairly large faces. --172.69.70.39 05:58, 31 May 2022 (UTC)
- I ran the calculations for the Trivia section. I used 12pt font which gave each number an area of 1/6 square inch (about 1 square cm) 162.158.106.237 06:57, 31 May 2022 (UTC)
- Simple: Exaggerated for comedic effect and to make the point it's unwieldy (plus avoid the fuss of figuring out a realistic size) NiceGuy1 (talk) 06:31, 4 June 2022 (UTC)

Should the title and picture file use "d" or the comic's difficult to type "ᴅ"? While False (talk) 21:55, 30 May 2022 (UTC)

- Since xkcd uses small caps as lowercase letters, the "ᴅ" should just be considered xkcd-font for "d", and as such need not be used on the title, which is not using the xkcd font.
- Ah! While False (talk) 06:15, 31 May 2022 (UTC)

If you really did want to generate a 16 bit integer with physical dice, it would be much simpler to roll a hex die four times. Clayot (talk) 23:30, 30 May 2022 (UTC)

- Rolling a binary die 16 times would also work. You can get binary dice for 1¢ each. 108.162.245.69 01:31, 31 May 2022 (UTC)
- The lowest-value coin of all is the Tiyin from Uzbekistan. Some 3,038 equate to one UK penny (and 2,000 tot up to one US cent) from https://www.bbc.co.uk/news/magazine-21572359. Arachrah (talk) 15:13, 31 May 2022 (UTC)
- Those 1¢ "dices" are not exactly guaranteed to be random. -- Hkmaly (talk) 06:12, 31 May 2022 (UTC)
- They seem as random as other dice? Am I wrong? 172.70.230.63 09:33, 31 May 2022 (UTC)
- You can reduce bias by taking two not quite fair coins. Flip them together. If both heads, or both tails, then record a 0. If different, record a 1. Arachrah (talk) 15:13, 31 May 2022 (UTC)
- Actually, it's better to flip one coin twice. If it's heads then tails, record a 0, if it's tails then heads, record a 1. If it's HH or TT, try again. 172.70.207.8 15:20, 2 June 2022 (UTC)

- You can reduce bias by taking two not quite fair coins. Flip them together. If both heads, or both tails, then record a 0. If different, record a 1. Arachrah (talk) 15:13, 31 May 2022 (UTC)

- They seem as random as other dice? Am I wrong? 172.70.230.63 09:33, 31 May 2022 (UTC)

I think the hardest part (or maybe second-hardest part) is figuring out which facet is the one on top. 162.158.78.109 00:46, 31 May 2022 (UTC)

- Roll it on a glass table, check from below which face it's landed on instead. Wait until it has settled safely, though, or it might land on
*your*face! 172.70.90.227 04:58, 31 May 2022 (UTC)- Good plan. Assuming standard dice design, subtract the value from 65537 to get the value of the uppermost face. --172.69.70.39 05:58, 31 May 2022 (UTC)
- Because computer binary counting starts with ZERO (and in this case ends with 65535) one has to subtract from 65535. This die would not have a 65536 and it would have a zero. Inquirer (talk) 22:38, 31 May 2022 (UTC)
- Notice that the parent comment says “assuming standard dice design” and standard dice start with 1 and end with their d number: a standard d4 has faces 1,2,3,4; a standard d6 has faces 1,2,3,4,5,6; a standard d10 1,2,3,[…],10; and a standard d100 has faces 1 through 100. Which is why rolling 2xd10 does NOT yield the same results as rolling 1xd100, because one cannot roll a 1 OR a 100 with two d10’s, and other numbers are over represented. This is why I have both a d12 and a d100 in my set of dice…John (talk) 11:40, 2 June 2022 (UTC)
- D10s are frequently (IME) numbered 0..9, with underlines to distinguish
__6__from__9__, whether or not that is as a deliberate sop to pairing up for percentiles ("It's the red dice first...", "It isn't!", "It is, it's*always*the red dice first, that's a 9 percent fail, not at 90 percent success!"). The 0 opposite 9, 1 opposite 8, etc. - If you're rolling 1..10s (depends upon the system being used for... and arguments about the original intentions, possibly, where 10 of something or zero of something turning up/discovered means a lot to what exactly happens next) you
*treat*them as full 10s, and double-zero can (again, hopefully understood in advance) be a "natural 100", rather than a natural-zero, to someone's obvious advantage or detriment. - Similarly, games with D4 may use 0..3 as its outcomes, or D3s (D6/2s) have 0,0,1,1,2,2 as faces. Or if you are somehow stuck with a 1-based die of the appropriate (or divisible) range, and need to play something that requires a 0-based one, you agree that MAXNUM->ZERO or N=N-1.
- From my recollections of the truly huge collection of multicoloured, multisized and variously multifaceted dice that was dragged out for wargaming/role-playing sessions, years of accumulations from various sources, the D6s (spotted, not "Hit", "Missfire", <arrows for miss direction>, or otherwise for other uses), D8s, D12s and D20s were habitually 1-upwards, and Ds with 3, 4 and 10 almost all 0-upwards. D6s were the most numerous, but D10s well up there (enough for colour-mismatched pairs for each of a whole battalion of participants, even if the Hit/Miss die had to be passed around at need, and the few big yellow D20s might need to be offered onwards/rolled on someone's behalf on occasion).
- In short, the 'standard' is perhaps more firmly that opposite sides add up to double the average (not possible with D4, which is also "point-marked", not one number per side), though I'd like to check a D3 to see if it's 0 opposite 2 (x2) and 1 opposite 1 (which also happens to be a 0..5-dice with the opposition rule, but modded by 3) or perhaps in a basic {1..6}mod3 conversion 1 opposes 0(=6), 2 opposite 2(=5), 0(=3) opposite 1(=4). Maybe next time I go a gaming I'll get the chance. 172.70.86.44 12:48, 2 June 2022 (UTC)
- HOW are you figuring any numbers are over represented in rolling 2xD10? There are 100 possibilities, 1 through 100, one chance per number, exactly equal... Each die has a 1 in 10 chance of rolling each value. Unless you're forgetting to pre-assign which die is the tens position and which is the ones... This is why any set with more than one D10 has then different colours so you can tell them apart... NiceGuy1 (talk) 05:11, 4 June 2022 (UTC)
- Not sure what you're asking here. It seems to bear very little relevence to the meaning of the thing you're replying to (wot I wrote, which might indicate the error in conveying is at my end). I did not
*intend*to suggest (as it is untrue) that 2D10≠1D100 (give or take adjusting what "00" means, which is an implementation issue, not a mathematical one), but I'll gladly clear up anything I left potentially saying something other than I thought it did. Quote the bit, and you can get a 'better' rewrite of it ASAP. 162.158.159.41 05:48, 4 June 2022 (UTC)- "Which is why rolling 2xd10 does NOT yield the same results as rolling 1xd100, because one cannot roll a 1 OR a 100 with two d10’s, and other numbers are over represented.", that line. A 1 is rolling 0 on the tens die and a 1 on the ones die. A 100 is 0 on both dice (or you make the range 0 to 99, in which case two 0s is 0). NOW I think you were thinking of multiplying the values, which is indeed bad (for example, it then becomes impossible to roll a 17, as no two single digit numbers multiply to 17. Also, 9x9 is 81, 9x10 is 90, making those the last two possible values before 100, the other 80s and 90s unachievable. And then what you say make sense, you can get 24 with 3x8 or 4x6, two chances = over-represented). NiceGuy1 (talk) 06:29, 4 June 2022 (UTC)
- Ah, no, that was User:John, not me (172.70.86.44). Teach me for replying based on seeing the Diffs page, and not counting the indent-colons correctly! You were replying to a point that I had actually
*not even noticed*, at the same 'level' as I had jumped in on the zero-based-range thing with my spiel that you weren't actually arguing with. (Not sure John was thinking dice-multiplied, either, as 1x1=1. Perhaps why I blanked that bit out.) - On the subject, though, the Babylon 5 RPG used an interesting double-dice system, for some things (either straight success/fail or modifying other offsets, possibly). Red D6 and Green D6 (or similar hue distinction) rolled together. Take the
*lowest*value of the two, and then call it negative if it was the red one. Equal rolls mean zero, except double-1 (critical/special failure of some kind) and -6 (likewise a success). Gives a slightly modified normalised-around-zero distribution (intentionally or otherwise) with the possible results being ((-Critical -5 -4 -4 -3 -3 -3 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 0 +1 +1 +1 +1 +1 +2 +2 +2 +2 +3 +3 +3 +4 +4 +5 +Critical)), if you order the 36 possibilities. Similar to 2D6 added, minus 7 (to bunch up the unexceptionalism towards the baseline), but two of the middlingest possibilities removed and given special status at the either end for that little possible pizzaz! ;) - It reminded me of the experiment with monkeys where they were taught to recognise values (as number of bananas, e.g.) and then taught that whichever of two options they chose, it was the
*other*one's value that dictated their reward. When done with abstract numbers (digits, or colours/shapes relating to numbers by training) they would "choose low, to get high", but when given*actual*quantities of reward-items, they'd instinctively "choose high", by instinct, immediately before their conscious brains kicked in and they realised they'd done the wrong thing. Or something like that (look for 30/40-year-old study, possibly shown to be flawed, these days)... - Anyway, it took a short while to train oneself to be somehow excited by 3 dots on a green when paired with six dots on a red, say, (or dissapointed with a green 6 in the light of any non-6 red) when previously the merest glance at the cumulative spots on thrown dice would suffice to satisfy the question of how well they fell for you. ;)
- Not useful for this comic, but had always been dying to mention it, from the beginning! 172.70.86.64 11:10, 4 June 2022 (UTC)
- LOL! Yes, I indented to answer John, his comment mystified me, :) And I did not check your identity, just understood by your response YOU were the one I was speaking to. :) The comments on here are so many and so LARGE I haven't read most, just that his caught my eye. THAT is an interesting if complicated dice system, wow! NiceGuy1 (talk) 05:03, 5 June 2022 (UTC)

- Ah, no, that was User:John, not me (172.70.86.44). Teach me for replying based on seeing the Diffs page, and not counting the indent-colons correctly! You were replying to a point that I had actually

- "Which is why rolling 2xd10 does NOT yield the same results as rolling 1xd100, because one cannot roll a 1 OR a 100 with two d10’s, and other numbers are over represented.", that line. A 1 is rolling 0 on the tens die and a 1 on the ones die. A 100 is 0 on both dice (or you make the range 0 to 99, in which case two 0s is 0). NOW I think you were thinking of multiplying the values, which is indeed bad (for example, it then becomes impossible to roll a 17, as no two single digit numbers multiply to 17. Also, 9x9 is 81, 9x10 is 90, making those the last two possible values before 100, the other 80s and 90s unachievable. And then what you say make sense, you can get 24 with 3x8 or 4x6, two chances = over-represented). NiceGuy1 (talk) 06:29, 4 June 2022 (UTC)

- Not sure what you're asking here. It seems to bear very little relevence to the meaning of the thing you're replying to (wot I wrote, which might indicate the error in conveying is at my end). I did not

- D10s are frequently (IME) numbered 0..9, with underlines to distinguish

- Notice that the parent comment says “assuming standard dice design” and standard dice start with 1 and end with their d number: a standard d4 has faces 1,2,3,4; a standard d6 has faces 1,2,3,4,5,6; a standard d10 1,2,3,[…],10; and a standard d100 has faces 1 through 100. Which is why rolling 2xd10 does NOT yield the same results as rolling 1xd100, because one cannot roll a 1 OR a 100 with two d10’s, and other numbers are over represented. This is why I have both a d12 and a d100 in my set of dice…John (talk) 11:40, 2 June 2022 (UTC)

- Because computer binary counting starts with ZERO (and in this case ends with 65535) one has to subtract from 65535. This die would not have a 65536 and it would have a zero. Inquirer (talk) 22:38, 31 May 2022 (UTC)

- Good plan. Assuming standard dice design, subtract the value from 65537 to get the value of the uppermost face. --172.69.70.39 05:58, 31 May 2022 (UTC)

What material should it be to be light enough to easily roll it but cheap enough that doing the 1,5 meters doest cost a fortune ? Sorry if the question is not clear. 141.101.69.30 05:50, 31 May 2022 (UTC)

- I recommend making it hollow. You could probably do something like this for $3000 if you made it out of 1/8th inch acrylic plate. 162.158.106.237 07:02, 31 May 2022 (UTC)
- At first I thought aluminum for sturdiness, but really you could make this out of cardboard for dirt cheap, lasercutting precise shapes, but you'd have to design its structural frame to keep it intact, exchanges design effort for price. 172.70.230.63 09:32, 31 May 2022 (UTC)

I disagree with this dice being really random. Like, sure, if thrown correctly, but that's going to be quite hard. -- Hkmaly (talk) 06:12, 31 May 2022 (UTC)

- True. For a rolled die to be random, it needs to roll far enough so that the initial orientation no longer governs the outcome. Say, ten times the circumference, or about 150 meters? -- Dtgriscom (talk) 10:28, 31 May 2022 (UTC)
- Interesting to consider the 'necessary minimum'. Simplify to a "wheel of fortune" (just one axis of continual rotation) it would depend upon the potential variation of imparted rotation. If (say) 'aiming' at two whole rotations has a (perhaps 'normal') spread of variance that relates to ±½ rotational uncertainty at the 1st and 3rd quartile of probability then the sub-first and above-third 'tails' might wrap around to (roughly) equalise the chances that 2±(whatever fraction) spins lands just about anywhere just about equally. Aiming at four whole rotations (similary ±1 spin at the given quartiles, and the tailing chancs 'filling in' above 5 rotations and below 3) would smooth things out, all else equal, but takes twice as much perceived/attempted effort for not much more 'randomising'.
- Similarly, requiring 10 full rolls (maybe honestly aiming for 10, but allowing it to be 7.5 or less if not obviously 'just nudged') seems overkill, in the single dimension.
- Except, of course that you also need enough distance (on top of whatever factor you consider practical as a variation-wrapping value, which might not be the ½-in-2 I give) to also roll
*sideways*. If for some reason you really don't want to roll 65536 or 1 (or is it 65535 and 0?), which may be on polar-opposite faces, you might make sure that they are directly to the left and right before you propel the die forwards*a little*, not caring which distribution of numbers is on/near the rolling-equator (2 is acceptible to you, and 65533, etc; other very low/high values conceivably placed on that thin band of "wheel-like chance" but you're just avoiding the very largest and smallest, or specifically just the one of them) but knowing that it's more unlikely to easily present the exact face(s) you dislike than it might be in a truly 'fair' roll. - Perhaps the best thing is to have a rolling track to send the thing down that puts it the required "two or so rotations" forward to then either hit a wall or climb slightly up a slope (at a roughly 45 degree angle) that then sends it back roughly sideways to the original vector for a similar distance with a perpendicular or even composite moment of rolling rotation, to bring 'initially axial' numbers fully into play... And that dog-leg would require a sligthly shorter length from launch-position to where the thoroughly mixed-up final stopping point should be, whilst significantly foiling the master-manipulators who actually try to arrange an initial setup that favours better final results (rather than just nudge it, uncaring, for a result not as totally random but certainly not more predominently of desired-for ranges than otherwise). 141.101.99.8 12:28, 31 May 2022 (UTC)
- At what point does the structural material the die is composed of, combined with its mass, create a smoothing effect that will destroy the fairness of the die. I mean a small plastic die is no problem. A 2-ton acrylic die would start grinding off the edges of some faces with every roll, would it not? 172.69.69.122 13:35, 31 May 2022 (UTC)

Should it be related to https://xkcd.com/221/ ? 162.158.183.246 08:07, 31 May 2022 (UTC)

I'm going to wait, I think - I don't think there's room in my attic for this as well as all the Betamax kit, my drawers full of MiniDiscs and my Zune collection. No, I'll sit tight - I'm hearing encouraging things about the introduction of the Magic 65536-Ball... Yorkshire Pudding (talk) 09:41, 31 May 2022 (UTC)

- The number of sides on the die inside the ball is not what determines the name of the ball. It's the exterior housing which is colored in the manner of an Eight Ball. The classic design uses a d20, and is still called an Eight Ball, not a Twenty Ball. 172.70.130.195 18:00, 31 May 2022 (UTC)
- Full disclosure: I don't have any of those things in my attic. And I'm not
*entirely*sure, but I don't think Randall thinks rolling a d65536 is genuinely the hardest part of generating random 16-bit numbers. And Grape Nuts contain neither grapes nor nuts. Yorkshire Pudding (talk) 23:37, 31 May 2022 (UTC)

- Full disclosure: I don't have any of those things in my attic. And I'm not

I'm suprised the hidden message points to 2624. I would've thought it would point to 2626 to refer to itself. Maybe things didn't get published as intended? Or maybe Randall really just wanted to point people to the Voyager comic? Linux2647 (talk) 18:13, 31 May 2022 (UTC)

- I'm no ASCII expert, but from the description provided I'm pretty sure the comic URL would require the number representing "26" to show up twice. A die with, say, two 13,359 faces would obviously not be fair. If only Randall had published this as #2625 or #2627! (Or maybe he
*planned*to publish it last week and had to shuffle his schedule after finalizing this comic?) GreatWyrmGold (talk) 18:24, 31 May 2022 (UTC)- Probably the latter, seeing as it doesn't actually line up so that any of them are actually "26". The numbers are xk-cd-.c-om-/2-62-4/, so the 26 and 24 aren't lined up like that. 172.70.126.87 19:38, 31 May 2022 (UTC)
- To change the number from 24 to 26 would mean changing 13,359 to 13,871. The only way that would be a problem is if 13,871 was already in the comic, which it isn't. Convert 13,359 to hex, it's 342F. In ASCII, 34 is "4", 2F is "/". Add 2 you get 36, so the new hex number is 362F, which converted to decimal is 13,871. NiceGuy1 (talk) 11:37, 5 June 2022 (UTC)

- Perl code to decode the ASCII:
perl -E 'for (30827, 25444, 11875, 28525, 12082, 13874, 13359) { print chr($_ >> 8), chr($_ & 0xff) }; print "\n"'

**Remember that "die" is singular and "dice" is plural** Mushrooms (talk) 09:30, 1 June 2022 (UTC)

- Might be worth offering some easier alternatives..

Needless to say, 16 ordered coins (eg ordered by the date of their minting) provide a much easier alternative to a d65536.

Other (easy to find) d p^2 - such as 8 ordered d4, or 5 ordered d8 and a coin (or bit-shave a dice.) It's true some rules need to be applied (the highest number of the die is treated as a 0, and the order of the dice is strictly followed).

For example using a rainbow spectrum ordering of 6d8, I role: 7, 1, 2, 8, 3, 5. Each dice represents 3 bits - 111-001-010-000-011-101. We shave off the last two bits (because we want 16 bits, not 18, for a d65536) 1110 0101 0000 0111. Hex = E507, which is decimal 58,631.

While it takes a few seconds for a human to convert the number it is quite trivial to write a program to convert an image capture.

There are also specialist dice - such as d16 'hexidice' which provide 4 bits per ordered die, and far less human calculation.
There are even d256 hex dice made, but they suffer the same problem that a d65536 would have.

- how are you trivially converting image captures? i still use my keyboard. what's the update? 162.158.79.120 18:26, 1 June 2022 (UTC)
- For your D8 system, since a D8 absolutely SCREAMS octal, you'll get results from 001 to 1000 octal for each die roll. Just subtract 1, and it's a perfect 3 digit range, 000 to 111! Which feels better than 8, the highest roll, becoming 0, the lowest, like you're doing. And as the previous commenter asked, how is image capture trivial? Especially from a programming perspective? Seems like the ACTUAL trivial method is to put a calculator into scientific mode and just type in the hex number to convert... :) NiceGuy1 (talk) 05:11, 4 June 2022 (UTC)

- D8 is fine, and I tried that - but it's not so easy to composite the hex number from D8. With a D16 (there are two different styles, both easily available) it's really easy to get a nybble of randomness. Using e.g. visible spectrum ordering and suitable (eg red, orange, yellow, grass*, green, cyan, blue, purple) dice, it's trivial to order the dice to 4 bytes of randomness. (and a d65536 is only 2 bytes) (*I have no grass but I have a dark orange), so just now I rolled 0x6A5D391B.

- As for using a program to convert an image capture, it was sort of a joke. However, the real advantage over a calculator is that the calculator is a PRNG.
- Here is a link to 12 lines of code that would grab the dice numbers - similar code would be used to grab the colours.
- https://stackoverflow.com/questions/66027978/python-number-recognition-on-colored-screen
- Also, just for fun, have a look at the an system http://gamesbyemail.com/news/diceomatic
- Mainly I wrote this just for fun. (20040302 (talk) 11:19, 18 June 2022 (UTC))

I found an octahedral Goldberg with 65538 sides, 6 squares and 65532 irregular hexagons, notated GP₄(128,0). Can be constructed by chamfering a cube 7 times (Conway cccccccC). I don't think anything can be closer. SDSpivey (talk) 04:37, 2 June 2022 (UTC)

- I have had two designs in mind:
- Start with octahedron, subdivide each face triangle into 16,384 triangular faces (subdivide all original edges into 128ths, effectively, while "halving into quarter-sized triangles), pairing the triangles up into half that many 'diamonds' then inflating to touch the bounding sphere, keeping the diamonds planar and possibly equal area, but will also distort them (some into kites, others may be utterly irregular) so it'll be a (literal?) balancing act to make all tippings between faces equally possible.
- Start with a tetrahedron, subdivide likewise, stick with the triangles, have the same issue of inflating the faces towards the unit sphere while balancing the resulting distortions.

- I tried to work out something that seems to exactly match the image (or as exactly as I perceive it to be) with mildly distorted hexagons - albeit with the necessary pentagonal substitutions to carry the curvature - formed of (a similarly subdivided set of) sub-triangles drawn out on the original surfaces of either icosahedron or a snub-stellated extension onwards the dodecahedron, but I couldn't get the numbers to add up. Which is not to say that there isn't a way to do it. I was going to spend more time on this issue later, so if I get past the issues, then... Watch this space? 172.70.162.77 13:17, 2 June 2022 (UTC)

I WAS going to say a far simpler way is to roll a D6 and 4 D10s (what is WITH all the lowercase Ds? Every time I see dice named it's uppercase!), figuring that gives a range of 0 to 69,999, and throw out/re-roll results higher than 65,535. (I realize that probably adjusts the odds, but I would think minimally and equally). Then I realized the D6 can't give a result of 0, so the real range is 10,000 to 69,999. Oops! And a D7 feels weird and rare if it even exists, SO! 5 D10s and still throw out everything above 65,535. :) Oh, and I agree with the Warning text, NEEDS an explanation how these numbers turn into a URL. WITHOUT relying on writing a program or concepts like "big endian", just say what's being done to ONE number, come on! EDIT: Never mind, I figured it out and added a MUCH simpler explanation. :) NiceGuy1 (talk)

- I think a D7*2 exists, i.e. a D14div2 (two faces for each of seven digits), though they're rarer than D14s (same idea as a D10, but interlocked heptagonally-based pyramid 'ends') which are already niche. I saw one with days on (Mo/Tu/We/Th/Fr/Sa/Su, leastwise), which is the only vaguely obvious reason for one. Might as well have a spinner. But to save so much 'wasted' rolling, use a D8 and only reject the 8 (or, rather, 8=0, reroll the 7 and all the rest, to prevent actual statistical clumping, ditto onwards from any other 'bust'). 162.158.159.41 05:48, 4 June 2022 (UTC)
- Yup, didn't think about a D8 (which is extra stupid as I was discussing D8 higher up, LOL!) D'oh! And yes, I didn't think about rolling a day of the week, that would make a D7/D14 useful. Even if it was so labelled, just have Sunday equals 0, Monday is 1, etc. Range becomes 0 to 69999, only about 4,000 possibilities thrown out (I'd probably just re-roll the D7/D14). For a D8 I'd agree with your method.

**"hexakismyriapentakischiliapentahectatriacontakaihexahedron"** [From the Explanation] Would anyone care to take a stab at deciphering that word? As of this comment, Google only returns this page as a reference. These Are Not The Comments You Are Looking For (talk) 01:55, 7 June 2022 (UTC)

- I have not checked for accuracy/consistency with the accepted "large specific number prefixing" conventions, but "hexa" (6) "kismyria" (x10,000) "penta" (5) "kischilia" (x5,000) "penta" (5) "hecta" (x100) "tria" (3) "conta(kai?)" (x10) "hexa" (6) "hedron" (-faced 3d shape")... Possibly constructed by historic geometrical naming rules (historically may not have dealt with myriads enough to establish a firm usage-policy), possibly just the root number* Google Translated to modern Greek, in the latin alphabet and geometrised/de-spaced a bit. It was funny enough for me not to investigate too closely, but this is my impression. It'll be lost once the Incomplete is edited off, anyway, and was never part of the comic to be explained. The 'Incomplete' rewrites sometimes
*do*seem to need a bit of counter-nerdsniping, but as we don't have an explainexplainxkcd.com to discuss them, in Talk is as good a place as any... :) 172.70.85.211 09:11, 7 June 2022 (UTC)- (*) It's the "kai" that gets me. May be the difference between US number ("twelve thousand thirteen") and UK number ("twelve thousand and thirteen"), except for Greek, or "triacontakai" is "thirty", but that seems unweildy to me for "everyday" Greek (ancient or modern) and I'd have used "trideca" before realising that's probably "thirteen" (c.f. "dodecaedron", so... Anyway, to explain my assumption there. Really I could just look it up to be certain! 162.158.159.121 09:19, 7 June 2022 (UTC)
- I'm the one who named the polyhedron. Hexakismyria (60000) - pentakischilia (5000) - pentahecta (500) - triaconta (30) - kai - hexa (6) - hedron (3D). From what I found, "Kai" was supposed to be added when there's a tens and ones place as stated on wikipedia's polygon page, and "kis" was used for multiples of thousands as per another wiki. In both cases, if there's a naming convention flaw, it's best to get a Wikipedia-grade citation to fix things. --108.162.242.58 01:36, 11 June 2022 (UTC)

- (*) It's the "kai" that gets me. May be the difference between US number ("twelve thousand thirteen") and UK number ("twelve thousand and thirteen"), except for Greek, or "triacontakai" is "thirty", but that seems unweildy to me for "everyday" Greek (ancient or modern) and I'd have used "trideca" before realising that's probably "thirteen" (c.f. "dodecaedron", so... Anyway, to explain my assumption there. Really I could just look it up to be certain! 162.158.159.121 09:19, 7 June 2022 (UTC)
- Why'd you place your comment above mine from 2 days earlier? :) NiceGuy1 (talk) 03:42, 11 June 2022 (UTC)

It seems like it would be inappropriate for me to make the call, as I'm the one who made the fix, but can the "Don't remove this too soon" request for more information on the hidden message trivia be declared resolved? I feel I've made it clear (I feel like fully doing the conversion on every number would seem too bulky). Also, it begs the question, why THAT comic, is it worth mentioning that this makes it seem likely that THIS was supposed to be 2624, and he forgot to update the number? It would have been simple enough to just add 2 to the last number... NiceGuy1 (talk) 05:26, 5 June 2022 (UTC)