51–60 of 74 posts
Earlier quoted context omitted.
No.
Why? Is it because it haven't been found, or is there a proof of impossibility?
Probably says something about me that my immediate reaction to the number 65536 wasn’t 2^16, but rather the frequency of the timer crystal you had to swap into a Radio Shack tone dialer to make a “red box”[1] that would let you make free phone calls on US pay phones by simulating the analog coin code sound of a quarter being deposited. Fun fact that the “red box” was the first hackaday article[2] posted way back in 2…
There's an assumption here that a polytope with equal area faces will be fair. I'd like to see a proof. My mathematical intuition is that the probability of stopping on a face depends on the extent that nearby faces slow a rotation, which depends on the angle of attack across each face. Without symmetry, this will vary by face.
Earlier quoted context omitted.
No.
Why? Is it because it haven't been found, or is there a proof of impossibility?
From the broken first attempt: Each face has 3 vertices, shared between 6 faces, so the total number of vertices is 65536, and they become faces of my die. This should have tipped you off. If you have six triangular faces around every vertex, you have a flat Euclidean plane, not a sphere with positive curvature. For another example of this: https://m.youtube.com/watch?v=jfSTwqmrQDc
That's why "don't do math after midnight". But I don't get what's wrong with repeated throws of tetrahedron - 2 bits of result at a time - or even icosahedron, with re-throws if one of 4 "wrong" sides is up - 4 bits at a "good" throw...
Look at the humble d10 for inspiration. The trick is to avoid making a spherical-looking die. A fair d65536 could look like a pair of cones glued together, with 32768 sides per cone. Alternatively, one can make a fair 65536-sided cylinder with rounded ends.
In practice though I'd go with four of those: https://commons.wikimedia.org/wiki/File:D16_HEX_dice.JPG (assuming that I can get them in four different colors)
> This is of course hilariously cursed. It will look almost perfect, but very rarely give numbers outside the expected range. If the D65538 is fair, it is usable: you just discard the two unwanted values when they show up and roll again. Those faces could be labelled as "roll again". If you have a uniform source of random numbers from 1 to N, you can get a uniform distribution from 1 to M < N simply by discarding val…
Rejection sampling , that is. Unexpectedly, but obviously in retrospect, the common (ancient) wisdom of using that in the continuous case instead of figuring out tricky combinations of special functions to get the result from a bounded number of uniform samples... fails miserably on LuaJIT. Of course atan2() is not the fastest thing in the world, but on a compiler that only really understands loops with linear bodies…
I know it's not the point of TFA, but you can just roll a d8 6 times, generating 3 bits each time, for a total of 18 bits, and then discard two of them.
You can buy hexadecimal dice ie D16 with the sides labelled 0 through F, I have some, I use them to generate random numbers when it is important to me that I personally have confidence these are random numbers. With hex dice you can generate 16 bits with four rolls, four bits each time. Obviously you're more likely to already have a D6 somewhere, but then you're even more likely to own a coin, and 16 coin tosses is a…
I'm not sure this is still true. At least not here in Sweden. Everyone I know owns multiple board games which come with at least one D6 and in recent years I've had discussions with friends and family about us paying everything electronically nowadays. There has even been talk about the risk to our society of no one having cash anymore.
In fact, some weeks ago I needed a coin to show my kids when they asked about this physical money they'd heard of and I couldn't find one.
[0]https://www.popularmechanics.com/space/a27259/how-many-parti...
Probably says something about me that my immediate reaction to the number 65536 wasn’t 2^16, but rather the frequency of the timer crystal you had to swap into a Radio Shack tone dialer to make a “red box”[1] that would let you make free phone calls on US pay phones by simulating the analog coin code sound of a quarter being deposited. Fun fact that the “red box” was the first hackaday article[2] posted way back in 2…