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The cursed d65536

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Re: The cursed d65536

#61

Post by thematrixturtle »

hnuser123456 wrote: post #35
tlb wrote: post #19

I'd like a physics analysis of how flat/hard a surface you need to roll a D65536, how long it would take to settle, and how good a microscope you'd need to read the top face. Is there, like, 99designs for physics questions? I'd happily pay $99 for the answer, then post it here like I worked it out myself.

a 1ft diameter d65536 could be broken into surfaces with area 4.45 square millimeters, or a little over 2x2mm. With good eyes and enough squinting, a microscope might not be needed. maybe fill it with liquid with a tiny air bubble to find the top face 1in diameter, however, gives 0.175mmx0.175mm per face, or about the width of a hair by the width of a hair.

I wonder how much bias engraving or even painting the numbers on the die would introduce? The weight of "1" will be noticeably different to "58888".

Re: The cursed d65536

#62

Post by Someone »

ffhhj wrote: post #47
krapp wrote: post #46

Earlier quoted context omitted.

No.

Why? Is it because it haven't been found, or is there a proof of impossibility?

If you observe a black box producing a sequence N items, you can’t know whether it will, after that, repeat the same sequence at infinitum (it might just contain a circular tape of N items, for example), or keep producing a single identical item, or keep producing only two different items, etc.

Re: The cursed d65536

#63

Post by eesmith »

thematrixturtle wrote: post #61
hnuser123456 wrote: post #35

Earlier quoted context omitted.

a 1ft diameter d65536 could be broken into surfaces with area 4.45 square millimeters, or a little over 2x2mm. With good eyes and enough squinting, a microscope might not be needed. maybe fill it with liquid with a tiny air bubble to find the top face 1in diameter, however, gives 0.175mmx0.175mm per face, or about the width of a hair by the width of a hair.

I wonder how much bias engraving or even painting the numbers on the die would introduce? The weight of "1" will be noticeably different to "58888".

Use a 7-segment font and two paints with the same density, with one paint the same as the background color. For each digit, paint in all 7 segments. For each number, draw all 5 digits.

Re: The cursed d65536

#64

Post by bruce343434 »

A better approach would be to calculate the amount of needed nodes that would junction the vertices, and then push them apart (simulated annealing). Though it won't be a regular geometry.

Re: The cursed d65536

#65

Post by knome »

it would be easier to avoid edges altogether and regularly space flat circular areas leaving curved space between them. you can have any arbitrary number of faces if you give up on the faces touching.

Re: The cursed d65536

#66

Post by ufo »

mananaysiempre wrote: post #38
virchau13 wrote: post #34

Earlier quoted context omitted.

This sounds interesting - could you elaborate further on how rejection sampling "fails" on LuaJIT?

I mean, as far as correctness as concerned, of course it works, but performance-wise in a raytracer I was toying around with it was a dismal failure compared to the (traditionally shunned) analytic approach. The issue, as far as I understand it, is that LuaJIT only handles traces of two shapes: linear code; or linear loop prologue followed by linear loop body. The conditions of any branches (that could not be determi…

This is a cool story! Is that vector library public or is it an internal project? I'd love to take a look at the rest of it...

Re: The cursed d65536

#67

Post by shultays »

kazinator wrote: post #16

> 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…

If you are OK with roll again then you can just have a cylinder-ish shaped dice where numbers are on the sides (so it is N-edge polygon instead of a circle) and top and bottom is marked as "roll again"

even better, you can round the top and bottom. Either by semi spheres or pointy like a pencil tip. Then chances of "roll again" hitting would be really low!

Re: The cursed d65536

#68

Post by eternityforest »

kazinator wrote: post #16

> 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…

If we accept needing the user to run an "algorithm" like that, we could have a D256(Or whatever the next highest fair dice is) and actually have a practical-ish system.

Although hex D16s would probably be better.

D20s with 0-F plus two extras could be pretty awesome in a cyberpunk tabletop game. The other two could be "IOError" that makes the matrix glitch in a bad way, and superposition, that makes it glitch in a way you can use.

Re: The cursed d65536

#70

Post by JoeAltmaier »

hnuser123456 wrote: post #35
tlb wrote: post #19

I'd like a physics analysis of how flat/hard a surface you need to roll a D65536, how long it would take to settle, and how good a microscope you'd need to read the top face. Is there, like, 99designs for physics questions? I'd happily pay $99 for the answer, then post it here like I worked it out myself.

a 1ft diameter d65536 could be broken into surfaces with area 4.45 square millimeters, or a little over 2x2mm. With good eyes and enough squinting, a microscope might not be needed. maybe fill it with liquid with a tiny air bubble to find the top face 1in diameter, however, gives 0.175mmx0.175mm per face, or about the width of a hair by the width of a hair.

I'd look at the bottom face. Because you have a reference (the table) for the selected side, not just guessing which side is toppiest.
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