Fair Dice (Part 1) - Numberphile

Probability expert Professor Persi Diaconis (Stanford University) talking about dice.
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NUMBERPHILE

Videos by Brady Haran

[carpedm]

"There are 5 fair dice."
*angry d2 noises

[klaxoncow]

All a D&D player wants to know is whether the D20 is a fair dice. ;D

[z-beeblebrox]

I love this guy's name. It's like the name someone would have in a medieval fantasy story.
"Quick, m'lord! We must reach the king's statistician Persi Diaconis before sundown or all hope is lost! He's the only one who knows how to make a fair die out of non-regular polygons!"

[wvvwkx]

In high school our physics teacher used to choose people for oral exams by throwing a 30 sided die lol

[Tolop]

Your channel turned me from a person who thought they hated maths, to someone who appreciates its beauty, thanks!

[ChristopherFonseka]

Is it possible to make strategically unfair dice?

I've always wanted to make a 12 sided dice, with the same probabilities as two 6 sided die

[shanedk]

I once saw 7-sided dice, that were basically extruded pentagons. And my initial reaction was that there's no way such a die could be fair, but then I thought about it for a few minutes.

If you have a pentagon that's extruded very thinly, like a wafer, then it'll be biased in favor of the two pentagonal faces and the other 5 faces will hardly ever show up. If it's extruded several feet, then the two pentagonal faces will hardly ever show up and you'll usually get one of the 5 others. So there MUST be a sweet spot in the middle where the biases cancel out, and you'll get one of the pentagonal faces 2 out of 7 times!

[owdeezstrauz]

6:45 did he just say "fivegon"??? 😞

[derbistheeternal]

Dammit! I thought this video had the man with a thousand Klein bottles when I saw the thumbhnail but it was an impostor.

[SuperOm]

'Fair dice' feels like it should be a saying ...

[WillReddish]

6:47 I was waiting for him to mention a d10, then he invented it

[stevenmartinez]

For anyone interested, here are the names of the shapes shown at 7:20
Left to right, then top to bottom;

cube/hexahedron, octahedron, pentagonal hexecontahedron, pentagonal icosahedron. <only shape I'm not sure of>, rhombic dodecahedron, rhombic triacontahedron, triakis octahedron

tetrahedron, tetrahexahedron, triakis icosahedron, deltoidal hexecontahedron, triakis tetrahedron, deltoidal icosahedron, triangular bipyramid, disdyakis dodecahedron

disdyakis triacontahedron, dodecahedron, icosahedron, hexakis octahedron, deltoidal icosahedron, tetartoid/tetragonal pentagonal dodecahedron, trapezohedron, rhombohedron,

hexatetrahedron, irregular tetrahedron, irregular tetrahedron, irregular rhombic bipyramid, rhombic bipyramid, rhombic dodecahedron

Do correct me if I'm wrong.

[FirstnameLastname-bhqs]

"There are only five fair dice, d4, d6, d8, d12, and d20" *sweats in white wolf*

[irinore]

That d4 awakened a deep anger within me

[misdelivereddishwasher]

The way this man describes dice reinforces the idea that there's a very fine line between insanity and genius.

[cpt_nordbart]

what about this dice guy? did he end up with equal results for all 6 sides of a die?

[grapefruittango]

"I have a thirty sided dice" Who wants to bet that he got it to play D&D

[tommy_svk]

So I tried making an actual list of the fair dice as shown at 7:23, using these visuals and the original paper. Here's what I've got:
D6 - regular cube
D8 - regular octahedron
D60 - pentagonal hexecontahedron
D24 - pentagonal icositetahedron
D60 - pentakis dodecahedron
D12 - rhombic dodecahedron
D30 - rhombic triacontahedron
D24 - triakis octahedron
D4 - regular tetrahedron
D24 - tetrakis hexahedron
D60 - triakis icosahedron
D60 - deltoidal hexecontahedron
D12 - triakis tetrahedron
D24 - deltoidal icositetrahedron
The infinite family of bipyramids (pictured is the triagonal bipyramid I believe)
D48 - disdakys dodecahedron
D120 - disdakys triacontahedron
D12 - regular dodecahedron
D20 - regular icosahedron

After that I am kinda lost. The visuals are confusing me a bit, cause the deltoidal icositetrahedron and disdakys dodecahedron seem to be there twice (at positions 14 and 22 and positions 16 and 21 respectovely). The second to last shape also looks like just a regular octahedron, which is already listed before. The last one also looks like a rhombic dodecahedron, also already listed. Furthermore, after reading the original paper, I've come to understand that the fair dice are: 5 Platonic Solids, 13 duals of Archimedean Solids (known as Catalan Solids) and 2 infinite families. Based on the paper I think the infinite families are supposed to be bipyramids and trapezohedra.

But that's all I got and that's just 20 families. The video says there should be 30, but I can't figure out what the remaining solids in the video are supposed to represent and the paper seems to be talking about only 20 families as well, unless I missed something. If anyone has any ideas, please let me know.

[NonDelusional]

If all the dimples in a golf ball could be numbered, would it be fair??

[JossLun]

There is one of the interests of simulating chance: once they're balanced, all virtual die are fair.