an intransitive 19 dice set for 4 players

[YouhuaLi]

Hello,

I believe I have successfully created a 4-player intransitive dice set consisting of 19 dice. Each die has 19 × 9 = 171 faces. I’ve uploaded the results here: https://github.com/YouhuaLi/Intransitive_dice/blob/main/4_players_19_dice.txt. In the file, each row represents the values of a single die, with the values separated by spaces.

My result is a simple extension of your work, but I would still like your help in verifying it. This file contains a straightforward static analysis: https://github.com/YouhuaLi/Intransitive_dice/blob/main/4_players_19_dice_static_analysis.py, which reuses many of your validation methods.

Looking forward to your reply.

[NGeorgescu]

Dang. Wow, Nice. Indeed this looks like a solution for 19 dice with 9*19=171 faces each, with a 770/1539= 50.032% domination, with each die k beating the next k+g-th (mod 19) die for each g in {1, 4, 5, 6, 7, 9, 11, 16, 17}. Nice!

It looks like your set is based off of the domination graph (w) for 19 players. so you can just generate the chart like so:

w = (1, 4, 5, 6, 7, 9, 11, 16, 17)
n = len(w)*2+1
d = list(zip(*sorted([[(i+j*k)%n+i*n*len(w)+w.index(j)*n for k in range(n)] for i in range(n) for j in w])))

Essentially, for each face set across the dice, subtract the lowest number of that face set, and then d=0 die, has 9 faces for each of the 19 numbers (i), and then the d=1 die has a difference of w between it and the d=0 die.

this also works for w=(1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18) . it seems to also work for e.g. (1, 2, 4, 5, 8, 9, 10, 11, 13, 16, 18, 19, 20, 21, 22, 23, 25, 26, 31, 32, 36, 38, 40, 42, 44, 45, 46, 49, 50, 51, 52, 55, 62, 64, 65, 67, 72, 73, 76). Possibly this works for any cyclical domination tournament graph!

[YouhuaLi]

thanks for the verification. I didn't imagine the things can be done in 3 lines of python code!

And from your reply, I found a stupid bug in my previous gen-dice python program: https://github.com/YouhuaLi/Intransitive_dice/blob/main/gen_intransitive_dice.py and now I fixed it.

and it's so cool to see that this can work for most prime amount of dice. Thanks again for your inspiring work. Going to close this issue here.