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Comment by archargelod | Hacker News Reader

Can somebody explain why not just make a die with 5! sides, and roll it once to decide the order? With each side having a unique order printed e.g. 12345 -> 12354 -> ...

Especially, that 120-sided dice are already invented and commercially available.

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Because the question isn’t can you make a rice with 5! Sides but can you make it so 5 players can roll simultaneously individual dice with a minimal number of sides per dice and never tie and always be fair.

Sure you can fly a helicopter to the top of Everest, but it’s not the same as climbing Everest even if the outcome is the same.

I wanted to say "You actually can't fly a helicopter to the top of Everest, the air is too thin", but apparently it's been done exactly twice. Stripped down specially chopper and ideal weather conditions.

From the article: "During a dinner conversation at a gaming convention in 2012, Eric Harshbarger was asked by a board game designer if he could come up with dice that would determine who goes first — without the possibility of a tie. The idea was simple: settle the first turn quickly and get on with the game."

The original challenge was to design dice (I assume a single die would satisfy the requirement since the number of dice wasn't the point) that would quickly determine which of five players would go first. Nothing about the challenge required that there be five dice. A five-sided die would certainly be the simplest way, and would be marginally faster than having five players each roll a separate die and then compare the numbers.

How do you decide who gets to roll the single die?

Gee, you need a way to rank the players to decide.

> Gee, you need a way to rank the players to decide.

Do you also need to randomize a neural net before training it to play Tic-tac-toe? https://simple.wikipedia.org/wiki/Hacker_koan

The provenance doesn’t matter because they settled on a difficult mathematical problem to solve because it was difficult to solve and would require clever solutions that answered more fundamental mathematical questions than the banal problem of choosing who goes first in a game. That was just the framing that motivated the larger math question, in which the number of dice does matter, because it’s a more interesting question.

> Can somebody explain why not just make a die with 5! sides, and roll it once to decide the order?

Hey, that’s a good idea—now we just need to decide who rolls the die. …Well, if we had a set of die that each player could roll one of, and the highest number rolled gets to roll the 120-sided die. Of course, we’d have to ensure that there’s no chance of a tie.

Hmm… this idea has legs…

120 sided dice roll for a long time and don't have much room for printing

And how do you decide who is going to throw that one die?

Literally doesn't matter, player closest to dice at the moment you open the box.

That's why you need those 5 dice to decide it.

Or, like my gaming group does. Just roll again between whoever ties. And in the extremely rare event that you tie again, roll again. And if youve managed to get to the heat death of the universe and have tied three times, roll a fourth time.

And for the pedants, you arent rolling every microsecond for millennia to make it plausibly likely that you have that many ties. You are rolling a handful of times before a game.

Its an interesting math problem to solve, but its way more effort to solve than the real world solutions.

I get the impression one of the unwritten requirements is that each player gets to roll their own die

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