3 ms·
It's not stated plainly in the article what the problem is, so here: Each participant rolls a die. For there to be no possibility of a tie, no die can share a
by madibo3156 29d ago
It's not stated plainly in the article what the problem is, so here:
Each participant rolls a die. For there to be no possibility of a tie, no die can share a face number with another die—every face across all dice must be unique. For it to be fair, the distribution of numbers across all faces must be such that no die has an advantage over another die—the odds of rolling the highest number must be exactly the same for each die. The problem is in finding the combination of faces across five dice that satisfies these constraints. One difficulty of this is that each added player changes the whole equation—the odds get recalculated and new faces must be chosen. The secondary goal is to minimize the number of faces on the die.
- JackFr 29d agoArticle was really poor in stating this clearlly, to the extent it made no sense to me. Thank you.
- xp84 29d agoReally a trash article in general, revealing none of the solution, and not even exploring the problem in any way.
- jeremysalwen 29d agoThe key part is that they have to be fair when any subset of the dice is rolled together, not just when all five are rolled. Also if the dice are allowed to be different sizes then it's easier as well.
- jonhohle 29d agoThis is very much missing from the article. It makes the math problem more interesting, but the practical solution is much easier. There are possibly other applications in navigation, radio communication, or other domains that might make this a more interesting problem than just figuring out game ordering.
- asdftemp 29d agoCame here also to point this out, because there is an easy to find solution that lacks only this property. I find this restriction somewhat unsatisfying though, because the easy solution does have the property that, for any smaller number of players, there is a subset that is fair for them (so you could manufacture these dice and resolve any number of players up to the number you have). Requiring same size doesn't make it harder; you can take any solution and inflate the dice (take the lcm of all the sizes, duplicate the face numbers). edit: oops i just double checked my construction and while they give equal go-first probabilities they don't give equal permutation probabilities...
- jeremysalwen 27d agoSorry, by harder I meant for the same number of faces. E.g. the article is about 5 60 sided dice, which was a breakthrough, but there are other known solution where all the dice are less than 60 sided, but they are unequally sized.
- yuye 29d agoThank you, I didn't really understand what they were talking about. Personally, I feel there is an easier approach: Take a regular 12-sided die, assign numbers modulo N (N being the amount of players). Now you assign the first turn fairly for 2, 3, 4, 6 or 12 players. Add a d20 and that covers 5 or 10 players, too.
- geon 29d agoYou mean you roll a single die and use the value to index an array of players? That’s the pragmatic solution. The article is about an interesting mathematical puzzle, not actually solving a real problem. Also, an n-sided die is fair for 2 to n players if you discard rolls above the number of players.
- interroboink 29d agoThe article states: > The golf-ball-sized dice are now available to buy ... So, not entirely just a math puzzle. But probably dice only math nerds will buy (: I agree the math problem does not map well to a real problem players are having.
- nottorp 29d ago> But probably dice only math nerds will buy (: You don't have to buy them to use them. For example I own a baggie of D(4-20) dice but I don't and have never played tabletop RPGs. This set may end up too expensive for my "i know i'll never use it" budget, but other than that I'd get one.
- consp 29d agoThat would preclude everyone from having a throw. Which is likely more fair but doesn't feel fair.
- Lvl999Noob 29d agoThis made me think of a hypothetical game where the players roll dice to determine their order of turns. The rolling will continue until every player is assigned a turn. If some other player rolls multiple times in the middle then that player gets multiple turns. So for example with a 6 sided die and 2 players, faces 1, 3, 5 correspond to player 1 and 2, 4, 6 to player 2. They roll dice and the rolls come out as 1, 1, 5, 3, 5, 2. That means player 1 will get a turn 5 times per round while player 2 gets 1 turn. To make it fairer, player 2 would receive some sort of advantage corresponding to the lack of turns compared to player 1. The game would be designed in such a way that novices would prefer getting multiple turns in a round while experts would prefer to get a single turn for themselves and maximizing the total number of turns per round.
- mikae1 29d agoIs there are a reason why you mention die, not dice, so many times in your post? Do you actually mean die? Honest question since it's repeated.
- zamadatix 29d ago"Die" is a common singular form of "dice". The relative prevalence of "die" vs "dice" for this is regionally dependent. In general, English can't make up its mind with a lot of things involving words which end in a "sss" sound.
- dspillett 29d agoDie is singular, dice is plural. 1 die, 2 dice, 3 dice, … It used to be something people were corrected on, but these days dice is accepted as the singular too and die is starting to be seen as a little antiquated.
- mikae1 28d agoThanks.:)
- deleted 29d ago[deleted]
- Wilson2000 29d agoThanks came looking for this explanation
- kwar13 26d agook finally. the article made little sense