8 ms·

Snarky answer is to divide by 20. But I wonder if a die that large is even fair. Presumably a lot of the randomness in a coin or 6 sided die is that each bounce

Snarky answer is to divide by 20. But I wonder if a die that large is even fair. Presumably a lot of the randomness in a coin or 6 sided die is that each bounce can flip the object multiple times, generating a roughly uniform distribution after a few bounces. If its too large, it may only reach a portion of the neighboring values at each bounce.

dsp1234 10y ago
only reach a portion of the neighboring values at each bounce From the picture of the dice[0], it looks like it would still be fair enough due to the fact that there is a large difference in the numbers available 'nearby' any one spot. But since it's big (but not super big), I'd guess that it would probably be rolled towards some sort of back stop, which would allow for additional opportunities for it to bounce. [0] - http://www.newyorker.com/wp-content/uploads/2016/04/Roberts-Hundred-Twenty-Sided-Die-690x516-1461623452.jpg http://www.newyorker.com/wp-content/uploads/2016/04/Roberts-...
- LanceH 10y ago
  One of the problems with a d100 that I saw is that it can be rolled along an axis somewhat reliably. If the numbers are well distributed, the average and those above/below average may still be sufficient. Specific numbers would be avoided by putting them at the poles, or others given greater chance by putting them along the equator of the roll. I have not seen the d120, I don't know if the points would bounce it off its axis or not.
  - mseebach 10y ago
    If you want a random value in the range, that's probably fine, but it would be bad for a roulette-style game, where you bet on a single, specific number. If you can indeed roll it on an axis reliably, you can increase your odds significantly.
  - jonathankoren 10y ago
    True. The problem I remember about a friend's d100 was that it was basically a golf ball and the damn thing rolled and rolled and rolled...
    - mhd 10y ago
      Yes, it always was a neat gimmick, but in practice, using two ten-sided dice was a far superior approach. d30s were bad enough, but at least with them simulating (e.g. with a d6 and d10) wasn't as intuitive.
- logicallee 10y ago
  > it looks like it would still be fair enough [if it only reaches a portion of the neighboring values at each bounce] due to the fact that there is a large difference in the numbers available 'nearby' any one spot what is this, NSA logic day? :-D (This is my way of saying that your argument actually results in really low randomness. It means the random process has some memory and has far less distribution of states than you would expect. your argument is like saying a good way to get a random number between 1 and 1,000,000 is to flip a coin, then heads it's 170,158; tails it's 587,439. There's a large difference between 170,158 and 587,439 but those two numbers wouldn't be random AT ALL, because all the other numbers couldn't come up. you're saying the die would 'still be fair enough' because the numbers that can come up are far from each other... well, no...)
  - chronial 10y ago
    You are confusing the definitions of "fair" and "random".
    - deleted 10y ago
      [deleted]
    - logicallee 10y ago
      fair means random. (for dice, coins, etc)
      - logicallee 10y ago
        not sure how someone can downvote me, if you google "define dice fair" you get "In mathematics we say 'fair dice' when we mean that there is an equally likely chance of landing on any face", i.e. random and equally distributed.
  - dsp1234 10y ago
    I'm not really sure what the argument here is. Given the fact that each vertex of the die has 10 triangles that sum to 595, and including a non-malicious roll against a backdrop, I don't see how this die is any more or less fair than a normal d6 (which I believe we can concede is 'fair'). After all, if you want to cheat at dice, then you can cheat at dice regardless of any common understanding of 'fairness'. In particular, I was responding to the following comment, "If its too large, it may only reach a portion of the neighboring values at each bounce". My argument was only that if you drop the dice from say a distance of 3", and it doesn't bounce then at a minimum, you wouldn't get a large grouping of numbers that are all near each other (Even if you were able to somehow pick a specific 'vertex' to always land up, you're going to have a total average of 59.5). In other words, you couldn't drop the die such that you could guarantee a range of 110-120 (which you could for example do on a MTG spindown die, which is fair but not uniform). In other words, even if there is no bounce, a typical rolling of the dice would be 'good enough' for say a pen and paper RPG, and even just dropping it without the bounce is likely enough to give non-Vegas levels of 'fairness' even if 'it may only reach a portion of the neighboring values at each bounce'.
- btilly 10y ago
  According to the article, every vertex that sticks out has 10 triangles whose sum is 595. So it is as fair as can be managed at any point.
  - laxatives 10y ago
    That enforces that the mean value should be close to 60, but doens't say much about whether it is fair in that it should have also have a uniform distribution.
analog31 10y ago
When I was a kid, I played D&D once or twice, and noticed on one of the dice, that the edges were somewhat rounded off, and the faces had different areas. I don't know if it was by intent, but I was pretty sure that those dice would favor certain faces.

dsp1234 10y ago

only reach a portion of the neighboring values at each bounce From the picture of the dice[0], it looks like it would still be fair enough due to the fact that there is a large difference in the numbers available 'nearby' any one spot. But since it's big (but not super big), I'd guess that it would probably be rolled towards some sort of back stop, which would allow for additional opportunities for it to bounce. [0] - http://www.newyorker.com/wp-content/uploads/2016/04/Roberts-Hundred-Twenty-Sided-Die-690x516-1461623452.jpg http://www.newyorker.com/wp-content/uploads/2016/04/Roberts-...

LanceH 10y ago
One of the problems with a d100 that I saw is that it can be rolled along an axis somewhat reliably. If the numbers are well distributed, the average and those above/below average may still be sufficient. Specific numbers would be avoided by putting them at the poles, or others given greater chance by putting them along the equator of the roll. I have not seen the d120, I don't know if the points would bounce it off its axis or not.
- mseebach 10y ago
  If you want a random value in the range, that's probably fine, but it would be bad for a roulette-style game, where you bet on a single, specific number. If you can indeed roll it on an axis reliably, you can increase your odds significantly.
- jonathankoren 10y ago
  True. The problem I remember about a friend's d100 was that it was basically a golf ball and the damn thing rolled and rolled and rolled...
  - mhd 10y ago
    Yes, it always was a neat gimmick, but in practice, using two ten-sided dice was a far superior approach. d30s were bad enough, but at least with them simulating (e.g. with a d6 and d10) wasn't as intuitive.
logicallee 10y ago
> it looks like it would still be fair enough [if it only reaches a portion of the neighboring values at each bounce] due to the fact that there is a large difference in the numbers available 'nearby' any one spot what is this, NSA logic day? :-D (This is my way of saying that your argument actually results in really low randomness. It means the random process has some memory and has far less distribution of states than you would expect. your argument is like saying a good way to get a random number between 1 and 1,000,000 is to flip a coin, then heads it's 170,158; tails it's 587,439. There's a large difference between 170,158 and 587,439 but those two numbers wouldn't be random AT ALL, because all the other numbers couldn't come up. you're saying the die would 'still be fair enough' because the numbers that can come up are far from each other... well, no...)
- chronial 10y ago
  You are confusing the definitions of "fair" and "random".
  - deleted 10y ago
    [deleted]
  - logicallee 10y ago
    fair means random. (for dice, coins, etc)
    - logicallee 10y ago
      not sure how someone can downvote me, if you google "define dice fair" you get "In mathematics we say 'fair dice' when we mean that there is an equally likely chance of landing on any face", i.e. random and equally distributed.
- dsp1234 10y ago
  I'm not really sure what the argument here is. Given the fact that each vertex of the die has 10 triangles that sum to 595, and including a non-malicious roll against a backdrop, I don't see how this die is any more or less fair than a normal d6 (which I believe we can concede is 'fair'). After all, if you want to cheat at dice, then you can cheat at dice regardless of any common understanding of 'fairness'. In particular, I was responding to the following comment, "If its too large, it may only reach a portion of the neighboring values at each bounce". My argument was only that if you drop the dice from say a distance of 3", and it doesn't bounce then at a minimum, you wouldn't get a large grouping of numbers that are all near each other (Even if you were able to somehow pick a specific 'vertex' to always land up, you're going to have a total average of 59.5). In other words, you couldn't drop the die such that you could guarantee a range of 110-120 (which you could for example do on a MTG spindown die, which is fair but not uniform). In other words, even if there is no bounce, a typical rolling of the dice would be 'good enough' for say a pen and paper RPG, and even just dropping it without the bounce is likely enough to give non-Vegas levels of 'fairness' even if 'it may only reach a portion of the neighboring values at each bounce'.
btilly 10y ago
According to the article, every vertex that sticks out has 10 triangles whose sum is 595. So it is as fair as can be managed at any point.
- laxatives 10y ago
  That enforces that the mean value should be close to 60, but doens't say much about whether it is fair in that it should have also have a uniform distribution.

analog31 10y ago

When I was a kid, I played D&D once or twice, and noticed on one of the dice, that the edges were somewhat rounded off, and the faces had different areas. I don't know if it was by intent, but I was pretty sure that those dice would favor certain faces.