5 ms·

> 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 diff

> 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 11y ago
You are confusing the definitions of "fair" and "random".
- deleted 11y ago
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- logicallee 11y ago
  fair means random. (for dice, coins, etc)
  - logicallee 11y 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 11y 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'.
- logicallee 11y ago
  mathematically, if your "range" is one of the ten numbers 108, 43, 21, 18, 32, 40, 79, 50, 94, 59 then it is just as broken as if your "range" is 110-120. it's not considered fair. fair means random and evenly distributed. (when it comes to dice and coins.)
- laxatives 11y 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.
Dylan16807 11y ago
You're reading that post wrong. No matter how you lay out the numbers, a nice hard roll will give you a completely uniform result. The goal here is to make it harder to cheat when you can partially control how the die rolls. Nobody is pretending there is more entropy than the number of outcomes. What we want is a design that can't be influenced in favor of the roller, even when entropy is a bit low. Let's design two layouts for a d100. We'll say that you can roll each design two ways. You can roll it properly and get a random number from 1-100, or you can roll it improperly and it will stay within a cluster of 10 numbers, giving you a random number out of that cluster. The first layout puts similar numbers together. 1-10 are all together, as are 11-20, etc. The second design is laid out so that every tens digit show up in each cluster, and every ones digit shows up in each cluster. Both designs can give you equally random numbers. A proper roll gives you a uniform distribution over 100 numbers, and an improper roll gives you a uniform distribution over 10 numbers. But look at what happens when you apply certain functions to the output. A common use for the d100 might be emulating a d10. If you divide the first die by ten, a proper roll acts like a d10, and an improper roll lets the cheater pick what result they want. With the second die, a proper roll acts like a d10, and an improper roll also acts like a d10. Fairness is preserved when the imperfections in the randomness don't matter. Your coin method looks like it would be a fair way to pick lottery numbers if it was only used once. But it would be a fair way to pick even or odd indefinitely.
- logicallee 11y ago
  I don't think I'm reading that post wrong! The original poster said " But I wonder if a die that large is even fair." Then the response said it's "fair enough" because even if it only spins part of the way, you'll still get one of a group of dissimilar numbers. but that's not fair by the definition of what a fair die is. (it has a definition, if you search google you get "In mathematics we say 'fair dice' when we mean that there is an equally likely chance of landing on any face.") You're basically arguing that dice don't need to be fair. also you completely missed my jab at the NSA breaking RNG's while making them seem "random enough", i.e. getting to quite dissimilar next states while in fact having only a few possible next states.
  - 11y ago

chronial 11y ago

You are confusing the definitions of "fair" and "random".

deleted 11y ago
[deleted]
logicallee 11y ago
fair means random. (for dice, coins, etc)
- logicallee 11y 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 11y 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'.

logicallee 11y ago
mathematically, if your "range" is one of the ten numbers 108, 43, 21, 18, 32, 40, 79, 50, 94, 59 then it is just as broken as if your "range" is 110-120. it's not considered fair. fair means random and evenly distributed. (when it comes to dice and coins.)
laxatives 11y 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.

Dylan16807 11y ago

You're reading that post wrong. No matter how you lay out the numbers, a nice hard roll will give you a completely uniform result. The goal here is to make it harder to cheat when you can partially control how the die rolls. Nobody is pretending there is more entropy than the number of outcomes. What we want is a design that can't be influenced in favor of the roller, even when entropy is a bit low. Let's design two layouts for a d100. We'll say that you can roll each design two ways. You can roll it properly and get a random number from 1-100, or you can roll it improperly and it will stay within a cluster of 10 numbers, giving you a random number out of that cluster. The first layout puts similar numbers together. 1-10 are all together, as are 11-20, etc. The second design is laid out so that every tens digit show up in each cluster, and every ones digit shows up in each cluster. Both designs can give you equally random numbers. A proper roll gives you a uniform distribution over 100 numbers, and an improper roll gives you a uniform distribution over 10 numbers. But look at what happens when you apply certain functions to the output. A common use for the d100 might be emulating a d10. If you divide the first die by ten, a proper roll acts like a d10, and an improper roll lets the cheater pick what result they want. With the second die, a proper roll acts like a d10, and an improper roll also acts like a d10. Fairness is preserved when the imperfections in the randomness don't matter. Your coin method looks like it would be a fair way to pick lottery numbers if it was only used once. But it would be a fair way to pick even or odd indefinitely.

logicallee 11y ago
I don't think I'm reading that post wrong! The original poster said " But I wonder if a die that large is even fair." Then the response said it's "fair enough" because even if it only spins part of the way, you'll still get one of a group of dissimilar numbers. but that's not fair by the definition of what a fair die is. (it has a definition, if you search google you get "In mathematics we say 'fair dice' when we mean that there is an equally likely chance of landing on any face.") You're basically arguing that dice don't need to be fair. also you completely missed my jab at the NSA breaking RNG's while making them seem "random enough", i.e. getting to quite dissimilar next states while in fact having only a few possible next states.
- 11y ago