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Author Topic: Random Stuff Part III  (Read 645388 times)

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Kuildeous

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Re: Random Stuff Part III
« Reply #350 on: February 26, 2016, 09:54:41 am »
0

Well, one could argue that a d10 is not a platonic solid and thus the results are not evenly distributed, right? In that sense, d20 is "more random" I think. That's why I prefer d20 to d10 anyway.

Hmm, I can see that argument, but I think a d10 is still evenly distributed. The even and odd sides both have a 50% of coming up. Given that, each of the five numbers on that side have a 20% chance of coming up. So you still have a uniform distribution of results even though the d10 is not a platonic solid. Even the wonky dice like the d46 that are built like the d10 would be evenly distributed. I heard rumors of a d17, though I'd be really curious about that distribution.

I view the d20 and d100 as essentially identical. If all you care about are 5% increments, then both do the job just as well. Granted, you only need to roll 1 die with a d20 and 2 dice with a d100 (unless you use a heathen golf ball). If you need greater degrees of successes, then a d100 will let you capture the 2% chance of such-and-such happening. And really if you need more precision than that, you could technically implement a d1000 or even d10k roll, though that is probably not a game I would be interested in.
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Witherweaver

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Re: Random Stuff Part III
« Reply #351 on: February 26, 2016, 09:56:38 am »
0

Well, one could argue that a d10 is not a platonic solid and thus the results are not evenly distributed, right? In that sense, d20 is "more random" I think. That's why I prefer d20 to d10 anyway.

Hmm, I can see that argument, but I think a d10 is still evenly distributed. The even and odd sides both have a 50% of coming up. Given that, each of the five numbers on that side have a 20% chance of coming up. So you still have a uniform distribution of results even though the d10 is not a platonic solid. Even the wonky dice like the d46 that are built like the d10 would be evenly distributed. I heard rumors of a d17, though I'd be really curious about that distribution.

I view the d20 and d100 as essentially identical. If all you care about are 5% increments, then both do the job just as well. Granted, you only need to roll 1 die with a d20 and 2 dice with a d100 (unless you use a heathen golf ball). If you need greater degrees of successes, then a d100 will let you capture the 2% chance of such-and-such happening. And really if you need more precision than that, you could technically implement a d1000 or even d10k roll, though that is probably not a game I would be interested in.


Why do you think a d10's results are uniformly distributed?  It isn't regular.
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Watno

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Re: Random Stuff Part III
« Reply #352 on: February 26, 2016, 10:42:52 am »
+2

Well, one could argue that a d10 is not a platonic solid and thus the results are not evenly distributed, right? In that sense, d20 is "more random" I think. That's why I prefer d20 to d10 anyway.

Hmm, I can see that argument, but I think a d10 is still evenly distributed. The even and odd sides both have a 50% of coming up. Given that, each of the five numbers on that side have a 20% chance of coming up. So you still have a uniform distribution of results even though the d10 is not a platonic solid. Even the wonky dice like the d46 that are built like the d10 would be evenly distributed. I heard rumors of a d17, though I'd be really curious about that distribution.

I view the d20 and d100 as essentially identical. If all you care about are 5% increments, then both do the job just as well. Granted, you only need to roll 1 die with a d20 and 2 dice with a d100 (unless you use a heathen golf ball). If you need greater degrees of successes, then a d100 will let you capture the 2% chance of such-and-such happening. And really if you need more precision than that, you could technically implement a d1000 or even d10k roll, though that is probably not a game I would be interested in.


Why do you think a d10's results are uniformly distributed?  It isn't regular.

It's symmetric?
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Witherweaver

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Re: Random Stuff Part III
« Reply #353 on: February 26, 2016, 10:48:27 am »
0

Well, one could argue that a d10 is not a platonic solid and thus the results are not evenly distributed, right? In that sense, d20 is "more random" I think. That's why I prefer d20 to d10 anyway.

Hmm, I can see that argument, but I think a d10 is still evenly distributed. The even and odd sides both have a 50% of coming up. Given that, each of the five numbers on that side have a 20% chance of coming up. So you still have a uniform distribution of results even though the d10 is not a platonic solid. Even the wonky dice like the d46 that are built like the d10 would be evenly distributed. I heard rumors of a d17, though I'd be really curious about that distribution.

I view the d20 and d100 as essentially identical. If all you care about are 5% increments, then both do the job just as well. Granted, you only need to roll 1 die with a d20 and 2 dice with a d100 (unless you use a heathen golf ball). If you need greater degrees of successes, then a d100 will let you capture the 2% chance of such-and-such happening. And really if you need more precision than that, you could technically implement a d1000 or even d10k roll, though that is probably not a game I would be interested in.


Why do you think a d10's results are uniformly distributed?  It isn't regular.

It's symmetric?

What do you mean by this?  I'm pretty sure it does not have the same symmetries that a (regular) die with 4, 6, 8, 12, or 20 sides has.
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qmech

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Re: Random Stuff Part III
« Reply #354 on: February 26, 2016, 10:53:05 am »
+3

Well, one could argue that a d10 is not a platonic solid and thus the results are not evenly distributed, right? In that sense, d20 is "more random" I think. That's why I prefer d20 to d10 anyway.

Hmm, I can see that argument, but I think a d10 is still evenly distributed. The even and odd sides both have a 50% of coming up. Given that, each of the five numbers on that side have a 20% chance of coming up. So you still have a uniform distribution of results even though the d10 is not a platonic solid. Even the wonky dice like the d46 that are built like the d10 would be evenly distributed. I heard rumors of a d17, though I'd be really curious about that distribution.

I view the d20 and d100 as essentially identical. If all you care about are 5% increments, then both do the job just as well. Granted, you only need to roll 1 die with a d20 and 2 dice with a d100 (unless you use a heathen golf ball). If you need greater degrees of successes, then a d100 will let you capture the 2% chance of such-and-such happening. And really if you need more precision than that, you could technically implement a d1000 or even d10k roll, though that is probably not a game I would be interested in.


Why do you think a d10's results are uniformly distributed?  It isn't regular.

It's symmetric?

What do you mean by this?  I'm pretty sure it does not have the same symmetries that a (regular) die with 4, 6, 8, 12, or 20 sides has.

It has a transitive symmetry group: given any two faces A and B I can rotate (and reflect if necessary, although it isn't for a d10) so that A is now in the position formerly occupied by B.
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Witherweaver

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Re: Random Stuff Part III
« Reply #355 on: February 26, 2016, 11:02:29 am »
0

But it doesn't have edge and vertex symmetry.  Wouldn't this lead to a not perfectly uniform distribution?

Well, speaking intuitively.  I'm not quite sure how it all relates.
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Awaclus

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Re: Random Stuff Part III
« Reply #356 on: February 26, 2016, 11:04:07 am »
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I like the d100 because you immediately get the probability of the roll in a comprehensible format. When you have to roll 15 or higher on a d20, first you have to do 20-14=6 and then you get 6/20 as the odds and then you still have to turn that into 3/10 or 30/100 before you can actually have a good idea of how likely it is (it's not really difficult, but it's enough of a bother that I never actually do it). When you have to roll 30 or lower on a d100, you can immediately tell that the odds are 30%.
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LastFootnote

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Re: Random Stuff Part III
« Reply #357 on: February 26, 2016, 11:04:41 am »
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But it doesn't have edge and vertex symmetry.  Wouldn't this lead to a not perfectly uniform distribution?

Why would it?
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Watno

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Re: Random Stuff Part III
« Reply #358 on: February 26, 2016, 11:05:10 am »
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The sides are basically indistinguishable. How could one be more probable?
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Kuildeous

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Re: Random Stuff Part III
« Reply #359 on: February 26, 2016, 11:05:27 am »
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Why do you think a d10's results are uniformly distributed?  It isn't regular.

Like I said, you have two equal chances of landing on the odd or even side. You then have five equal chances of getting 1, 3, 5, 7, 9 or 2, 4, 6, 8, 0, depending on what the first one was. Of course, this assumes a perfectly cut d10 so that all the planes are congruent with congruent angles between them, but we have to make that assumption for all dice anyway.

I'm not sure how I can add to that. Without trying to sound like a cop-out, why would not being regular preclude even distribution? How does a d10 not achieve even distribution?
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Witherweaver

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Re: Random Stuff Part III
« Reply #360 on: February 26, 2016, 11:09:15 am »
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I'm just thinking that while the faces are "the same", the edges are not.  And so the rolling process isn't, uh.. uniform.
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Witherweaver

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Re: Random Stuff Part III
« Reply #361 on: February 26, 2016, 11:10:01 am »
+1

Why do you think a d10's results are uniformly distributed?  It isn't regular.

Like I said, you have two equal chances of landing on the odd or even side. You then have five equal chances of getting 1, 3, 5, 7, 9 or 2, 4, 6, 8, 0, depending on what the first one was. Of course, this assumes a perfectly cut d10 so that all the planes are congruent with congruent angles between them, but we have to make that assumption for all dice anyway.

I'm not sure how I can add to that. Without trying to sound like a cop-out, why would not being regular preclude even distribution? How does a d10 not achieve even distribution?

It's the "equal chance" part that isn't clear.  You're just restating 'uniform'.
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LastFootnote

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Re: Random Stuff Part III
« Reply #362 on: February 26, 2016, 11:11:12 am »
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Why do you think a d10's results are uniformly distributed?  It isn't regular.

Like I said, you have two equal chances of landing on the odd or even side. You then have five equal chances of getting 1, 3, 5, 7, 9 or 2, 4, 6, 8, 0, depending on what the first one was. Of course, this assumes a perfectly cut d10 so that all the planes are congruent with congruent angles between them, but we have to make that assumption for all dice anyway.

I'm not sure how I can add to that. Without trying to sound like a cop-out, why would not being regular preclude even distribution? How does a d10 not achieve even distribution?

It's the "equal chance" part that isn't clear.  You're just restating 'uniform'.

That's what "uniform" means. An equal chance of each result.
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Witherweaver

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Re: Random Stuff Part III
« Reply #363 on: February 26, 2016, 11:12:09 am »
0

Why do you think a d10's results are uniformly distributed?  It isn't regular.

Like I said, you have two equal chances of landing on the odd or even side. You then have five equal chances of getting 1, 3, 5, 7, 9 or 2, 4, 6, 8, 0, depending on what the first one was. Of course, this assumes a perfectly cut d10 so that all the planes are congruent with congruent angles between them, but we have to make that assumption for all dice anyway.

I'm not sure how I can add to that. Without trying to sound like a cop-out, why would not being regular preclude even distribution? How does a d10 not achieve even distribution?

It's the "equal chance" part that isn't clear.  You're just restating 'uniform'.

That's what "uniform" means. An equal chance of each result.

Yes I know this.  My point is Kuildeous is not explaining, he's restating.
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LastFootnote

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Re: Random Stuff Part III
« Reply #364 on: February 26, 2016, 11:13:37 am »
0

Why do you think a d10's results are uniformly distributed?  It isn't regular.

Like I said, you have two equal chances of landing on the odd or even side. You then have five equal chances of getting 1, 3, 5, 7, 9 or 2, 4, 6, 8, 0, depending on what the first one was. Of course, this assumes a perfectly cut d10 so that all the planes are congruent with congruent angles between them, but we have to make that assumption for all dice anyway.

I'm not sure how I can add to that. Without trying to sound like a cop-out, why would not being regular preclude even distribution? How does a d10 not achieve even distribution?

It's the "equal chance" part that isn't clear.  You're just restating 'uniform'.

That's what "uniform" means. An equal chance of each result.

Yes I know this.  My point is Kuildeous is not explaining, he's restating.

So…you're arguing just to argue, and being obstinate just for the sake of being obstinate?
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Witherweaver

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Re: Random Stuff Part III
« Reply #365 on: February 26, 2016, 11:14:53 am »
0

Why do you think a d10's results are uniformly distributed?  It isn't regular.

Like I said, you have two equal chances of landing on the odd or even side. You then have five equal chances of getting 1, 3, 5, 7, 9 or 2, 4, 6, 8, 0, depending on what the first one was. Of course, this assumes a perfectly cut d10 so that all the planes are congruent with congruent angles between them, but we have to make that assumption for all dice anyway.

I'm not sure how I can add to that. Without trying to sound like a cop-out, why would not being regular preclude even distribution? How does a d10 not achieve even distribution?

It's the "equal chance" part that isn't clear.  You're just restating 'uniform'.

That's what "uniform" means. An equal chance of each result.

Yes I know this.  My point is Kuildeous is not explaining, he's restating.

So…you're arguing just to argue, and being obstinate just for the sake of being obstinate?

No, I'm saying why is it uniform.
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Witherweaver

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Re: Random Stuff Part III
« Reply #366 on: February 26, 2016, 11:16:25 am »
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Or really I'm saying wondering how different symmetries lead to the end distribution.
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pacovf

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Re: Random Stuff Part III
« Reply #367 on: February 26, 2016, 11:45:48 am »
+1

Or really I'm saying wondering how different symmetries lead to the end distribution.

It has a transitive symmetry group: given any two faces A and B I can rotate (and reflect if necessary, although it isn't for a d10) so that A is now in the position formerly occupied by B.
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Witherweaver

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Re: Random Stuff Part III
« Reply #368 on: February 26, 2016, 11:58:47 am »
+1

Or really I'm saying wondering how different symmetries lead to the end distribution.

It has a transitive symmetry group: given any two faces A and B I can rotate (and reflect if necessary, although it isn't for a d10) so that A is now in the position formerly occupied by B.

Yes but the vertices don't enjoy the same symmetry.

But maybe there's just two sets of vertex symmetries ("top" <-> "bottom" and the "sides".. or maybe the sides themselves break into two groups, I have to actually look at a die), which gives what Kuildeous is getting at.
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Watno

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Re: Random Stuff Part III
« Reply #369 on: February 26, 2016, 12:02:29 pm »
+2

I have to actually look at a die
That sounds like an awesome idea.
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pacovf

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Re: Random Stuff Part III
« Reply #370 on: February 26, 2016, 12:04:26 pm »
0

Or really I'm saying wondering how different symmetries lead to the end distribution.

It has a transitive symmetry group: given any two faces A and B I can rotate (and reflect if necessary, although it isn't for a d10) so that A is now in the position formerly occupied by B.

Yes but the vertices don't enjoy the same symmetry.

But maybe there's just two sets of vertex symmetries ("top" <-> "bottom" and the "sides".. or maybe the sides themselves break into two groups, I have to actually look at a die), which gives what Kuildeous is getting at.

You realize that's it's the faces that give you the number, not the vertices, right?
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Witherweaver

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Re: Random Stuff Part III
« Reply #371 on: February 26, 2016, 12:12:28 pm »
+1

But you roll the die, you don't just pick a face at random.  There is a physical process. 

I'm not saying you're all wrong, I'm just wondering if not being regular can effect the rolling process.

Also, the "side edges" on ten sided dice around rounded.. maybe that effect plays equally on all the outcomes.  But the extent to which they're rounded should effect the extent to which the die can tumble about that plane, and if it can't really do that, then it's final result seems dependent upon its initial configuration when you start the roll.  It's not crazy to think you lose "randomness".

But, please, keep treating me like an idiot, because that's fun.
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Watno

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Re: Random Stuff Part III
« Reply #372 on: February 26, 2016, 12:14:44 pm »
+1

If you roll a regular die, like a d6, there's a physical process as well?
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Witherweaver

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Re: Random Stuff Part III
« Reply #373 on: February 26, 2016, 12:16:30 pm »
0

If you roll a regular die, like a d6, there's a physical process as well?

Well, yes, so I suppose the same orientation/tumbling issue applies there.

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Re: Random Stuff Part III
« Reply #374 on: February 26, 2016, 12:29:07 pm »
+1

I find the arrogance some here are showing in this argument annoying. WW is trying to understand what you mean, you're not helping him at all. I still don't fully get it. I think vertices should matter, for example: In an ideal die throw, we can assume that the die is randomly rotated, with a random momentum, when it hits the table. The by far most likely case is that the die hits the table on a vertex. Not all vertices are "the same", so it is not clear why we would get a uniform distribution going from here.
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