Air bubble in dice-affecting rolls?

[arscott]

Hmm. Interesting Video.

Casino dice are flung across the table, though--I'm not sure that the average roll of a sharp-edged d6 at a D&D table is going to provide enough kinetic energy to randomize the result (or at least, not without knocking over some miniatures along the way).

 

[Surgoshan]

Heck no.More or less, unless you're actually running a trial of a few thousand rolls or more and tracking the frequency of each result, it should be minor. What's more, if a 20-sider adds up to 21 on opposite sides like most do, it will have an average roll identical to a fair die.-O

1) I agree that the effect will be minor. However, I roll my d20 a couple dozen times a game. When you go through the weeks, through the campaign, it adds up.

2) I disagree that the average will be the same. You're assuming that the irregularities are regular. That is, that the die has been flattened so that it's thinner in one direction than the other. If this were true then you'd be right; the average would be the same. The die would show a marked preference for two faces, say 9 and 12. However, that's not the case. The irregularities of the dice are random, so the center of gravity has in fact shifted. The interaction between the shape of the die and the center of gravity will be somewhat complex, but the end result will be a marked preference for a certain face, or a collection of faces around a certain point on the face of the die.

The end result is that the average will not be the same, and that certain rolls will be favored over others.

For example, let's say that a die is formed so that the it's narrower 8-13 than it is 2-19. By your assumption, the die would land on 8 or 13 more often than anything else (and, frankly, that'd still be pretty ). However, in reality the center of gravity will be randomly shifted so that either 8 or 13 will be preferred. And we know that that preference will show because the rounding of the edges means that the die will roll further and thus be more free to find its optimax* solution. The irregularity of the die and its rounded edges add up to an unpleasant combination; its preferred face will show quite strongly.

Do air bubbles affect rolls? Yes. Even more strongly than you might think. Air has an incredibly low density; the center of gravity of a die with a bubble will be radically shifted and the face closest to the bubble will be favored.

* Optimax in the sense that nature seeks the minimum potential energy.

 

[frankthedm]

What does everyone else do about the pieces of the sprue left on gamescience dice? Mine had some pretty big pieces that definitely affected rolling, so I had to shave them off... which probably also affected rolling. At least tumbled dice look regular.

Sprue? Now that does sound somewhat unprofessional to leave on. Still, a careful cut with an X-acto blade ought to work.

I like my gamescience dice more for aesthetics than for ultimate statistical randomness.

they do look like rock candy .

 

[Achan hiArusa]

Interesting and informative video, I've seen his diagrams for years. I only have one complaint, I cringed everytime he used "dice" for a single die.

 

[Wulf Ratbane]

Well, I have to admit his pitch slipped a little when he kept talking about killing off PCs like it was a bad thing.

 

[Pbartender]

Yes. Got 20 minutes of free time? Let Mr. Zocchi explain.

Mr. Zocchi makes a few particular mistakes...

To make a perfectly random die, you need all the faces and edges to be perfectly uniform. Sharp edge are NOT required, so long as the rounded edges are all perfectly uniform with each other. Granted... Sharp edges are much, much easier to make uniform. Likewise, the faces should all be of the same size, shape and flatness -- there, he truly is in the right and does take the advantage.

Also, the center of mass of the die must be in the exact geometrical center of the die. No matter what Mr. Zocchi says, ANY blemish -- even his little sprue mark -- makes a difference. His dice may stack perfectly, but they will tend to roll toward whatever number is opposite the divot. For that matter the numbers engraved on the dice themselves can make a difference. A "20" sits opposite of the "1", but engraving a 20 shaves a lot more material out of the die than engraving a "1", therefore, even perfect dice will tend to roll high, on average (the lower numbers tend to have more mass on their sides than the higher numbers).

 

[Alan Shutko]

I have a noticeable one on my 6-sider. And I don't know how much of a difference it makes. According to Lou, it doesn't make a difference; he talks about it in the video. I don't know if I believe him.

I had a big one on my d20. If it were the d6 I don't think it would make a difference, but it stuck out so far on my d20 that it was noticeably unstable ju balancing it there by hand, let alone rolling it.

Still, it's way better than my Dwarven Stones, which are beautiful, but sometimes visibly distorted.

 

[Obryn]

I had a big one on my d20. If it were the d6 I don't think it would make a difference, but it stuck out so far on my d20 that it was noticeably unstable ju balancing it there by hand, let alone rolling it.

Yeah, on a d20 it's a big deal. Fortunately, I don't have any noticeable pointy things sticking out of most of my d20's - except for one, which I think is green.

On the other hand, my tan gamescience d20 is somewhat ... bulbous? I can't think of a better term. The supposed-to-be-flat sides are bowed outwards, meaning it doesn't sit flat.

Still, it's way better than my Dwarven Stones, which are beautiful, but sometimes visibly distorted.

Well, when you use rock instead of plastic, I think that's somewhat expected.

-O

 

[Dedekind]

If folks are actually concerned about bias in a die, perform a chi-square test on it. I've performed probably 100 tests of 200 trials or more, and I have yet to find a commercial die that shows any bias over 200 trials.

I've done similar things. I've never found a d20 that didn't give an average statistically indistiguishable from 10.5. However, my concern with a chi-squared test is that it may not detect a bias for/against a particular number. For example, if 3 and 17 are underrepresented and 5 and 15 are over represented, I think chi-squared wouldn't reject.

I've tried testing the relative significance of individual numbers and I have been able to find a bias on one of my dice against 1, 4, 14, and 16, and in favor of 5. I'll point out that 1 and 4, and 14 and 16 share a point, while 5 shares a side with 4. But I'm only dealing with N=200 and my test is really only a t-test that way isn't perfect. (One day I will double my power and add another 600 rolls, but even then I'm sure there is a better way to do this then what I know about.)

 

[starwed]

my concern with a chi-squared test is that it may not detect a bias for/against a particular number. For example, if 3 and 17 are underrepresented and 5 and 15 are over represented, I think chi-squared wouldn't reject.

A chi-squared test would: it tests whether a particular distribution fits the data.