Are 3D dice fair?

Hey guys, funny thing this... my players think that icons on the map effect the 3D dice (like bouching off of a wall. Now it's happened more then once that the die bounched off of something and came down on a low number. Personally I think: If it can bounce off on a low number, it can also bounce off on a high one. So yeah, how fair are the 3D dice exactly?

That's what I thought :P I'll be sure to inform them next time if they mention.

That paper is about the RNG and it sounds like the method that the 3D dice use is different (even if the RNG is involved to randomize starting parameters). That said, I'm pretty confident that they are 'fair dice'. I'm simply addressing the relevancy of the post about the RNG. Randomness is 'clumpy'. It doesn't ensure a smooth distribution. If it did than every roll of 6d6 should produce a total of 21 (because you have 1 1, 1 2, 1 3, etc...). Further more humans are pattern matching machines. We are hardwired to recognize patterns even when there are things in the way to break up that pattern. It's a feature of evolution as the monkeys that could see the tiger in the tall grass ran away and those that couldn't got et. That evolutionary pressure has led to lots of false positives, however. Basically it would be better for a monkey to run away from a tiger that wasn't there then it would be for a monkey to stick around when one was there. That's why you can see faces in the front of cars or the boles of trees and why when a person looks at clouds they can see different animals. So when the clumpiness of random numbers meets up with the human ability to see patterns you will get of these false identifications of patterns. This is where a fair number of things like 'lucky t-shirts' and the like come from. Probably a lot of lucky dice are similar, although it is possible for a die to be strongly biased as well. Which brings us to the last point that people often miss about PRNGs (pseudo-random number generators, which is probably what the RNG actually is). While it is possible for a die to be strongly biased it is impossible for a die to be totally unbiased. There will always be imperfections in the mixing and density of the resins, the precision of the shape, the carving of the numbers, etc. Any die subjected to enough rolls that are analyzed through statistical methods such as a Chi-squared test will eventually fail, even the dice used in Atlantic City casinos (which are a very simple shape and fairly rigidly controlled) will eventually fail because of micro-imperfections. What this means is that a PRNG doesn't have to be completely random. It just has to be 'random enough', and although nobody has done a statistical analysis of the 3D dice I am fairly comfortable in saying that the methods Kristin describes should produce dice that are probably more than 'random enough', especially with shapes such as D12's and D20's.

One other thing to consider is that physical d20 dice are not actually random. Most of them are short on the 10-11 axis and long on the 1-20 axis so you will see less 1s and 20s. Additionally, they are sometimes improperly weighted. You can test the axis length with a micrometer and the weighting by floating the dice in a high saline solution. If you roll them while floating weighted dice will change direction at the end of the roll. The faster the direction change the more weighted the die. - Gauss

Okami said: Which brings us to the last point that people often miss about PRNGs (pseudo-random number generators, which is probably what the RNG actually is). Any computer-generated random number is going to be a PRNG unless the generator is pulling from an appropriately entropic source (random.org uses atmospheric noise). Eric's thread says the Roll20 RNG uses a server-side entropic source to select the seed, but from there the RNG is pseudorandom.

Gauss said: One other thing to consider is that physical d20 dice are not actually random. Most of them are short on the 10-11 axis and long on the 1-20 axis so you will see less 1s and 20s. Additionally, they are sometimes improperly weighted. You can test the axis length with a micrometer and the weighting by floating the dice in a high saline solution. If you roll them while floating weighted dice will change direction at the end of the roll. The faster the direction change the more weighted the die. - Gauss thats why you buy game science dice ;-)

Game Science dice are more accurate but not completely. The #14 (face opposite the 7 where the flashing is) is rarely rolled. Now, you are supposed to file that down but people rarely file it down to the proper level. As a result that face gets rolled far less often. <a href="http://www.awesomedice.com/blog/353/d20-dice-randomness-test-chessex-vs-gamescience/" rel="nofollow">http://www.awesomedice.com/blog/353/d20-dice-randomness-test-chessex-vs-gamescience/</a> - Gauss

It also looks like they were comparing a Game Science die against one of the cheaper Chessex dice. Huge math nerd that I am I actually used micrometers on my dice and rolled Chi-Square tests on them at one point. It turns out that certain 'lines' of Chessex dice are less accurate than others (I believe that I found that the Lustrous line tended to do very well). I don't think it was simply a result of the materials as the geometric accuracy of the dice seemed to much lower on some lines than others. Perhaps Chessex contracts out the actual manufacturing to different companies or they use different molding processes (and subsequently different molds) for the different materials.

While I haven't done a chi-square test on my dice I did measure 20+ d20s with a micrometer. I found differences in chessex dice even in the same line (I have about 8 of the same chessex line). - Gauss

Kristin C. said: The only thing the dice can collide with are themselves and the boundaries of the play space (otherwise they could roll to rest where you couldn't see them). The throw trajectory &amp; force as well as what side the dice starts on before the throw is randomized. And that alone should make the dice completely random. Think about it: Even if the physics engine was really, really, really bad, and would ALWAYS roll the opposite side of what the dice starts at, it would be random. Because the side it starts at is random, using the Roll20 RNG and therefor the side opposite of it is random too. Now the one thing that could make it biased would be if actually the 1-20 axis was biased or so, like real dice sometimes are, but I assume the 3D model is perfectly balanced,

Man..... So much nerd talk.. i'm so in love! ;-)

Nerdvana