# REALLY fair d20 gaming dice **URL:** \ **Category:** The Game Room\ **Created:** [August 29, 2017, 5:17pm UTC](https://boards.straightdope.com/t/really-fair-d20-gaming-dice/795041 "2017-08-29T17:17:15Z")\ **Posts on this page:** 15\ **Page:** 1
**Author:** ![Lumpy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lumpy/32/446_2.png) [@Lumpy](https://boards.straightdope.com/u/Lumpy)\ **Post date:** [August 29, 2017, 5:17pm UTC](https://boards.straightdope.com/t/really-fair-d20-gaming-dice/795041/1 "2017-08-29T17:17:15Z")
More than simply having opposite faces sum to the same number; the linked article goes into why one particular arrangement is as unbiased as mathematically possible (that is, random manufacturing flaws won’t make the dice roll a consistently higher or lower than average result). > **[nbd.pdf](https://www2.oberlin.edu/math/faculty/bosch/nbd.pdf)** > > 15.92 MB ---
**Author:** ![eunoia](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/eunoia/32/97_2.png) [@eunoia](https://boards.straightdope.com/u/eunoia)\ **Post date:** [August 29, 2017, 5:29pm UTC](https://boards.straightdope.com/t/really-fair-d20-gaming-dice/795041/2 "2017-08-29T17:29:40Z")
This puts into question every RPG session every played! :eek: Way over my head, but forwarded to someone who is on this like a fat kid on a Smartie. ---
**Author:** ![Hypno-Toad](https://avatars.discourse-cdn.com/v4/letter/h/b2d939/32.png) [@Hypno-Toad](https://boards.straightdope.com/u/Hypno-Toad)\ **Post date:** [August 29, 2017, 5:39pm UTC](https://boards.straightdope.com/t/really-fair-d20-gaming-dice/795041/3 "2017-08-29T17:39:58Z")
I wonder if this would have any effect on a game of\* Infinity\*. You generally try to roll low except for a few situations. But when you are rolling directly against an opponent, you have to roll enough to meet the success threshold but higher than your opponent. So you need to use the entire range of numbers, not just the high end or low end. ---
**Author:** ![What\_Exit](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/what_exit/32/10652_2.png) [@What\_Exit](https://boards.straightdope.com/u/What_Exit)\ **Post date:** [August 29, 2017, 6:33pm UTC](https://boards.straightdope.com/t/really-fair-d20-gaming-dice/795041/4 "2017-08-29T18:33:00Z")
But in the end, has it ever really mattered? The playing field is level and the dice rolling should be secondary to the role playing. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [August 29, 2017, 6:40pm UTC](https://boards.straightdope.com/t/really-fair-d20-gaming-dice/795041/5 "2017-08-29T18:40:53Z")
[Moderating] This is a gaming topic, so off to the Game Room it goes. [Not moderating] I’ve been aware of that paper for a while, and use their results (and the principles behind them) when designing my own dice. I’ve known for a long time that it’s bad for high or low values on a die to be clustered, but wasn’t sure how to quantify clustering. My first d12, for instance, had the 7-8-9-10-11 faces surrounding the 12, which meant that with a little bit of practice at “aiming” for the 12, you could almost always get an above-average result, and that’s clearly not desirable. It’s nice to see that other people are noticing this. ---
**Author:** ![BigT](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bigt/32/12044_2.png) [@BigT](https://boards.straightdope.com/u/BigT)\ **Post date:** [August 29, 2017, 9:50pm UTC](https://boards.straightdope.com/t/really-fair-d20-gaming-dice/795041/6 "2017-08-29T21:50:20Z")
> [@What\_Exit](#): > > But in the end, has it ever really mattered? The playing field is level and the dice rolling should be secondary to the role playing. That entirely depends on how you play. Even in heavy narrative games, if you’re always getting high scores, it can mean you’re supernaturally persuasive or whatever, and all your ideas work, no matter how good they actually are. But, in heavy fighting games, it means whether or not the game is balanced. ---
**Author:** ![Quartz](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/quartz/32/267_2.png) [@Quartz](https://boards.straightdope.com/u/Quartz)\ **Post date:** [August 30, 2017, 2:06am UTC](https://boards.straightdope.com/t/really-fair-d20-gaming-dice/795041/7 "2017-08-30T02:06:42Z")
That is some good work. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [August 30, 2017, 2:10am UTC](https://boards.straightdope.com/t/really-fair-d20-gaming-dice/795041/8 "2017-08-30T02:10:38Z")
Oh, and make sure to read all the way to the part about their d120. That is a true mathematical tour de force. ---
**Author:** ![BigT](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bigt/32/12044_2.png) [@BigT](https://boards.straightdope.com/u/BigT)\ **Post date:** [September 3, 2017, 1:39am UTC](https://boards.straightdope.com/t/really-fair-d20-gaming-dice/795041/9 "2017-09-03T01:39:20Z")
I hadn’t actually looked at the PDF. It appears to be the same sort of thing discussed in the [Numberphile videos](https://www.youtube.com/watch?v=8UUPlImm0dM&list=PLt5AfwLFPxWKdwptEcseLGWnCKRjIx55T&index=2) on fair dice. They include the d120. ---
**Author:** ![BigT](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bigt/32/12044_2.png) [@BigT](https://boards.straightdope.com/u/BigT)\ **Post date:** [September 3, 2017, 2:11am UTC](https://boards.straightdope.com/t/really-fair-d20-gaming-dice/795041/10 "2017-09-03T02:11:02Z")
Well, I thought it was from those videos where I learned about numerical symmetry, but maybe not. ---
**Author:** ![gazpacho](https://avatars.discourse-cdn.com/v4/letter/g/6f9a4e/32.png) [@gazpacho](https://boards.straightdope.com/u/gazpacho)\ **Post date:** [September 3, 2017, 2:20am UTC](https://boards.straightdope.com/t/really-fair-d20-gaming-dice/795041/11 "2017-09-03T02:20:17Z")
> [@BigT](#): > > I hadn’t actually looked at the PDF. It appears to be the same sort of thing discussed in the [Numberphile videos](https://www.youtube.com/watch?v=8UUPlImm0dM&list=PLt5AfwLFPxWKdwptEcseLGWnCKRjIx55T&index=2) on fair dice. They include the d120. There are a lot of good Numberhile videos with Professor Persi Diaconis. This one where he discusses coin flipping is really good also. I like his discussion of how they measured how many times a coin rotated when being flipped. This should be the play list for all of the videos with Professor Diaconis. https://www.youtube.com/embed/AxJubaijQbI?feature=oembed&wmode=opaque&list=PLt5AfwLFPxWLoz8cdew3MHrwfswn-HUrT > [@Chronos](#): > > Oh, and make sure to read all the way to the part about their d120. That is a true mathematical tour de force. Good paper, well crafted die but I wonder how much of the fairness is lost by misreading which face is on top. It really looks impractical. I remember from my D&D days that mistakes were made reading a D20. D120 looks like a real pain. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [September 3, 2017, 4:19am UTC](https://boards.straightdope.com/t/really-fair-d20-gaming-dice/795041/12 "2017-09-03T04:19:57Z")
Hey, it’s no worse than the Zocchihedron. Or at least, no more than 20% worse. But given how sloppy in general the Zocchihedron was, I’m guessing it’s not even that bad. The reviews I’ve seen say that it actually rolls fairly well, coming to a stop reasonably quickly. And it’s significantly larger than a standard die (about two inches), which helps (some) with the readability. ---
**Author:** ![Alessan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/alessan/32/465_2.png) [@Alessan](https://boards.straightdope.com/u/Alessan)\ **Post date:** [September 3, 2017, 4:55am UTC](https://boards.straightdope.com/t/really-fair-d20-gaming-dice/795041/13 "2017-09-03T04:55:38Z")
> [@BigT](#): > > That entirely depends on how you play. Even in heavy narrative games, if you’re always getting high scores, it can mean you’re supernaturally persuasive or whatever, and all your ideas work, no matter how good they actually are. > > But, in heavy fighting games, it means whether or not the game is balanced. If players are unusually lucky, just throw stronger monsters at them. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [September 3, 2017, 8:10pm UTC](https://boards.straightdope.com/t/really-fair-d20-gaming-dice/795041/14 "2017-09-03T20:10:56Z")
And then their luck runs out, and you get a TPK. You can balance for players being overpowered, but you can’t balance for luck. ---
**Author:** ![Alessan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/alessan/32/465_2.png) [@Alessan](https://boards.straightdope.com/u/Alessan)\ **Post date:** [September 3, 2017, 9:58pm UTC](https://boards.straightdope.com/t/really-fair-d20-gaming-dice/795041/15 "2017-09-03T21:58:56Z")
“Balancing” of this sort in pen-and-paper RPGs is pretty much a myth anyway. You make an semi-educated guess and hope for the best.