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).
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.
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.
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.
[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.
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.
That is some good work.
Oh, and make sure to read all the way to the part about their d120. That is a true mathematical tour de force.
I hadn’t actually looked at the PDF. It appears to be the same sort of thing discussed in the Numberphile videos on fair dice. They include the d120.
Well, I thought it was from those videos where I learned about numerical symmetry, but maybe not.
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.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.
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.
If players are unusually lucky, just throw stronger monsters at them.
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.
“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.