Numerically Balanced d20s

[urchin]

I think these are cool and thought maybe someone here might too.  Numerically balanced dice!

These d20s are ideally numerically balanced in the sense that:
    - The average value of any pair of opposite faces is 10.5
    - For each vertex, the set of five faces that share that vertex have values that total 52 or 53 (as close as you can get to an average of 10.5 across 5 integers)
    - For each face, the set of three three faces that share edges with that face have values that total 31 or 32 (as close as you can get to an average of 10.5 across 3 integers)

My former undergraduate research advisor was the one who found this numbering and he gave me a pair:



I've been thinking of what kind of Pathfinder character these dice might inspire. A two-weapon fighter, perhaps, so I could roll this color-inverted pair of d20s together. Maybe a LN cleric devoted to balance and order. Maybe a mathematical monk.

What unusual sources have you drawn character inspiration from?

[Brave Sir Robin]

How different are they from normal d20s? Personally I refuse to use any die that doesn't have opposite sides that sum to a consistent number.

[urchin]

Nov 23, 2017 0:38:31 GMT Brave Sir Robin said:

How different are they from normal d20s? Personally I refuse to use any die that doesn't have opposite sides that sum to a consistent number.

Standard polyhedral dice do have the opposite face property (unless they're those spin-down kind that people use for MtG life counters). The other properties are not typical.

The opposite-face property keeps the die's expected value the same if it is pressed, making one pair of sides larger and more likely to come up. The third property (balanced faces around each face) functions similarly. The second property (balanced faces around each vertex) minimize change in the die's expected value if a vertex becomes more rounded through pressing or being shaved down.

I don't think dice loading is a serious concern personally, and think of this more as a fun curiosity, but there is real world motivation behind it.

Check out your d20s and add up the faces around a few vertices to notice the differences.

[Alex Newall]

So what you are saying is that I can load my dice to punish players and STILL be using perfectly valid dice?

MWAHAHAHAAHAHAHAHAHAHAHAHAAAAAA!

[cannonlongshot]

You're telling me standard D20s don't have opposite faces that sum to a constant number? You tell me this the week BEFORE I start a new 5th Ed. campaign?!

WHY DIDN'T I STICK TO 2D6 SYSTEMS

[urchin]

Nov 23, 2017 9:21:34 GMT -8 Alex Newall said:
So what you are saying is that I can load my dice to punish players and STILL be using perfectly valid dice?

Not sure loaded dice are perfectly valid, but if you were exceptionally dexterous you could potentially skew the expected value of your dice rolls on standard dice slightly by aiming for certain vertices. Theoretically. Over many rolls. There are probably better ways to punish players.

Nov 28, 2017 6:34:32 GMT -8 cannonlongshot said:
You're telling me standard D20s don't have opposite faces that sum to a constant number?

They do have that property, but not the other properties. This is more of a mathematical curiosity than a serious practical concern. I fear I've mislead people on that, sorry if that's the case!