Sunday, August 26, 2012

A d20 in a d5's clothing (a.k.a. Polyhedrous Perversity)

Sure, you've maybe heard of polymorphous perversity, especially if you're a fan or Woody Allen. But I'd like to coin a new term... "polyhedrous perversity." Specifically, I'm talking about the icosahedron (d20) pictured here, parading around as a d5. Yes! It is numbered 1 to 5, four times. It's something I picked up in the dice bin of a FLGS. Not that I had a use for it (as I have not yet succumbed to the temptation that is DCC.)

I've heard tell of a d6 numbered 1 to 3 twice, but can't seem to find much info on this d20 in d5 clothing (or anyone/anywhere else who might be selling them.) Come on you P.A. (Polyhedrals Anonymous) members, help me out on this.


  1. So, are you saying it's actually just a d20, and it's appearing to me as a d5 because I'm crazy?

  2. Well with true D5s selling for $5, this is a reasonable alternative. I have at least half a dozen six-sided D3s. I've been hoping to find eight-sided D4s (they roll instead of skittering or plopping like four siders). The do make a twelve sided D4, but it's huge. I suppose an Average die would blow your mind. Six sided marked 2,3,3,4,4,5. Came into being in the 70s for some of the miniature wargaming rules, particulary WRG Ancients.

    1. (now you've gone and done it ;-)

      Actually, the Average die sounds right up Richard's alley.
      In fact (on p.14 of The D30 DM Comapanion) there's a nice table that uses the d30 to generate a center-weighted probability distribution (dare I say) superior to the Average die. (... because it still produces the '1' and '6' values)

      The mean (average) of the d6, the 'Average Die', and Richard's "bell-curved 1-6" d30 table are all 3.5. The difference lies in "the spread" of the probability-density distribution.

      here's 1d6:
      1: 16.67%: @@@@@@@@@@@@@@@@
      2: 16.67%: @@@@@@@@@@@@@@@@
      3: 16.67%: @@@@@@@@@@@@@@@@
      4: 16.67%: @@@@@@@@@@@@@@@@
      5: 16.67%: @@@@@@@@@@@@@@@@
      6: 16.67%: @@@@@@@@@@@@@@@@

      here's the Average Die:
      2: 16.67%: @@@@@@@@@@@@@@@@
      3: 33.33%: @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
      4: 33.33%: @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
      5: 16.67%: @@@@@@@@@@@@@@@@

      here's the "bell-curved 1--6" table fromThe D30 DM Comapanion:
      1: 10.00%: @@@@@@@@@@
      2: 16.67%: @@@@@@@@@@@@@@@@
      3: 23.33%: @@@@@@@@@@@@@@@@@@@@@@@
      4: 23.33%: @@@@@@@@@@@@@@@@@@@@@@@
      5: 16.67%: @@@@@@@@@@@@@@@@
      6: 10.00%: @@@@@@@@@@

      The standard deviation (a mathematical measure of "spread") for the d6, Average die, and the table are 1.70, 0.95, 1.45 respectively.

      What does this mean?
      The last couple of days I've actually been asking myself how the central limit theorem applies to dice in an RPG context (rather than a classroom context)---especially where "character competence" is concerned. I'm growing partial to weighting the distribution towards the desired value, rather than equiprobable values of failure and success.

    2. Don't let Mr. Welborn fool you. The bell-curved charts in the d30 DM Companion may have come from my original thoughts/applications, but the "dice probability calculator" program he wrote really helped us refine them. The "Copy and Editorial Assistance" credit he receives should probably also included "Technical Advisor" just for his statistics assistance alone.

    3. Saroe, there are 12 sided D4s out there as well.

    4. Also (concerning skittering dice)

      There's two camps here: randomization occurs in the hand/cup (before the throw); randomization occurs in the bouncing/rolling (after the throw).

      I find that dice respond to the surface on which they are rolled.
      ... namely, by how much energy is reflected back into the die's bounce.

      Different dice respond better to different surfaces

      For example: roll the Zocchi/Gamescience d5 on a glass table-top, and watch the fun.

      In my game bag (with my books), I have the back from a masonite clipboard with felt glued to one side, and a second (denser) piece of masonite.
      I use the dense masonite for Zocchi dice, the felt surface for others.

      I suspect a nice firm piece of leather would make a good absorptive surface as well ... flatter than the felt ... for highly faceted dice. (d30 / d100)

  3. Oh. Just realized what you meant. No. I did not get this at Madness (in Plano, TX). It came from Roll2Play in Coppell.

  4. I think they are made by Chessex, I got one in a pound of dice. Don't know what they are for, though.