Tuesday, March 13, 2012

d30 Emulator

I am sure I am treading over well-worn ground here, but I was walking to the grocery store last night and wondering what all those poor unfortunates who don't possess d30s do when they come across a d30 table?  How do they emulate a d30 roll?

Again, I doubt that this is wholly original, but here is what I came up with:

You take two dice, a d6 and a d10, and roll them as if they were percentile dice, using the d6 as a modified d3 for the tens column like this:

d6 roll
Modified d30% "tens" result

So, using this system, I could roll the d6 to obtain a 0, 10, or 20 result for my "tens" column, then roll the d10 for the "ones" column and obtain a final result of 1-30.  Of course, the "00" roll = 30.

Make sense?

Does anybody do this differently, or is d30 emulation even a very big thing? I assume it doesn't come up too often. . .

The reason I ask is because in time -- probably several years from now -- I plan to release the Lands of Ara Gazetteer, which will include a great many region-specific encounter tables. Yet I happen to strongly favor d30 encounter tables for my home game, and therefore most of my own Arandish encounter tables use that die. So I started wondering whether I would need to convert those tables to d20 rolls, or else suggest a d30 conversion technique somewhere early in the Gazetteer? Or maybe include multiple versions of each table -- though the latter option seems like a big hassle.


  1. I'd roll 3 dice - a d20, d10 and d6. If the d6 came up 1-4 then ignore the d10, if a 5 or 6 is rolled then add the d10 to the d20.

  2. David- That's not the same distribution as a d30. For example, instead of a 1 in 30 chance of a 30, you have a 1 in 600. To emulate a single die, you have to avoid schemes that add multiple dice together.

    Carter- I use this technique to emulate arbitrary dice, too. You can generate flat probabilities for most any range, if you can accept re-rolls for numbers that don't share prime factors with the standard polyhedra. It gives me a cheaper alternative to Zocchi dice!

  3. Generally speaking, a particular die type can be emulated if you can convert it into a matrix: in this way you have an uniform distribution, giving you a 1-on-N probability for N-sized dice.

    If you wanna emulate the d30, you have only 2 choices: a 3x10 matrix and a 5x6 matrix.

    A 3x10 matrix needs a d10 working as a d10 and a d6 working as a static shift die: that's the solution you've already shown.

    A 5x6 matrix need a d6 working as a d6 and a d10 working as a static shift d5 (with 0/6/12/18/24 faces).

    That's all. ^_^

  4. I've used a d6 and a d10 before. In my magic items chart I made a D30 table and just added a little side bar with 1-2, 3-4, and 5-6, with a note at the top that a D6 & D10 will work.

    Treasure Hoards and Magic Items

    Definitely keep your D30 tables!

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  6. Yes, definitely keep the d30 tables, but include your emulator as an appendix.

  7. @Hamel: Thanks for the mathematical breakdown there, I was wondering about the 5 x 6 = 30 thing myself.

    @Kelvin: Thanks for the suggestion, I would very much like to keep my original d309 tables intact, yet I hate to screw anybody over or make them feel excluded. Sounds like appendicizing the emulator should get the job done.

  8. EDIT: That should read "d30 tables" -- "d309 tables" would be a wholly different matter!

  9. I believe the same approach is described in the first few pages of the 1e DMG, around that bell curve and what some blogger called the "peyote-fueled discussion of probability".

  10. @Spawn: Thanks for the citation, I'll pull that down and look that up. Good old EGG!