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
Result
Modified d30% "tens" result
1-2
0
0
3-4
1
10
5-6
2
20

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.

10 comments:

  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.

    ReplyDelete
  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!

    ReplyDelete
  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. ^_^

    ReplyDelete
  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!

    ReplyDelete
  5. This comment has been removed by the author.

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

    ReplyDelete
  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.

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

    ReplyDelete
  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".

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

    ReplyDelete