## d34

pl. n. **d34s**; also **34-sider**, **thirty-four-sider**, **34-sided die**, **thirty-four-sided die**

n. “dee thurr tee for,” abbrev. for a 34-sided die. See **xdn**.

Addendum: This article mocks the d34, saying “…there is absolutely no reason you would want to use a d34 or even multiples.” This, of course, is entirely incorrect.

Three 34-sided dice minus 2 (3d34-2), added together, produce numbers from 1 – 100 on a bell curve distribution, which is extremely helpful when producing percentile stats or determining percentile successes. I’m writing an RPG right now, and I would be using 3d34-2 for success rolls — if I thought anyone who might want to play my game actually owned three 34-sided dice, or would be willing to buy them.

As it is, I’m sticking with regular percentile dice (2d10). But if it were up to me…

Addendum #2: Here are four ways to produce a 1-100 bell curve. Thanks to everyone in the comments below, and at the Reddit discussion, for the input!

### Submitted by:

Kunochan

### 9 Comments to “d34”

### Comments

thouis23 April 2013 at 9:51 pm #Take the average of 3 rolls of percentile dice, and you get basically the same distribution.

Kunochan23 April 2013 at 10:07 pm #I am no mathematician, but I don’t see how the average of three flat percentile dice rolls would produce a bell curve.

I Googled it, and couldn’t find an example. Somebody did suggest 20d6-20, though. Not exactly easy to use.

thouis23 April 2013 at 10:18 pm #Think of it this way: divide a d100 (percentile) by 3. This is approximately a d34-2/3. You can also look up the Central Limit Theorem.

(I can go into more detail, but it’s probably not that interesting for most people to hear about variance, limit distributions, etc. I’m not a mathematician, but I know enough to be dangerous… to a conversation.)

Kunochan23 April 2013 at 10:28 pm #Okay, but 3d34 adds together the totals, it doesn’t average them.

As for the Central Limit Theorem, that requires “sufficiently large numbers” of variables. Is three large enough?

By the way, I’m not saying you’re wrong — I have no idea if you’re right or wrong. But if you’re right, I just don’t get it. That may well be my ignorance.

Anonymous Coward23 April 2013 at 10:49 pm #> Okay, but 3d34 adds together the totals, it doesn’t average them.

A (0, sqrt(3)) normal distribution is still a normal distribution.

> As for the Central Limit Theorem, that requires “sufficiently large numbers” of variables. Is three large enough?

http://www.wolframalpha.com/input/?i=3d34

thouis23 April 2013 at 10:51 pm #Averaging 3 d100s is like dividing by 3, then summing, so you end up with sum(three d34 – 2/3) = (sum of three d34s) – 2.

The CLT applies at surprisingly few values, sometimes. Averages of uniform variables tend very quickly to “Normally” (i.e., bell-curve) distributed.

Kunochan23 April 2013 at 10:46 pm #Well, it appears you are correct, sir:

http://anydice.com/program/21b3

blazecc23 April 2013 at 10:51 pm #anydice.com

paste in:

output 3d34-2

output 3d100/3

Noah Easterly24 April 2013 at 3:12 am #Also, if you have a die bag that’s just a standard pack (d4, d6, d8, d10, d12, d20), plus a couple extra d10 for WoD and a couple extra d20 for D&D, you can generate 0-100 on a normal curve with: d4+d6+d8+4d10+d12+2d20-10