I was reading Darths & Droids, and R2’s player mentions that he got a set of “binary dice”, just for playing robot characters. He’s talking about “regular” dice numbered in base2 notation, and it got me curious. So, I went looking to see if anyone has done such a thing.

I already have a bunch of the exact inverse: the “Ubiquity dice” designed for the Ubiquity System (*Hollow Earth Expedition*, *Desolation*, *Fantastic World*, & *All For One*), which produce a binary bell curve distribution: the basic die is just a glorified penny, giving you results of 0 or 1. But then they have dice that give the same results as flipping 2 or 3 coins (or rolling 2 or 3 of the basic binary dice), in one die. So, just like the odds of flipping 3 coins and getting 3 heads is 1-in-8, a Ubiquity “d3” [their notation, not mine] is an octahedron with a *3* on only one face (and 3 *2*s, 3 *1*s, and 1 *0*). For that matter, any number of game systems really boil down to flipping a pile of coins—any game system where you roll a dice pool and half the results on each die are successes (Primetime Adventures, Maelstrom Storytelling, and Prince Valiant come immediately to mind, but they’re far from the only ones). So, boiling it down to d2s numbered *0* and *1* makes perfect sense, and it *is* really nice to be able to cut how many physical dice you need to roll by as much as 2/3rds.

But, I digress. Those are all instances of dice that are approximating the distribution of a random binary event. I’m talking about dice that have the usual distribution (i.e., flat), but are simply notated in binary. So, back to my search. Unfortunately, other than scribbling on a blank die (or using stickers), I didn’t turn anything up. A person commenting that it didn’t make much sense to have binary-notated dice, except with faces in multiples of 2 (so, of the standard dice shapes, only the d4, d8, and d16 would qualify)–which seems a little strange to me. Notating in binary is purely an affectation, if you haven’t made any other changes, so why would you care that the highest number on the die didn’t happen to be a power of 2? Someone else commented that orientation would be an issue, much more so than with decimal dice. But that is easily conquered—after all, we figured out to put underscores on the *6* or *9* (and any other problematic numbers) once decimal dice got above 8 sides; I think we can figure out something equally-obvious for binary-notated dice. Perhaps a decimal point (“binary point”?) at the small end of the number, to indicate the zero position?

In any case, the only binary-notated dice I was able to find were d6s with *0* and *1* each on 3 faces. Which means they aren’t even d6s, they’re d2s. Nothing that can generate a number bigger than 1, with binary notation.

I did find two interesting variations that I hadn’t thought of: A set of tiles that solves the positional issue by using explicit values (in base10). There are 5 tiles, numbered 1, 2, 4, 8, 16, respectively, on one side, and blank on the other. Give them a good toss, and add up the ones that are face up.

But, again, that’s back to where we started, with a binary distribution, and decidedly non-binary notation.

The other thing I found are actually called “Boolean dice”, because “binary dice” was already taken. However, probably due to my really poor programming (and logic-gate) skills, I can’t really make sense of them. In what way are the dice “binary”? It’s true, they all have faces with either a single pip, or nothing, on them, so I get that. But I’m not understanding the chosen distribution: there are 10 dice in a set: 1 with all blank faces, 1 with a single pipped face, 2 with 2, 2 with 3, 2 with 4, 1 with 5, and 1 with all six faces pipped.

And the distribution of the overall results doesn’t, on first blush, produce a binary bell curve: the odds of getting a 9 with those dice does approximate the odds of flipping 9 out of 9 heads—but it’s only an approximation, and the odds of getting 0 on those dice is way off [since it’s impossible]. Which also means the odds of getting a 1 are way off. So, anybody see the math behind these, or what makes them “Boolean” or “binary”, other than merely the fact that each individual die only has two possible results, though with varying odds? Or is that sufficient? Opinions? Insights?

Finally, the die that wins the coolness award—or would, if it weren’t just a theoretical construct. Check out the “polarised binary laser dice“, which consist of a series of polarizing objects, nested one inside another, magnetically suspended, which orient randomly within a set of constrained possibilities when you toss the die. The die is read by shining light through it onto a light meter, and measuring the per cent that comes through, enabling you to generate numbers with a binary distribution, such as 0 to 255. I want one of those!

Oh, and as an aside, I propose that “u1”, “u2”, and “u3” be used for notating the Ubiquity dice, rather than “d1”, “d2”, and “d3”. Though I *have* seen “d1” used before to mean a die with two equally-possible results, 0 and 1 (in order to distinguish it from a d2, which also has two equally-possible results, but those are 1 and 2), extending that for “multiple” binary dice just doesn’t work. There is already a well-established meaning for dX, and it just adds confusion for it to have a special meaning in just one game system. I thought about “b1”, “b2”, etc., for “single-binary die”, and so on, but a b looks an awful lot like a d, and might be misread if both were being talked about in the same context for some reason. And, really, why not give the folks behind the Ubiquity System a little credit? While the actual idea is obvious, and I’m sure has been discussed before, they’re the ones who actually did it, and, at least for now, the only source of the dice.

Where did you find those binary dice tiles? I saw them mentioned on Boardgamegeek but I can’t find anywhere that sells them!

Roll a couple of popsickle sticks, one side labeled “1”, the other blank. Read from left to right, e.g. 1-1-1-0 = 14. That should give a bell curve.