Ever tried to roll a three? If you’re a Dungeons & Dragons player or a board game geek, you’ve probably seen a "d3" mentioned in a rulebook somewhere. But if you reach into your velvet dice bag, you won't find a triangle-faced solid that rolls fairly. Physics is kind of a jerk like that. In the world of tabletop gaming, the 3 sided dice roll is a mathematical necessity that often lacks a physical body.
Geometry hates the number three. To have a "fair" die, every side needs to be congruent, meaning they have the same shape and size. In 3D space, the simplest regular convex polyhedron is the tetrahedron—the d4. It has four sides. You can’t make a stable, three-sided "Platonic" solid because a shape with only three faces can't actually enclose a volume in three dimensions without some serious cheating.
So, how do we actually do it?
The math behind the 3 sided dice roll
Most people just cheat. Well, not cheat at the game, but cheat the physics. If you need a 3 sided dice roll, the most common method is using a standard six-sided die (d6). You just divide the result by two and round up. Roll a 1 or 2? That’s a 1. Roll a 3 or 4? That’s a 2. Roll a 5 or 6? That’s a 3. It’s simple. It’s elegant. It’s also kinda boring.
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Some folks prefer the "modulo" approach, though it’s a bit more "mathy" for a casual Friday night. You take the result of a d6 and use the remainder. But honestly, most players just want to see a number on a face.
Physical "d3" designs that actually exist
Despite the laws of the universe trying to stop us, manufacturers like Bescon and Koplow Games have gotten creative. You can actually buy things marketed as 3-sided dice. They usually fall into one of three weird categories.
First, there’s the "Triangular Prism." Imagine a long, three-sided log with rounded ends so it can't land on the tips. It rolls like a rolling pin. These are cool, but they tend to skitter off the table and under the couch more than regular dice.
Then you have the "Shield" style. These look like a thick guitar pick or a fat triangle with rounded edges. They don't really roll; they more "flop." If you've ever used the dice from the game Genesys or certain Star Wars RPGs, you know that non-standard shapes can feel a bit clunky.
Finally, there’s the "Long Die" or "Roman Die" style. These are four-sided prisms where the ends are tapered or rounded so it can only land on one of the three long rectangular faces. Technically, it’s a d4 with one side ignored, or a shape designed specifically to hide the fourth possibility.
Why not just use a d4?
A lot of gamers ask this. A d4 has four sides. If you want a 1-3 range, you can just roll a d4 and reroll any 4. This is called "filtering." It’s mathematically perfect, but it slows down the game. If you're playing a high-intensity combat encounter in Pathfinder, rerolling every few seconds feels like a chore.
The digital advantage
In the digital realm, a 3 sided dice roll is just a line of code. It's easy. A Random Number Generator (RNG) doesn't care about Platonic solids or the limits of Euclidean geometry.
random.randint(1, 3)
That’s it. Whether you’re using Roll20, Foundry VTT, or just Googling "roll a d3," the computer just picks a number. There’s no physical weight, no "feel" of the tumble. Some people hate that. They miss the tactile "clack-clack" of plastic on wood. But for a d3, digital is objectively the most "fair" way to get a result without the dice leaning or sliding.
Strange variations and the "D-Total"
Have you ever heard of Lou Zocchi? He’s a legend in the dice world and the founder of GameScience. He’s obsessed with precision. He once helped market a "D-Total" die, which is a complex monstrosity that can represent a d2, d3, d4, d5, d6, d8, d10, d12, d20, and more, all on one shape. To get a 3 sided dice roll out of it, you have to look for specific color-coded symbols. It’s a feat of engineering, but it requires a manual just to read your damage roll.
Most collectors prefer "deadeye" dice. These are d6s that are literally printed with 1, 1, 2, 2, 3, 3 on the faces. It's the most practical physical solution. You get the familiar roll of a cube but the specific probability of a three-sided result.
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How to handle a d3 at your table tonight
If you find yourself needing a 3 sided dice roll right now and you don't own a weird prism or a specialized d6, here is the hierarchy of what you should do, ranked by how much they annoy your Dungeon Master.
- The d6 Half-Up: Roll a standard die. 1-2 = 1, 3-4 = 2, 5-6 = 3. This is the industry standard. It’s fast. Everyone understands it.
- The d4 Reroll: Roll a d4. If it’s a 4, roll again. It’s slightly more annoying but keeps the "low number" feel.
- The "1-2-3, 1-2-3" d6: Just read the pips and ignore the actual value. If you roll a 4, it’s a 1. 5 is a 2. 6 is a 3. This is confusing for some people mid-game, so use it with caution.
- Digital Apps: Use your phone. It’s boring but accurate.
Basically, don't overthink it. The 3 sided dice roll is a ghost. It’s a number disguised as a physical object. Whether you use a fancy custom-molded prism or just do the mental math on a dusty d6 you found under the radiator, the result is the same. Just make sure the whole table agrees on the method before you roll, otherwise, you're asking for an argument when that "6" hits the table.
Actionable Next Steps
- Audit your dice bag: If you play games that frequently require d3s (like Warhammer 40k or certain OSR titles), buy a pack of "d6-d3s." These are cubes labeled 1-3 twice. It saves a lot of mental energy during long sessions.
- Check your RNG settings: If playing online, ensure your macro is set to
1d3and not1d6/2, as some older systems might handle rounding differently than you expect. - Embrace the prism: If you want a conversation starter, look for a "triangular dipyramid" or a long-die d3. They look like crystals and add a unique aesthetic to your rolling tray.