How to read a D4 Die correctly! (and…why they are fair)

Dice (otherwise known as “shiny little math rocks”, “the root of all my TPKs”, and “the reason my partner has locked me out of our joint bank account”) are a fundamental part of Dungeons & Dragons

D&D may be a game of collaborative storytelling, where the dungeon master describes the world, the players describe or roleplay their actions, and the dungeon master describes the results.

But, when the fat hits the fire and the difference between success and failure hang in the balance, dice are the little oracles that show us exactly what happens next. 

When the dragon exhales a cloud of fiery death; when your sword plunges towards the goblin’s throat; when you crack open a treasure chest, strike out into the wilderness, rest in troll-infested caverns; whenever uncertainty rears its ugly, CR30 head, it’s time to reach for the shiny pile of polyhedral plastic. 

Today, we’re going to be talking about the smallest die in D&D, the d4 (Alright, yes I know there are technically d3s and even d2s – otherwise known as flipping a coin – but both of those require some mathematical finagling to get a result; I’m talking about the smallest die you can throw and read the resulting number straight off the face); or, the four-sided die. 

How do I read a d4? 

The d4 is an odd fish among the six polyhedral shapes that are used in D&D 5e, in that there are two different ways in which they’re made – each of which is read slightly differently. 

Both “top read” and “bottom read” d4s are the same shape: a four-sided polyhedron that looks like one of the pyramids of Giza. 

Pyramids of Giza
Looks like someone upcast Magic Missile to 4th level. 

There are “top read” d4s, which have the resulting number written near each vertex of the shape so each face appears to have three numbers facing outwards. Throw one, look at the number near the top, and that’s the result. 

“Bottom read” d4s, on the other hand, have their numbers facing inwards. To read one, look at the number along the bottom edge of the die when it lands. 

Whether your d4 is a “bottom read” or a “top read”, the result of the die roll is always the number that’s the right way up. 

What do I use a d4 for? 

As the smallest die in D&D 5e, d4s are one of the most common damage dice for low level monsters and simple one-handed weapons. 

Weapons that deal 1d4 damage include…

Weapon NameCostDamageWeightProperties
Club1 sp1d4 bludgeoning2 lb.Light
Dagger2 gp1d4 piercing1 lb.Finesse, light, thrown (range 20/60)
Light hammer2 gp1d4 bludgeoning2 lb.Light, thrown (range 20/60)
Sickle1 gp1d4 slashing2 lb.Light
Dart5 cp1d4 piercing1/4 lb.Finesse, thrown (range 20/60)
Sling1 sp1d4 bludgeoningAmmunition (range 30/120)
Whip2 gp1d4 slashing3 lb.Finesse, reach

 

Potions of Healing also use d4s to restore health to the creature that drinks them, as does the spell Healing Word

Also, spells like Bane, Bless, and Guidance all make their targets either subtract or add the result of a d4 from or to their d20 rolls when doing things like making an ability check, saving throw, or attack roll. 

Is a d4 a “fair” die?

There’s actually some very interesting statistical and geometric theory as to why certain dice are “fair” (meaning they actually have an equal chance of coming up with each of their results).

It’s all laid out in a very interesting (not to mention strangely soothing) video by probability Professor Persi Diaconis from Stanford University, but the upshot is that there are only five possible polyhedral shapes that can physically be “fair” dice.

One of those shapes is a d4, meaning that you have an exactly equal chance (25% in this case) of it landing on each face (excluding factors like the surface you’re throwing it on, micro-degradations in the die itself, whether its sides are indented for each number, the weight of the paint, and I assume the Nigerian stock market on the third Tuesday of every month because chaos theory is wild like that).

Now, get out there and roll some math rocks.