The d4, properly introduced
The oldest dice ever found are four-sided. The Royal Game of Ur, buried with Sumerian royalty around 2600 BC, came with tetrahedral dice, two corners tipped in shell to mark the throw. The shape barely tumbles, which is why every board game since has preferred the cube, and why gamers nicknamed it the caltrop: step on one barefoot and you will remember it.
Roll it for: small damage rolls in tabletop rpgs; any four-way decision; the historical recreation of the royal game of ur. And if the d4 isn't the die your game asks for, the full dice roller has the other five.
- 4, numbered 1 to 4
- Tetrahedron, a Platonic solid
- 25% — exactly 1 in 4
- 2.5
- averages 5; totals range 2 to 8
- two 4s in a row: 1 in 16
D4 — frequently asked
A 4-sided die shaped as a tetrahedron, one of the five Platonic solids. Four faces, lands on a point, never rolls far. Faces are numbered 1 to 4, and on a fair d4 each lands with exactly a 25% chance.
One in 4, or 25%, the same as every other face. Rolling two 4s back to back happens once in 16 attempts. The roller here uses rejection sampling on a cryptographic generator, so those odds hold exactly.
2.5. A fair die averages the midpoint of its range, so 2×d4 averages 5 and 3×d4 averages 7.5. Single rolls are flat: an average result is no more likely than a 4 or a 1.
Small damage rolls in tabletop RPGs; Any four-way decision; The historical recreation of the Royal Game of Ur. Beyond those, any decision with 4 options maps onto it directly.