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What Is a 4-Sided Die (D4)?
A 4-sided die, or D4, is shaped as a regular tetrahedron with four equilateral triangular faces. It is one of the five Platonic solids and is the simplest polyhedral die used in gaming. Each face is numbered 1 through 4. Unlike other dice, a D4 doesn't roll easily and tends to land flat on one face, with the result read from the top vertex or the base numbers.
In Dungeons & Dragons, the D4 is primarily used for small weapon damage (daggers, darts) and low-level healing spells. It also appears in various probability exercises due to its simple, uniform distribution.
D4 Probability Formula
The variance of a single D4 roll is 1.25, and the standard deviation is approximately 1.118. For N dice, the expected sum is 2.5N with variance 1.25N.
D4 Probability Table
| Outcome | Probability | Cumulative |
|---|---|---|
| 1 | 25.00% | 25.00% |
| 2 | 25.00% | 50.00% |
| 3 | 25.00% | 75.00% |
| 4 | 25.00% | 100.00% |
Common Uses of D4 Dice
- RPG Damage: Daggers, darts, and other small weapons deal 1d4 damage.
- Healing: Low-level cure spells often heal 1d4 hit points.
- Random Selection: Perfect for choosing among 4 options fairly.
- Education: Demonstrates uniform discrete probability distributions.
Frequently Asked Questions
Why is the D4 shaped like a pyramid?
The D4 is a regular tetrahedron, one of the five Platonic solids. This shape ensures each of the four faces has an equal probability of being the landing face. It is the only convex polyhedron with exactly four faces.
How do you read a D4?
There are two common numbering schemes: vertex-read (the number at the top point) or base-read (the number printed on the base edges). Most modern D4s use vertex-read numbering where you look at the number displayed at the apex.
What is the average roll of a D4?
The expected value is 2.5. Over many rolls, your average should converge to this value by the law of large numbers.