Where the d3 shows up
- Small damage. Older editions and Pathfinder use 1d3 for the smallest hits, such as a Medium character's unarmed strike or a Tiny creature's bite.
- How many? How many goblins come round the corner, how many rounds a spell lingers, how many coins are left in the purse.
- One of three. Three doors, three suspects, three rumors in the tavern. Number them and roll.
- Wargames. Warhammer rolls a D3 all the time: damage, extra attacks, how many models come back. Same die, same odds.
Reading a d3
A real d3 is a long triangular die. It cannot stand on its pointed ends, so it always tips onto one of its three long sides, and what points up is a ridge, not a face. Each ridge has its number printed on the two faces beside it, and the number on the top ridge is the roll. The roller above draws it the same way.
Rolling a d3 with a d6
If you have no d3, roll a d6 and halve it, rounding up: 1-2 is a 1, 3-4 is a 2, 5-6 is a 3. It is exactly as fair as a d3. This page just saves you the sum.
Is it fair?
Each number comes up one time in three. The number comes from your browser's cryptographic random generator, and the roller throws away the few values that would tilt the result, so 1, 2 and 3 are dead even.
Your odds on a d3
Every face of a fair d3 is 1 in 3, about 33.3%. For a number or higher:
| You need | Chance |
|---|---|
| 2 or higher | 66.7% |
| 3 | 33.3% |
Waiting for a 3? The chance of at least one climbs with every roll:
| Rolls | At least one 3 |
|---|---|
| 1 | 33.3% |
| 2 | 55.6% |
| 3 | 70.4% |
| 4 | 80.2% |
| 5 | 86.8% |
| 6 | 91.2% |
Two d3s add up to 2 through 6:
| Total | Exactly | This or more |
|---|---|---|
| 2 | 11.1% | 100% |
| 3 | 22.2% | 88.9% |
| 4 | 33.3% | 66.7% |
| 5 | 22.2% | 33.3% |
| 6 | 11.1% | 11.1% |
The dice calculator works out any roll, the coin flip sits one size down and the d4 one size up.
Questions
What does 1d3 mean?
One three-sided die, a roll of 1, 2 or 3. The number in front is how many dice, so 2d3 is two d3 added together (2 to 6) and 1d3 + 1 gives 2 to 4. The Dice Notation Guide covers the rest.
What is the average roll on a d3?
Exactly 2. Each extra d3 adds 2, so 2d3 averages 4 and 3d3 averages 6.
How do I roll a d3 with a d6?
Roll the d6 and halve it, rounding up: 1-2 is a 1, 3-4 is a 2, 5-6 is a 3. Another way: 1-3 count as themselves and 4-6 count as the roll minus 3. Both are perfectly fair. A d12 divided by 4, rounded up, works too.
Do real d3 dice exist?
Yes. The common one is a long triangular prism that rolls along its sides. There are also d6s marked 1, 1, 2, 2, 3, 3. They are rare in game stores, which is why most tables halve a d6.
What is a D3 in Warhammer?
The same thing: a number from 1 to 3, each equally likely. Warhammer players roll a D6 and halve it, rounding up. If a rule says D3 damage, each hit averages 2.
Is this d3 roller random and fair?
Yes. Each roll comes from your browser's cryptographic random number generator, and the few values that would tilt the result are thrown away, so 1, 2 and 3 are each exactly 1 in 3. Roll up to 20 d3 at once and add a modifier.