The seven common polyhedral dice
A die is named for its number of possible faces. A D6 has six outcomes, while a D20 has twenty. The standard tabletop set combines several shapes because different ranges are useful for different jobs: small dice create compact results, large dice allow finer distinctions, and multiple dice create bell-shaped totals.
| Die | Range | Average | Common uses |
|---|---|---|---|
| D4 | 1-4 | 2.5 | Light damage, short durations, small random choices |
| D6 | 1-6 | 3.5 | Board games, dice pools, family games, character generation |
| D8 | 1-8 | 4.5 | Moderate damage, healing, eight-direction tables |
| D10 | 1-10 | 5.5 | Decimal systems, damage, paired percentile rolls |
| D12 | 1-12 | 6.5 | Heavy damage, months, clocks, twelve-entry tables |
| D20 | 1-20 | 10.5 | Attack rolls, ability checks, saves, initiative |
| D100 | 1-100 | 50.5 | Percent chances, random tables, treasure and encounter results |
D4: small range, meaningful steps
The four-sided die is useful when every point matters. A one-point increase changes the expected result noticeably, so designers often use D4s for minor weapons, temporary bonuses, or effects that should remain controlled.
D6: the universal game die
The cube is easy to read, easy to stack, and familiar to nearly everyone. Rolling several D6s is especially useful because totals cluster around the middle. Three D6s, for example, produce 10 or 11 far more often than 3 or 18.
D20 and D100: broad, flat ranges
On a single D20, every face has the same 5% chance. On a D100, every numbered result has a 1% chance. These dice are ideal when a game needs clear percentage-like odds rather than a clustered total.
How dice notation works
Dice notation compresses a complete instruction into a short expression. The number before the letter D tells you how many dice to roll; the number after it tells you how many faces each die has.
- 1d20: roll one twenty-sided die.
- 2d6: roll two six-sided dice and add them.
- 4d8 + 3: roll four D8s, total them, then add three.
- 1d20 - 1: roll a D20 and subtract one.
- 2d20, keep highest: the usual procedure for advantage.
Modifiers shift every possible result by the same amount. A +4 modifier does not make high faces more likely; it simply turns a natural range of 1-20 into a final range of 5-24.
Understanding dice probability
For one fair die, the chance of a specific face is one divided by the number of faces. A chosen face on a D8 has a 1-in-8 chance, or 12.5%. The chance of rolling at least a target number is the count of successful faces divided by the total faces.
To roll 15 or higher on a D20, six faces succeed: 15, 16, 17, 18, 19, and 20. Six divided by twenty equals 30%. A +3 modifier changes the required natural roll to 12, so nine faces succeed and the chance becomes 45%.
Why two dice feel different from one
Two D6s can total 2 through 12, but those totals are not equally likely. There is only one way to roll 2, while there are six ways to roll 7. The resulting distribution forms a peak around 7. This makes 2d6 more predictable than a hypothetical single D11, even though both cover eleven possible totals.
Advantage and disadvantage
Rolling two D20s and keeping the higher result improves the average and sharply reduces low outcomes. Keeping the lower does the opposite. The effect is strongest around middle target numbers and smaller near automatic extremes.
Building useful dice pools
A dice pool is a group rolled together. Some systems add all values; others count successes, keep selected dice, or remove matching results. Before rolling, identify quantity, die size, modifier, and whether any keep-or-drop rule applies.
Use one large die when you want every result to be equally likely. Use several smaller dice when you want ordinary outcomes to occur often and extremes to feel rare. Use success counting when the exact total matters less than how many dice meet a threshold.
- 1d20: volatile, dramatic, and easy to compare with a target.
- 2d6: moderate range with a strong center.
- 3d6: reliable middle results with rare extremes.
- 6d6: useful for large damage rolls and games such as Farkle.
Physical dice and digital dice
Physical dice depend on geometry, material, wear, the throwing surface, and the throw itself. Digital rollers use software to generate motion and determine a settled face. A physics-based roller adds visible rotation, collisions, friction, and bounces so the result is presented through a familiar dice-tray experience.
Visual realism and mathematical fairness are related but different. Attractive textures do not determine randomness, and a long animation does not automatically improve it. A trustworthy tool should avoid changing results after the roll, clearly display individual values, and preserve enough history for players to verify the sequence.