4D6 Roller
Rolling 4D6 produces a total between 4 and 24 with an expected average of 14.0. The total 14 is the mode with 146 out of 1,296 combinations (11.27%).
âš™ Advanced Expression (NdM±K) â–¼
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Roll History
0Exact Mathematical Probability
Combinatorial EngineCalculates discrete binomial distributions, probability density, and cumulative odds for the active dice expression.
View Full Probability Table & Combinations â–¼
| Total | Ways | Exact % | ≥ At Least | ≤ At Most |
|---|
Roll N Times (Multi-Trial Simulation)
Execute up to 10,000 repeated trials to calculate empirical distributions and statistics.
Empirical Frequency Table
| Roll Total | Hits (Count) | Frequency Bar | Percentage |
|---|---|---|---|
| Click "Run Trials" to simulate rolls and generate frequency data. | |||
Probability Curve & Mathematical Mechanics
Four six-sided dice (4D6) are prominent in modern character creation rules (where players roll 4d6 and discard the lowest die). Rolling all four dice raw gives a tight bell curve spanning from 4 to 24 with 1,296 possible outcomes.
There are 6^4 = 1,296 possible combinations. Totals between 12 and 16 account for over 50% of all rolls. A total of 24 (rolling four sixes) has an odds of 1 in 1,296 (0.077%).
Prominent Tabletop Games Using 4D6
- • Character stat rolling: 4d6 drop lowest (standard heroic generation)
- • Spell damage: Ice Storm (4d6 cold) and Guiding Bolt at 3rd level
- • Medium dice pools in Shadowrun and Champions
4D6 Distribution Overview
| Total Sum | Permutations | Exact Probability |
|---|---|---|
| 4 | 1/1296 | 0.08% |
| 10 | 80/1296 | 6.17% |
| 14 | 146/1296 | 11.27% |
| 18 | 80/1296 | 6.17% |
| 24 | 1/1296 | 0.08% |