Generators & Randomness
Dice Average and Probability Calculator
Calculate exact dice averages and target odds from plain notation. Compare rolls with advantage, rerolls, keep rules, and capped explosions.
Worked example result
Select Load example to use these values in the calculator.
- Dice expression
- 4d6dl1
- Target total
- 15
Average
- Exact mean
- 15869/1296
- Standard deviation
- 2.8468
- Minimum
- 3
- Maximum
- 18
- Median
- 12
- Most likely total
- 13
Target odds
- P(total >= 15)
- 23.1481% (25/108)
- P(total <= 15)
- 86.9599% (1127/1296)
Relative probability
- 30.0772% (1/1296)
- 40.3086% (1/324)
- 50.7716% (5/648)
- 61.6204% (7/432)
- 72.9321% (19/648)
- 84.7840% (31/648)
- 97.0216% (91/1296)
- 109.4136% (61/648)
- 1111.4198% (37/324)
- 1212.8858% (167/1296)
- 1313.2716% (43/324)
- 1412.3457% (10/81)
- 1510.1080% (131/1296)
- 167.2531% (47/648)
- 174.1667% (1/24)
- 181.6204% (7/432)
Exact distribution
| Total | Chance | Chance of at least this total |
|---|---|---|
| 3 | 0.0772% (1/1296) | 100.0000% (1/1) |
| 4 | 0.3086% (1/324) | 99.9228% (1295/1296) |
| 5 | 0.7716% (5/648) | 99.6142% (1291/1296) |
| 6 | 1.6204% (7/432) | 98.8426% (427/432) |
| 7 | 2.9321% (19/648) | 97.2222% (35/36) |
| 8 | 4.7840% (31/648) | 94.2901% (611/648) |
| 9 | 7.0216% (91/1296) | 89.5062% (145/162) |
| 10 | 9.4136% (61/648) | 82.4846% (1069/1296) |
| 11 | 11.4198% (37/324) | 73.0710% (947/1296) |
| 12 | 12.8858% (167/1296) | 61.6512% (799/1296) |
| 13 | 13.2716% (43/324) | 48.7654% (79/162) |
| 14 | 12.3457% (10/81) | 35.4938% (115/324) |
| 15 | 10.1080% (131/1296) | 23.1481% (25/108) |
| 16 | 7.2531% (47/648) | 13.0401% (169/1296) |
| 17 | 4.1667% (1/24) | 5.7870% (25/432) |
| 18 | 1.6204% (7/432) | 1.6204% (7/432) |
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The calculation combines integer probability weights. It applies rerolls and capped explosions before keep/drop and group advantage rules.
The result includes the total distribution, average, spread, and optional target probabilities.
- Compare two ability score rules before choosing one for a game.
Write dice terms and select probability comparisons
- Enter Dice expression with dice groups joined by + or -.
- Add keep, drop, reroll, explosion, or advantage notation as required.
- Optionally enter Compare with and Target total, then select Calculate exact dice odds.
Drop the lowest die from 4d6
Input: 4d6dl1
Settings: Target total: 18; Compare with: blank
Result: 12.2446
The exact mean equals 15869/1296. The chance of reaching 18 equals 1.6204% (7/432).
Expression limits and independent rolls
- The model assumes independent, fair dice.
- Explosions stop after four extra rolls per die.
- Parentheses, multiplication, and repeated rerolls are unsupported.
- Standard deviation uses approximation. Large probability fractions may display percentages only.