Probabilities of small dice pools
The tables show the probabilities to get a certain amount of successes against a difficulty number rolling a certain number of six-sided dice (d6). A success is when a die shows the required difficulty number or higher.
| 1d6 | # Successes | |
|---|---|---|
| Difficulty | 0 | 1 |
| 1 | 0 % | 100 % |
| 2 | 16.66 % | 83.33 % |
| 3 | 33.33 % | 66.66 % |
| 4 | 50 % | 50 % |
| 5 | 66.66 % | 33.33 % |
| 6 | 83.33 % | 16.66 % |
| 2d6 | # Successes | ||
|---|---|---|---|
| Difficulty | 0 | 1+ | 2 |
| 1 | 0 % | 0 % | 100 % |
| 2 | 2.77 % | 97.22 % | 69.44 % |
| 3 | 11.11 % | 88.88 % | 44.44 % |
| 4 | 25.00 % | 75.00 % | 25.00 % |
| 5 | 44.44 % | 55.55 % | 11.11 % |
| 6 | 69.44 % | 30.55 % | 2.77 % |
Impossible
Chances for success almost non-existent.
0.00 - 16.66 %
0.00 - 16.66 %
Unlikely
It will be a rare that a player rolls this result.
16.67 - 33.33 %
16.67 - 33.33 %
Unfavorable
Chances for success are quite bad.
33.34 - 49.99 %
33.34 - 49.99 %
Balanced
Chances for success are balanced.
50.00 - 66.66 %
50.00 - 66.66 %
Good
Chances for success are quite good.
66.67 - 83.33 %
66.67 - 83.33 %
Safe
Chances for success are dead certain.
83.34 - 99.99 %
83.34 - 99.99 %
| 3d6 | # Successes | |||
|---|---|---|---|---|
| Difficulty | 0 | 1+ | 2+ | 3 |
| 1 | 0% | 0% | 0% | 100% |
| 2 | 0.46 % | 99.54 % | 92.59 % | 57.87 % |
| 3 | 3.70 % | 96.29 % | 74.07 % | 29.63 % |
| 4 | 12.5 % | 87.5 % | 50.0 % | 12.5 % |
| 5 | 29.63 % | 70.37 % | 25.93 % | 3.70% |
| 6 | 57.87 % | 42.13 % | 7.41 % | 0.46% |
| 4d6 | # Successes | ||||
|---|---|---|---|---|---|
| Difficulty | 0 | 1+ | 2+ | 3+ | 4 |
| 1 | 0% | 0% | 0% | 0% | 100% |
| 2 | 0.07 % | 99.92 % | 98.38 % | 86.80 % | 48.23 % |
| 3 | 1.23 % | 98.76 % | 88.88 % | 59.26 % | 19.75 % |
| 4 | 6.25 % | 93.75 % | 68.75 % | 31.25 % | 6.25 % |
| 5 | 19.75 % | 80.25 % | 40.74 % | 11.11 % | 1.23 % |
| 6 | 48.22 % | 51.77 % | 13.19 % | 1.62 % | 0.08 % |
| 5d6 | # Successes | |||||
|---|---|---|---|---|---|---|
| Difficulty | 0 | 1+ | 2+ | 3+ | 4+ | 5 |
| 1 | 0 % | 0 % | 0 % | 0 % | 0 % | 100 % |
| 2 | 0.01 % | 99.98 % | 99.66 % | 96.45 % | 80.38 % | 40.19 % |
| 3 | 0.41 % | 99.59 % | 95.47 % | 79.01 % | 46.09 % | 13.17 % |
| 4 | 3.13 % | 96.88 % | 81.25 % | 50 % | 18.75 % | 3.13 % |
| 5 | 13.17% | 86.83% | 53.90% | 20.97% | 4.53% | 0.41% |
| 6 | 40.18% | 59.81% | 19.62% | 3.55% | 0.33% | 0.01% |
Impossible
Chances for success almost non-existent.
0.00 - 16.66 %
0.00 - 16.66 %
Unlikely
It will be a rare that a player rolls this result.
16.67 - 33.33 %
16.67 - 33.33 %
Unfavorable
Chances for success are quite bad.
33.34 - 49.99 %
33.34 - 49.99 %
Balanced
Chances for success are balanced.
50.00 - 66.66 %
50.00 - 66.66 %
Good
Chances for success are quite good.
66.67 - 83.33 %
66.67 - 83.33 %
Safe
Chances for success are dead certain.
83.34 - 99.99 %
83.34 - 99.99 %
D6 Pools where 3+ is a success
The table below shows the probabilities to get a certain amount of successes rolling a certain number of six-sided dice (d6). Each die showing a 3 or higher counts as one success.
| # Successes | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| # Dice ▼ | 0 | 1+ | 2+ | 3+ | 4+ | 5+ | 6+ | 7+ | 8+ | 9+ | 10+ |
| 1 | 33.33 % | 66.66 % | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
| 2 | 11.11 % | 88.88 % | 44.44 % | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
| 3 | 3.70 % | 96.29 % | 74.07 % | 29.62 % | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
| 4 | 1.23 % | 98.76 % | 88.88 % | 59.25 % | 19.75 % | N/A | N/A | N/A | N/A | N/A | N/A |
| 5 | 0.41 % | 99.58 % | 95.47 % | 79.01 % | 46.09 % | 13.16 % | N/A | N/A | N/A | N/A | N/A |
| 6 | 0.14 % | 99.86 % | 98.22 % | 89.98 % | 68.04 % | 35.12 % | 8.78 % | N/A | N/A | N/A | N/A |
| 7 | 0.05 % | 99.95 % | 99.31 % | 95.47 % | 82.67 % | 57.06 % | 26.34 % | 5.85 % | N/A | N/A | N/A |
| 8 | 0.015 % | 99.98 % | 99.74 % | 98.03 % | 91.21 % | 74.13 % | 46.82 % | 19.51 % | 3.90 % | N/A | N/A |
| 9 | 0.005 % | 99.99 % | 99.91 % | 99.17 % | 95.76 % | 85.52 % | 65.03 % | 37.72 % | 14.31 % | 2.60 % | N/A |
| 10 | 0.002 % | 99.99 % | 99.96 % | 99.66 % | 98.03 % | 92.34 % | 78.69 % | 55.93 % | 29.91 % | 10.41 % | 1.73 % |
| 11 | 0.0005 % | 99.99 % | 99.98 % | 99.86 % | 99.12 % | 96.14 % | 87.79 % | 71.10 % | 47.25 % | 23.41 % | 7.51 % |
| 12 | 0.00018 % | 99.99 % | 99.99 % | 99.95 % | 99.61 % | 98.12 % | 93.35 % | 82.23 % | 63.15 % | 39.31 % | 18.11 % |
| 13 | < 0.0001 % | 99.99 % | 99.99 % | 99.98 % | 99.83 % | 99.12 % | 96.53 % | 89.65 % | 75.87 % | 55.20 % | 32.24 % |
| 14 | < 0.0001 % | 99.99 % | 99.99 % | 99.99 % | 99.93 % | 99.59 % | 98.25 % | 94.24 % | 85.05 % | 68.98 % | 47.55 % |
| 15 | < 0.0001 % | 99.99 % | 99.99 % | 99.99 % | 99.97 % | 99.82 % | 99.15 % | 96.92 % | 91.17 % | 79.69 % | 61.83 % |
D6 Pools where 4+ is a success
The table below shows the probabilities to get a certain amount of successes rolling a certain number of six-sided dice (d6). Each die showing a 4 or higher counts as one success.
| # Successes | ||||||
|---|---|---|---|---|---|---|
| #Dice | 0 | 1+ | 2+ | 3+ | 4+ | 5 |
| 1 | 50 % | 50 % | N/A | N/A | N/A | N/A |
| 2 | 25 % | 75 % | 25 % | N/A | N/A | N/A |
| 3 | 12.5 % | 87.5 % | 50 % | 12.5% | N/A | N/A |
| 4 | 6.25 % | 93.75 % | 68.75 % | 31.25 % | 6.25 % | N/A |
| 5 | 3.13% | 96.87% | 81.25% | 50% | 18.75% | 3.12% |
D6 Pools where 5+ is a success
The table below shows the probabilities to get a certain amount of successes rolling a certain number of six-sided dice (d6). Each die showing a 5 or higher counts as one success.
| # Successes | ||||||
|---|---|---|---|---|---|---|
| #Dice | 0 | 1+ | 2+ | 3+ | 4+ | 5 |
| 1 | 66.66 % | 33.33 % | N/A | N/A | N/A | N/A |
| 2 | 44.44 % | 55.55 % | 11.11 % | N/A | N/A | N/A |
| 3 | 29.63 % | 70.37 % | 25.92 % | 3.70% | N/A | N/A |
| 4 | 19.75 % | 80.25 % | 40.74 % | 11.11 % | 1.23 % | N/A |
| 5 | 13.16% | 86.83% | 53.90% | 20.98% | 4.52% | 0.41% |
D6 Pools where 6+ is a success
The table below shows the probabilities to get a certain amount of successes rolling a certain number of six-sided dice (d6). Each die showing a 6 counts as one success.
| # Successes | ||||||
|---|---|---|---|---|---|---|
| #Dice | 0 | 1+ | 2+ | 3+ | 4+ | 5 |
| 1 | 83.33 % | 16.66 % | N/A | N/A | N/A | N/A |
| 2 | 69.44 % | 30.55 % | 2.77 % | N/A | N/A | N/A |
| 3 | 57.87 % | 42.12 % | 7.40 % | 0.46% | N/A | N/A |
| 4 | 48.22 % | 51.77 % | 13.19 % | 1.62 % | 0.07 % | N/A |
| 5 | 40.18% | 59.81% | 19.62% | 3.54% | 0.33% | 0.01% |
Unlikely
Chances for success almost non-existent.
0.00 - 16.66 %
0.00 - 16.66 %
Low
It will be a rare that a player rolls this result.
16.67 - 33.33 %
16.67 - 33.33 %
Possible
Chances for success are quite bad.
33.34 - 49.99 %
33.34 - 49.99 %
Fair
Chances for success are balanced.
50.00 - 66.66 %
50.00 - 66.66 %
Good
Chances for success are quite good.
66.67 - 83.33 %
66.67 - 83.33 %
Likely
Chances for success are very high.
83.34 - 99.99 %
83.34 - 99.99 %