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
Difficulty01
10 %100 %
216.66 %83.33 %
333.33 %66.66 %
450 %50 %
566.66 %33.33 %
683.33 %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 %
3d6# Successes
Difficulty01+2+3
10%0%0%100%
20.46 %99.54 %92.59 %57.87 %
33.70 %96.29 %74.07 %29.63 %
412.5 %87.5 %50.0 %12.5 %
529.63 %70.37 %25.93 %3.70%
657.87 %42.13 %7.41 %0.46%
4d6# Successes
Difficulty01+2+3+4
10%0%0%0%100%
20.07 %99.92 %98.38 %86.80 %48.23 %
31.23 %98.76 %88.88 %59.26 %19.75 %
46.25 %93.75 %68.75 %31.25 %6.25 %
519.75 %80.25 %40.74 %11.11 %1.23 %
648.22 % 51.77 %13.19 %1.62 %0.08 %
5d6# Successes
Difficulty01+2+3+4+5
10 %0 %0 %0 %0 %100 %
20.01 %99.98 %99.66 %96.45 %80.38 %40.19 %
30.41 %99.59 %95.47 %79.01 %46.09 %13.17 %
43.13 %96.88 %81.25  %50 %18.75 %3.13 %
513.17%86.83%53.90%20.97%4.53%0.41%
640.18%59.81%19.62%3.55%0.33%0.01%

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/AN/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%