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
Difficulty01+2
10 %0 %100 %
22.77 %97.22 %69.44 %
311.11 %88.88 %44.44 %
425.00 %75.00 %25.00 %
544.44 %55.55 %11.11 %
669.44 %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 ▼01+2+3+4+5+6+7+8+9+10+
133.33 %66.66 %N/AN/AN/AN/AN/AN/AN/AN/AN/A
211.11 %88.88 %44.44 %N/AN/AN/AN/AN/AN/AN/AN/A
33.70 %96.29 %74.07 %29.62 %N/AN/AN/AN/AN/AN/AN/A
41.23 %98.76 %88.88  %59.25 %19.75 %N/AN/AN/AN/AN/AN/A
50.41 %99.58 %95.47 %79.01 %46.09 %13.16 %N/AN/AN/AN/AN/A
60.14 %99.86 %98.22 %89.98 %68.04 %35.12 %8.78 %N/AN/AN/AN/A
70.05 %99.95 %99.31 %95.47 %82.67 %57.06 %26.34 %5.85 %N/AN/AN/A
80.015 %99.98 %99.74 %98.03 %91.21 %74.13 %46.82 %19.51 %3.90 %N/AN/A
90.005 %99.99 %99.91 %99.17 %95.76 %85.52 %65.03 %37.72 %14.31 %2.60 %N/A
100.002 %99.99 %99.96 %99.66 %98.03 %92.34 %78.69 %55.93 %29.91 %10.41 %1.73 %
110.0005 %99.99 %99.98 %99.86 %99.12 %96.14 %87.79 %71.10 %47.25 %23.41 %7.51 %
120.00018 %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
#Dice01+2+3+4+5
150 %50 %N/AN/AN/AN/A
225 %75 %25 %N/AN/AN/A
312.5 %87.5 %50 %12.5%N/AN/A
46.25 %93.75 %68.75  %31.25 %6.25 %N/A
53.13%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
#Dice01+2+3+4+5
166.66 %33.33 %N/AN/AN/AN/A
244.44 %55.55 %11.11 %N/AN/AN/A
329.63 %70.37 %25.92 %3.70%N/AN/A
419.75 %80.25 %40.74  %11.11 %1.23 %N/A
513.16%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
#Dice01+2+3+4+5
183.33 %16.66 %N/AN/AN/AN/A
269.44 %30.55 %2.77 %N/AN/AN/A
357.87 %42.12 %7.40 %0.46%N/AN/A
448.22 %51.77 %13.19  %1.62 %0.07 %N/A
540.18%59.81%19.62%3.54%0.33%0.01%