Dice notation

95d20

95d20
95 to 1900
mean 997.5

Rolling 95d20 gives a total between 95 and 1,900, with a mean of 997.5 and a standard deviation of 56.2028. There are 3,961,408,125,713,216,879,677,197,516,800,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 equally likely ordered outcomes, and the most likely total is 997 or 998 at 0.709%.

The roll

Notation95d20

Dice95

Faces per die20

Minimum total95all 95 dice showing 1

Maximum total1,900all 95 dice showing 20

Distinct totals1,806

Mean997.5n(f + 1)/2 + modifier, exact

Variance3,158.75n(f² − 1)/12, exact

Standard deviation56.20275794≈

Counting the outcomes

Ordered outcomes3,961,408,125,713,216,879,677,197,516,800,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,00020^95, every die distinguishable

Most likely total997 and 998two totals share the peak

Chance of that total0.708672%≈

Ways to roll it28,073,379,273,494,511,354,402,139,632,998,825,687,507,590,173,135,060,886,848,543,613,852,752,654,280,304,766,766,376,791,756,722,565,449,375,913,989,098,096,000exact count

Chance of the minimum2.5243549 × 10^-122%≈1 in 3,961,408,125,713,216,879,677,197,516,800,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

Chance of the maximum2.5243549 × 10^-122%≈1 in 3,961,408,125,713,216,879,677,197,516,800,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

Shape of the distribution

1,806 distinct totals, too many to list individually.

1st percentile867≈1.028% of rolls are this or lower

5th percentile905≈5.085% of rolls are this or lower

25th percentile960≈25.545% of rolls are this or lower

50th percentile997≈50% of rolls are this or lower

75th percentile1,035≈75.023% of rolls are this or lower

95th percentile1,090≈95.099% of rolls are this or lower

99th percentile1,128≈99.02% of rolls are this or lower

Chance of rolling at least

276100%≈

546100%≈

99850%≈

1,4494.21323135 × 10^-15%≈

1,7201.21232809 × 10^-46%≈

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