Dice notation

84d20

84d20
84 to 1680
mean 882
mode 882

Rolling 84d20 gives a total between 84 and 1,680, with a mean of 882 and a standard deviation of 52.8488. There are 19,342,813,113,834,066,795,298,816,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 equally likely ordered outcomes, and the most likely total is 882 at 0.754%.

The roll

Notation84d20

Dice84

Faces per die20

Minimum total84all 84 dice showing 1

Maximum total1,680all 84 dice showing 20

Distinct totals1,597

Mean882n(f + 1)/2 + modifier, exact

Variance2,793n(f² − 1)/12, exact

Standard deviation52.84884105≈

Counting the outcomes

Ordered outcomes19,342,813,113,834,066,795,298,816,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,00020^84, every die distinguishable

Most likely total882

Chance of that total0.753518%≈

Ways to roll it145,751,631,878,954,505,826,933,285,656,347,031,391,629,247,378,847,243,737,212,001,633,522,343,667,033,548,814,387,771,724,200,036,517,060,080exact count

Chance of the minimum5.16987883 × 10^-108%≈1 in 19,342,813,113,834,066,795,298,816,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

Chance of the maximum5.16987883 × 10^-108%≈1 in 19,342,813,113,834,066,795,298,816,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

Shape of the distribution

1,597 distinct totals, too many to list individually.

1st percentile759≈1.014% of rolls are this or lower

5th percentile795≈5.087% of rolls are this or lower

25th percentile846≈25.12% of rolls are this or lower

50th percentile882≈50.377% of rolls are this or lower

75th percentile918≈75.478% of rolls are this or lower

95th percentile969≈95.108% of rolls are this or lower

99th percentile1,005≈99.037% of rolls are this or lower

Chance of rolling at least

244100%≈

483100%≈

88250.3768%≈

1,2812.62918372 × 10^-13%≈

1,5204.59974596 × 10^-41%≈

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