Recognised as Dice notation
85d20
- 85d20
- 85 to 1700
- mean 892.5
Rolling 85d20 gives a total between 85 and 1,700, with a mean of 892.5 and a standard deviation of 53.1625. There are 386,856,262,276,681,335,905,976,320,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 equally likely ordered outcomes, and the most likely total is 892 or 893 at 0.749%.
The roll
Notation85d20
Dice85
Faces per die20
Minimum total85all 85 dice showing 1
Maximum total1,700all 85 dice showing 20
Distinct totals1,616
Mean892.5n(f + 1)/2 + modifier, exact
Variance2,826.25n(f² − 1)/12, exact
Standard deviation53.16248677≈
Counting the outcomes
Ordered outcomes386,856,262,276,681,335,905,976,320,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,00020^85, every die distinguishable
Most likely total892 and 893two totals share the peak
Chance of that total0.749056%≈
Ways to roll it2,897,768,798,179,467,840,245,924,722,578,214,505,450,839,541,025,989,302,380,824,693,752,322,832,273,763,793,429,815,564,968,886,345,526,974,875exact count
Chance of the minimum2.58493941 × 10^-109%≈1 in 386,856,262,276,681,335,905,976,320,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
Chance of the maximum2.58493941 × 10^-109%≈1 in 386,856,262,276,681,335,905,976,320,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
Shape of the distribution
1,616 distinct totals, too many to list individually.
1st percentile769≈1.025% of rolls are this or lower
5th percentile805≈5.09% of rolls are this or lower
25th percentile857≈25.547% of rolls are this or lower
50th percentile893≈50.749% of rolls are this or lower
75th percentile928≈75.053% of rolls are this or lower
95th percentile980≈95.104% of rolls are this or lower
99th percentile1,016≈99.025% of rolls are this or lower
Chance of rolling at least
247100%≈
489100%≈
89350%≈
1,2961.89038518 × 10^-13%≈
1,5391.01318592 × 10^-41%≈
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