Dice notation

80d20

80d20
80 to 1600
mean 840
mode 840

Rolling 80d20 gives a total between 80 and 1,600, with a mean of 840 and a standard deviation of 51.5752. There are 120,892,581,961,462,917,470,617,600,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 equally likely ordered outcomes, and the most likely total is 840 at 0.772%.

The roll

Notation80d20

Dice80

Faces per die20

Minimum total80all 80 dice showing 1

Maximum total1,600all 80 dice showing 20

Distinct totals1,521

Mean840n(f + 1)/2 + modifier, exact

Variance2,660n(f² − 1)/12, exact

Standard deviation51.57518783≈

Counting the outcomes

Ordered outcomes120,892,581,961,462,917,470,617,600,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,00020^80, every die distinguishable

Most likely total840

Chance of that total0.772057%≈

Ways to roll it933,359,558,585,281,886,423,980,714,887,660,693,456,010,488,055,977,510,123,350,626,440,261,149,235,264,936,692,813,983,090,019,081,776exact count

Chance of the minimum8.27180613 × 10^-103%≈1 in 120,892,581,961,462,917,470,617,600,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

Chance of the maximum8.27180613 × 10^-103%≈1 in 120,892,581,961,462,917,470,617,600,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

Shape of the distribution

1,521 distinct totals, too many to list individually.

1st percentile720≈1.016% of rolls are this or lower

5th percentile755≈5.07% of rolls are this or lower

25th percentile805≈25.211% of rolls are this or lower

50th percentile840≈50.386% of rolls are this or lower

75th percentile875≈75.403% of rolls are this or lower

95th percentile925≈95.129% of rolls are this or lower

99th percentile960≈99.036% of rolls are this or lower

Chance of rolling at least

232100%≈

460100%≈

84050.386%≈

1,2201.16619978 × 10^-12%≈

1,4483.62564944 × 10^-39%≈

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