Dice notation

36d20

36d20
36 to 720
mean 378
mode 378

Rolling 36d20 gives a total between 36 and 720, with a mean of 378 and a standard deviation of 34.5977. There are 68,719,476,736,000,000,000,000,000,000,000,000,000,000,000,000 equally likely ordered outcomes, and the most likely total is 378 at 1.148%.

The roll

Notation36d20

Dice36

Faces per die20

Minimum total36all 36 dice showing 1

Maximum total720all 36 dice showing 20

Distinct totals685

Mean378n(f + 1)/2 + modifier, exact

Variance1,197n(f² − 1)/12, exact

Standard deviation34.59768778≈

Counting the outcomes

Ordered outcomes68,719,476,736,000,000,000,000,000,000,000,000,000,000,000,00020^36, every die distinguishable

Most likely total378

Chance of that total1.148251%≈

Ways to roll it789,072,020,995,954,317,420,136,112,337,803,371,615,594,200exact count

Chance of the minimum1.45519152 × 10^-45%≈1 in 68,719,476,736,000,000,000,000,000,000,000,000,000,000,000,000

Chance of the maximum1.45519152 × 10^-45%≈1 in 68,719,476,736,000,000,000,000,000,000,000,000,000,000,000,000

Shape of the distribution

685 distinct totals, too many to list individually.

1st percentile298≈1.057% of rolls are this or lower

5th percentile321≈5.13% of rolls are this or lower

25th percentile355≈25.849% of rolls are this or lower

50th percentile378≈50.574% of rolls are this or lower

75th percentile401≈75.075% of rolls are this or lower

95th percentile435≈95.169% of rolls are this or lower

99th percentile458≈99.023% of rolls are this or lower

Chance of rolling at least

104100%≈

207100%≈

37850.5741%≈

5490%≈

6521.62075211 × 10^-17%≈

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