Recognised as Dice notation

44d20

44d20
44 to 880
mean 462
mode 462

Rolling 44d20 gives a total between 44 and 880, with a mean of 462 and a standard deviation of 38.2492. There are 1,759,218,604,441,600,000,000,000,000,000,000,000,000,000,000,000,000,000,000 equally likely ordered outcomes, and the most likely total is 462 at 1.039%.

The roll

Notation44d20

Dice44

Faces per die20

Minimum total44all 44 dice showing 1

Maximum total880all 44 dice showing 20

Distinct totals837

Mean462n(f + 1)/2 + modifier, exact

Variance1,463n(f² − 1)/12, exact

Standard deviation38.249183≈

Counting the outcomes

Ordered outcomes1,759,218,604,441,600,000,000,000,000,000,000,000,000,000,000,000,000,000,00020^44, every die distinguishable

Most likely total462

Chance of that total1.039429%≈

Ways to roll it18,285,829,820,610,603,959,637,582,274,969,009,577,428,037,285,922,497,100exact count

Chance of the minimum5.68434189 × 10^-56%≈1 in 1,759,218,604,441,600,000,000,000,000,000,000,000,000,000,000,000,000,000,000

Chance of the maximum5.68434189 × 10^-56%≈1 in 1,759,218,604,441,600,000,000,000,000,000,000,000,000,000,000,000,000,000,000

Shape of the distribution

837 distinct totals, too many to list individually.

1st percentile373≈1.016% of rolls are this or lower

5th percentile399≈5.119% of rolls are this or lower

25th percentile436≈25.311% of rolls are this or lower

50th percentile462≈50.52% of rolls are this or lower

75th percentile488≈75.517% of rolls are this or lower

95th percentile525≈95.152% of rolls are this or lower

99th percentile551≈99.053% of rolls are this or lower

Chance of rolling at least

128100%≈

253100%≈

46250.5197%≈

6718.35170372 × 10^-7%≈

7962.47821681 × 10^-21%≈

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