Recognised as Dice notation

4d820

4d820
4 to 3280
mean 1,642
mode 1642

Rolling 4d820 gives a total between 4 and 3,280, with a mean of 1,642 and a standard deviation of 473.4269. There are 452,121,760,000 equally likely ordered outcomes, and the most likely total is 1,642 at 0.081%.

The roll

Notation4d820

Dice4

Faces per die820

Minimum total4all 4 dice showing 1

Maximum total3,280all 4 dice showing 820

Distinct totals3,277

Mean1,642n(f + 1)/2 + modifier, exact

Variance224,133n(f² − 1)/12, exact

Standard deviation473.42686869≈

Counting the outcomes

Ordered outcomes452,121,760,000820^4, every die distinguishable

Most likely total1,642

Chance of that total0.081301%≈

Ways to roll it367,578,940exact count

Chance of the minimum2.21179357 × 10^-10%≈1 in 452,121,760,000

Chance of the maximum2.21179357 × 10^-10%≈1 in 452,121,760,000

Shape of the distribution

3,277 distinct totals, too many to list individually.

1st percentile576≈1.004% of rolls are this or lower

5th percentile860≈5.006% of rolls are this or lower

25th percentile1,312≈25.048% of rolls are this or lower

50th percentile1,642≈50.041% of rolls are this or lower

75th percentile1,972≈75.017% of rolls are this or lower

95th percentile2,424≈95.017% of rolls are this or lower

99th percentile2,708≈99.003% of rolls are this or lower

Chance of rolling at least

33299.8914%≈

82395.8232%≈

1,64250.0407%≈

2,4614.1972%≈

2,9520.11%≈

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