Recognised as Dice notation

9d100

9d100
9 to 900
mean 454.5

Rolling 9d100 gives a total between 9 and 900, with a mean of 454.5 and a standard deviation of 86.5982. There are 1,000,000,000,000,000,000 equally likely ordered outcomes, and the most likely total is 454 or 455 at 0.453%.

The roll

Notation9d100

Dice9

Faces per die100

Minimum total9all 9 dice showing 1

Maximum total900all 9 dice showing 100

Distinct totals892

Mean454.5n(f + 1)/2 + modifier, exact

Variance7,499.25n(f² − 1)/12, exact

Standard deviation86.59821014≈

Counting the outcomes

Ordered outcomes1,000,000,000,000,000,000100^9, every die distinguishable

Most likely total454 and 455two totals share the peak

Chance of that total0.452935%≈

Ways to roll it4,529,350,801,080,000exact count

Chance of the minimum1 × 10^-16%≈1 in 1,000,000,000,000,000,000

Chance of the maximum1 × 10^-16%≈1 in 1,000,000,000,000,000,000

Shape of the distribution

892 distinct totals, too many to list individually.

1st percentile256≈1.022% of rolls are this or lower

5th percentile312≈5.085% of rolls are this or lower

25th percentile395≈25.094% of rolls are this or lower

50th percentile454≈50% of rolls are this or lower

75th percentile514≈75.269% of rolls are this or lower

95th percentile597≈95.038% of rolls are this or lower

99th percentile653≈99.012% of rolls are this or lower

Chance of rolling at least

9899.9999%≈

23299.5805%≈

45550%≈

6770.4357%≈

8110.0002%≈

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