Dice notation

90d10

90d10
90 to 900
mean 495
mode 495

Rolling 90d10 gives a total between 90 and 900, with a mean of 495 and a standard deviation of 27.2489. There are 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 equally likely ordered outcomes, and the most likely total is 495 at 1.462%.

The roll

Notation90d10

Dice90

Faces per die10

Minimum total90all 90 dice showing 1

Maximum total900all 90 dice showing 10

Distinct totals811

Mean495n(f + 1)/2 + modifier, exact

Variance742.5n(f² − 1)/12, exact

Standard deviation27.24885319≈

Counting the outcomes

Ordered outcomes1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,00010^90, every die distinguishable

Most likely total495

Chance of that total1.461579%≈

Ways to roll it14,615,786,698,841,561,369,944,959,191,566,195,353,879,505,580,317,403,926,959,872,129,388,565,881,505,390,562,968,052exact count

Chance of the minimum1 × 10^-88%≈1 in 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

Chance of the maximum1 × 10^-88%≈1 in 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

Shape of the distribution

811 distinct totals, too many to list individually.

1st percentile432≈1.082% of rolls are this or lower

5th percentile450≈5.125% of rolls are this or lower

25th percentile477≈26.066% of rolls are this or lower

50th percentile495≈50.731% of rolls are this or lower

75th percentile513≈75.111% of rolls are this or lower

95th percentile540≈95.251% of rolls are this or lower

99th percentile558≈99.02% of rolls are this or lower

Chance of rolling at least

171100%≈

293100%≈

49550.7308%≈

6987.78783704 × 10^-13%≈

8191.3872769 × 10^-38%≈

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