Dice notation

98d10

98d10
98 to 980
mean 539
mode 539

Rolling 98d10 gives a total between 98 and 980, with a mean of 539 and a standard deviation of 28.4341. There are 100,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 equally likely ordered outcomes, and the most likely total is 539 at 1.401%.

The roll

Notation98d10

Dice98

Faces per die10

Minimum total98all 98 dice showing 1

Maximum total980all 98 dice showing 10

Distinct totals883

Mean539n(f + 1)/2 + modifier, exact

Variance808.5n(f² − 1)/12, exact

Standard deviation28.43413442≈

Counting the outcomes

Ordered outcomes100,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,00010^98, every die distinguishable

Most likely total539

Chance of that total1.400848%≈

Ways to roll it1,400,847,570,487,018,446,424,152,137,399,824,237,820,256,780,329,223,966,658,770,240,584,725,100,387,355,667,521,375,484,520,200exact count

Chance of the minimum1 × 10^-96%≈1 in 100,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

Chance of the maximum1 × 10^-96%≈1 in 100,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

Shape of the distribution

883 distinct totals, too many to list individually.

1st percentile473≈1.054% of rolls are this or lower

5th percentile492≈5.101% of rolls are this or lower

25th percentile520≈25.792% of rolls are this or lower

50th percentile539≈50.7% of rolls are this or lower

75th percentile558≈75.33% of rolls are this or lower

95th percentile586≈95.258% of rolls are this or lower

99th percentile605≈99.041% of rolls are this or lower

Chance of rolling at least

186100%≈

319100%≈

53950.7004%≈

7605.37118483 × 10^-14%≈

8924.20548818 × 10^-42%≈

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