Dice notation

28d10

28d10
28 to 280
mean 154
mode 154

Rolling 28d10 gives a total between 28 and 280, with a mean of 154 and a standard deviation of 15.1987. There are 10,000,000,000,000,000,000,000,000,000 equally likely ordered outcomes, and the most likely total is 154 at 2.61%.

The roll

Notation28d10

Dice28

Faces per die10

Minimum total28all 28 dice showing 1

Maximum total280all 28 dice showing 10

Distinct totals253

Mean154n(f + 1)/2 + modifier, exact

Variance231n(f² − 1)/12, exact

Standard deviation15.19868415≈

Counting the outcomes

Ordered outcomes10,000,000,000,000,000,000,000,000,00010^28, every die distinguishable

Most likely total154

Chance of that total2.610467%≈

Ways to roll it261,046,730,157,780,861,858,821,136exact count

Chance of the minimum1 × 10^-26%≈1 in 10,000,000,000,000,000,000,000,000,000

Chance of the maximum1 × 10^-26%≈1 in 10,000,000,000,000,000,000,000,000,000

Shape of the distribution

253 distinct totals, too many to list individually.

1st percentile119≈1.132% of rolls are this or lower

5th percentile129≈5.358% of rolls are this or lower

25th percentile144≈26.691% of rolls are this or lower

50th percentile154≈51.305% of rolls are this or lower

75th percentile164≈75.42% of rolls are this or lower

95th percentile179≈95.328% of rolls are this or lower

99th percentile189≈99.054% of rolls are this or lower

Chance of rolling at least

53100%≈

9199.9992%≈

15451.3052%≈

2170.0012%≈

2558.99693337 × 10^-12%≈

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