Recognised as Dice notation

12d87

12d87
12 to 1044
mean 528
mode 528

Rolling 12d87 gives a total between 12 and 1,044, with a mean of 528 and a standard deviation of 86.9943. There are 188,031,682,201,497,672,618,081 equally likely ordered outcomes, and the most likely total is 528 at 0.453%.

The roll

Notation12d87

Dice12

Faces per die87

Minimum total12all 12 dice showing 1

Maximum total1,044all 12 dice showing 87

Distinct totals1,033

Mean528n(f + 1)/2 + modifier, exact

Variance7,568n(f² − 1)/12, exact

Standard deviation86.99425268≈

Counting the outcomes

Ordered outcomes188,031,682,201,497,672,618,08187^12, every die distinguishable

Most likely total528

Chance of that total0.452816%≈

Ways to roll it851,438,382,858,949,242,683exact count

Chance of the minimum5.31825269 × 10^-22%≈1 in 188,031,682,201,497,672,618,081

Chance of the maximum5.31825269 × 10^-22%≈1 in 188,031,682,201,497,672,618,081

Shape of the distribution

1,033 distinct totals, too many to list individually.

1st percentile328≈1.026% of rolls are this or lower

5th percentile385≈5.095% of rolls are this or lower

25th percentile469≈25.295% of rolls are this or lower

50th percentile528≈50.226% of rolls are this or lower

75th percentile587≈75.068% of rolls are this or lower

95th percentile671≈95.027% of rolls are this or lower

99th percentile728≈99.007% of rolls are this or lower

Chance of rolling at least

115100%≈

27099.8879%≈

52850.2264%≈

7860.1171%≈

9410%≈

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