Dice notation
90d12
- 90d12
- 90 to 1080
- mean 585
- mode 585
Rolling 90d12 gives a total between 90 and 1,080, with a mean of 585 and a standard deviation of 32.749. There are 13,375,565,248,934,352,031,245,861,515,653,274,879,560,267,436,972,842,215,671,280,963,977,858,996,049,651,078,858,079,966,593,024 equally likely ordered outcomes, and the most likely total is 585 at 1.216%.
The roll
Notation90d12
Dice90
Faces per die12
Minimum total90all 90 dice showing 1
Maximum total1,080all 90 dice showing 12
Distinct totals991
Mean585n(f + 1)/2 + modifier, exact
Variance1,072.5n(f² − 1)/12, exact
Standard deviation32.74904579≈
Counting the outcomes
Ordered outcomes13,375,565,248,934,352,031,245,861,515,653,274,879,560,267,436,972,842,215,671,280,963,977,858,996,049,651,078,858,079,966,593,02412^90, every die distinguishable
Most likely total585
Chance of that total1.21612%≈
Ways to roll it162,662,862,138,348,655,079,548,132,563,302,225,953,830,392,413,960,342,879,269,252,979,176,866,242,909,181,425,566,235,777,712exact count
Chance of the minimum7.47631955 × 10^-96%≈1 in 13,375,565,248,934,352,031,245,861,515,653,274,879,560,267,436,972,842,215,671,280,963,977,858,996,049,651,078,858,079,966,593,024
Chance of the maximum7.47631955 × 10^-96%≈1 in 13,375,565,248,934,352,031,245,861,515,653,274,879,560,267,436,972,842,215,671,280,963,977,858,996,049,651,078,858,079,966,593,024
Shape of the distribution
991 distinct totals, too many to list individually.
1st percentile509≈1.048% of rolls are this or lower
5th percentile531≈5.119% of rolls are this or lower
25th percentile563≈25.605% of rolls are this or lower
50th percentile585≈50.608% of rolls are this or lower
75th percentile607≈75.367% of rolls are this or lower
95th percentile639≈95.195% of rolls are this or lower
99th percentile661≈99.034% of rolls are this or lower
Chance of rolling at least
189100%≈
338100%≈
58550.6081%≈
8332.61343418 × 10^-13%≈
9812.6723382 × 10^-40%≈
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