Dice notation
72d12
- 72d12
- 72 to 864
- mean 468
- mode 468
Rolling 72d12 gives a total between 72 and 864, with a mean of 468 and a standard deviation of 29.2916. There are 502,400,097,982,381,769,107,236,122,732,050,273,895,047,153,411,352,306,345,065,163,470,377,798,598,656 equally likely ordered outcomes, and the most likely total is 468 at 1.359%.
The roll
Notation72d12
Dice72
Faces per die12
Minimum total72all 72 dice showing 1
Maximum total864all 72 dice showing 12
Distinct totals793
Mean468n(f + 1)/2 + modifier, exact
Variance858n(f² − 1)/12, exact
Standard deviation29.29163703≈
Counting the outcomes
Ordered outcomes502,400,097,982,381,769,107,236,122,732,050,273,895,047,153,411,352,306,345,065,163,470,377,798,598,65612^72, every die distinguishable
Most likely total468
Chance of that total1.359087%≈
Ways to roll it6,828,052,088,558,902,766,486,464,444,643,120,881,900,699,668,915,078,401,893,502,915,724,118,892,184exact count
Chance of the minimum1.99044547 × 10^-76%≈1 in 502,400,097,982,381,769,107,236,122,732,050,273,895,047,153,411,352,306,345,065,163,470,377,798,598,656
Chance of the maximum1.99044547 × 10^-76%≈1 in 502,400,097,982,381,769,107,236,122,732,050,273,895,047,153,411,352,306,345,065,163,470,377,798,598,656
Shape of the distribution
793 distinct totals, too many to list individually.
1st percentile400≈1.049% of rolls are this or lower
5th percentile420≈5.248% of rolls are this or lower
25th percentile448≈25.317% of rolls are this or lower
50th percentile468≈50.68% of rolls are this or lower
75th percentile488≈75.762% of rolls are this or lower
95th percentile516≈95.109% of rolls are this or lower
99th percentile536≈99.043% of rolls are this or lower
Chance of rolling at least
151100%≈
270100%≈
46850.6795%≈
6661.54707866 × 10^-10%≈
7853.07312747 × 10^-32%≈
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