Dice notation
65d12
- 65d12
- 65 to 780
- mean 422.5
Rolling 65d12 gives a total between 65 and 780, with a mean of 422.5 and a standard deviation of 27.8313. There are 14,021,064,691,527,197,542,117,777,666,481,419,913,141,060,406,757,937,147,493,789,972,037,632 equally likely ordered outcomes, and the most likely total is 422 or 423 at 1.43%.
The roll
Notation65d12
Dice65
Faces per die12
Minimum total65all 65 dice showing 1
Maximum total780all 65 dice showing 12
Distinct totals716
Mean422.5n(f + 1)/2 + modifier, exact
Variance774.58333333n(f² − 1)/12, exact
Standard deviation27.83133725≈
Counting the outcomes
Ordered outcomes14,021,064,691,527,197,542,117,777,666,481,419,913,141,060,406,757,937,147,493,789,972,037,63212^65, every die distinguishable
Most likely total422 and 423two totals share the peak
Chance of that total1.429842%≈
Ways to roll it200,479,059,467,746,214,016,685,863,708,193,648,205,110,018,772,909,118,332,687,285,103,060exact count
Chance of the minimum7.132126 × 10^-69%≈1 in 14,021,064,691,527,197,542,117,777,666,481,419,913,141,060,406,757,937,147,493,789,972,037,632
Chance of the maximum7.132126 × 10^-69%≈1 in 14,021,064,691,527,197,542,117,777,666,481,419,913,141,060,406,757,937,147,493,789,972,037,632
Shape of the distribution
716 distinct totals, too many to list individually.
1st percentile358≈1.062% of rolls are this or lower
5th percentile377≈5.3% of rolls are this or lower
25th percentile404≈25.931% of rolls are this or lower
50th percentile423≈51.43% of rolls are this or lower
75th percentile441≈75.218% of rolls are this or lower
95th percentile468≈95.079% of rolls are this or lower
99th percentile487≈99.036% of rolls are this or lower
Chance of rolling at least
137100%≈
244100%≈
42350%≈
6011.89401911 × 10^-9%≈
7093.65952078 × 10^-29%≈
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