Dice notation
83d12
- 83d12
- 83 to 996
- mean 539.5
Rolling 83d12 gives a total between 83 and 996, with a mean of 539.5 and a standard deviation of 31.4497. There are 373,287,478,235,381,034,393,962,523,902,039,073,204,463,124,969,101,258,180,197,911,419,313,783,888,595,604,186,595,328 equally likely ordered outcomes, and the most likely total is 539 or 540 at 1.266%.
The roll
Notation83d12
Dice83
Faces per die12
Minimum total83all 83 dice showing 1
Maximum total996all 83 dice showing 12
Distinct totals914
Mean539.5n(f + 1)/2 + modifier, exact
Variance989.08333333n(f² − 1)/12, exact
Standard deviation31.44969528≈
Counting the outcomes
Ordered outcomes373,287,478,235,381,034,393,962,523,902,039,073,204,463,124,969,101,258,180,197,911,419,313,783,888,595,604,186,595,32812^83, every die distinguishable
Most likely total539 and 540two totals share the peak
Chance of that total1.266024%≈
Ways to roll it4,725,908,415,564,249,621,656,768,378,318,873,944,278,044,276,142,177,583,752,588,591,791,921,640,714,441,137,134,380exact count
Chance of the minimum2.67890047 × 10^-88%≈1 in 373,287,478,235,381,034,393,962,523,902,039,073,204,463,124,969,101,258,180,197,911,419,313,783,888,595,604,186,595,328
Chance of the maximum2.67890047 × 10^-88%≈1 in 373,287,478,235,381,034,393,962,523,902,039,073,204,463,124,969,101,258,180,197,911,419,313,783,888,595,604,186,595,328
Shape of the distribution
914 distinct totals, too many to list individually.
1st percentile466≈1.004% of rolls are this or lower
5th percentile488≈5.247% of rolls are this or lower
25th percentile518≈25.248% of rolls are this or lower
50th percentile539≈50% of rolls are this or lower
75th percentile561≈75.756% of rolls are this or lower
95th percentile591≈95.086% of rolls are this or lower
99th percentile613≈99.078% of rolls are this or lower
Chance of rolling at least
174100%≈
311100%≈
54050%≈
7683.16715174 × 10^-12%≈
9053.14973341 × 10^-37%≈
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