Dice notation
33d12
- 33d12
- 33 to 396
- mean 214.5
Rolling 33d12 gives a total between 33 and 396, with a mean of 214.5 and a standard deviation of 19.8305. There are 410,186,270,246,002,225,336,426,103,593,500,672 equally likely ordered outcomes, and the most likely total is 214 or 215 at 2.002%.
The roll
Notation33d12
Dice33
Faces per die12
Minimum total33all 33 dice showing 1
Maximum total396all 33 dice showing 12
Distinct totals364
Mean214.5n(f + 1)/2 + modifier, exact
Variance393.25n(f² − 1)/12, exact
Standard deviation19.83053202≈
Counting the outcomes
Ordered outcomes410,186,270,246,002,225,336,426,103,593,500,67212^33, every die distinguishable
Most likely total214 and 215two totals share the peak
Chance of that total2.001841%≈
Ways to roll it8,211,277,599,539,705,460,244,343,046,723,732exact count
Chance of the minimum2.4379168 × 10^-34%≈1 in 410,186,270,246,002,225,336,426,103,593,500,672
Chance of the maximum2.4379168 × 10^-34%≈1 in 410,186,270,246,002,225,336,426,103,593,500,672
Shape of the distribution
364 distinct totals, too many to list individually.
1st percentile169≈1.139% of rolls are this or lower
5th percentile182≈5.339% of rolls are this or lower
25th percentile201≈25.687% of rolls are this or lower
50th percentile214≈50% of rolls are this or lower
75th percentile228≈75.907% of rolls are this or lower
95th percentile247≈95.191% of rolls are this or lower
99th percentile260≈99.006% of rolls are this or lower
Chance of rolling at least
69100%≈
12499.9999%≈
21550%≈
3050.0001%≈
3601.28548017 × 10^-14%≈
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