Dice notation
36d12
- 36d12
- 36 to 432
- mean 234
- mode 234
Rolling 36d12 gives a total between 36 and 432, with a mean of 234 and a standard deviation of 20.7123. There are 708,801,874,985,091,845,381,344,307,009,569,161,216 equally likely ordered outcomes, and the most likely total is 234 at 1.918%.
The roll
Notation36d12
Dice36
Faces per die12
Minimum total36all 36 dice showing 1
Maximum total432all 36 dice showing 12
Distinct totals397
Mean234n(f + 1)/2 + modifier, exact
Variance429n(f² − 1)/12, exact
Standard deviation20.71231518≈
Counting the outcomes
Ordered outcomes708,801,874,985,091,845,381,344,307,009,569,161,21612^36, every die distinguishable
Most likely total234
Chance of that total1.917958%≈
Ways to roll it13,594,521,618,814,837,432,015,618,986,816,248,776exact count
Chance of the minimum1.41083148 × 10^-37%≈1 in 708,801,874,985,091,845,381,344,307,009,569,161,216
Chance of the maximum1.41083148 × 10^-37%≈1 in 708,801,874,985,091,845,381,344,307,009,569,161,216
Shape of the distribution
397 distinct totals, too many to list individually.
1st percentile186≈1.069% of rolls are this or lower
5th percentile200≈5.298% of rolls are this or lower
25th percentile220≈25.802% of rolls are this or lower
50th percentile234≈50.959% of rolls are this or lower
75th percentile248≈75.73% of rolls are this or lower
95th percentile268≈95.207% of rolls are this or lower
99th percentile282≈99.062% of rolls are this or lower
Chance of rolling at least
76100%≈
135100%≈
23450.959%≈
3330%≈
3928.70754761 × 10^-16%≈
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