Dice notation
19d12
- 19d12
- 19 to 228
- mean 123.5
Rolling 19d12 gives a total between 19 and 228, with a mean of 123.5 and a standard deviation of 15.0471. There are 319,479,999,370,622,926,848 equally likely ordered outcomes, and the most likely total is 123 or 124 at 2.629%.
The roll
Notation19d12
Dice19
Faces per die12
Minimum total19all 19 dice showing 1
Maximum total228all 19 dice showing 12
Distinct totals210
Mean123.5n(f + 1)/2 + modifier, exact
Variance226.41666667n(f² − 1)/12, exact
Standard deviation15.04714812≈
Counting the outcomes
Ordered outcomes319,479,999,370,622,926,84812^19, every die distinguishable
Most likely total123 and 124two totals share the peak
Chance of that total2.628576%≈
Ways to roll it8,397,773,337,294,253,140exact count
Chance of the minimum3.1300864 × 10^-19%≈1 in 319,479,999,370,622,926,848
Chance of the maximum3.1300864 × 10^-19%≈1 in 319,479,999,370,622,926,848
Shape of the distribution
210 distinct totals, too many to list individually.
1st percentile89≈1.15% of rolls are this or lower
5th percentile99≈5.555% of rolls are this or lower
25th percentile113≈25.459% of rolls are this or lower
50th percentile123≈50% of rolls are this or lower
75th percentile134≈76.618% of rolls are this or lower
95th percentile148≈95.161% of rolls are this or lower
99th percentile158≈99.042% of rolls are this or lower
Chance of rolling at least
40100%≈
7199.9855%≈
12450%≈
1760.0192%≈
2074.10514516 × 10^-8%≈
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