Dice notation
13d20
- 13d20
- 13 to 260
- mean 136.5
Rolling 13d20 gives a total between 13 and 260, with a mean of 136.5 and a standard deviation of 20.7906. There are 81,920,000,000,000,000 equally likely ordered outcomes, and the most likely total is 136 or 137 at 1.896%.
The roll
Notation13d20
Dice13
Faces per die20
Minimum total13all 13 dice showing 1
Maximum total260all 13 dice showing 20
Distinct totals248
Mean136.5n(f + 1)/2 + modifier, exact
Variance432.25n(f² − 1)/12, exact
Standard deviation20.79062289≈
Counting the outcomes
Ordered outcomes81,920,000,000,000,00020^13, every die distinguishable
Most likely total136 and 137two totals share the peak
Chance of that total1.895961%≈
Ways to roll it1,553,171,442,288,700exact count
Chance of the minimum1.22070313 × 10^-15%≈1 in 81,920,000,000,000,000
Chance of the maximum1.22070313 × 10^-15%≈1 in 81,920,000,000,000,000
Shape of the distribution
248 distinct totals, too many to list individually.
1st percentile89≈1.128% of rolls are this or lower
5th percentile102≈5.12% of rolls are this or lower
25th percentile122≈25.247% of rolls are this or lower
50th percentile136≈50% of rolls are this or lower
75th percentile151≈76.255% of rolls are this or lower
95th percentile171≈95.376% of rolls are this or lower
99th percentile184≈99.014% of rolls are this or lower
Chance of rolling at least
38100%≈
7599.8897%≈
13750%≈
1980.1317%≈
2350%≈
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