Recognised as Dice notation
3d516
- 3d516
- 3 to 1548
- mean 775.5
Rolling 3d516 gives a total between 3 and 1,548, with a mean of 775.5 and a standard deviation of 257.9995. There are 137,388,096 equally likely ordered outcomes, and the most likely total is 775 or 776 at 0.145%.
The roll
Notation3d516
Dice3
Faces per die516
Minimum total3all 3 dice showing 1
Maximum total1,548all 3 dice showing 516
Distinct totals1,546
Mean775.5n(f + 1)/2 + modifier, exact
Variance66,563.75n(f² − 1)/12, exact
Standard deviation257.9995155≈
Counting the outcomes
Ordered outcomes137,388,096516^3, every die distinguishable
Most likely total775 and 776two totals share the peak
Chance of that total0.145349%≈
Ways to roll it199,692exact count
Chance of the minimum7.27865098 × 10^-7%≈1 in 137,388,096
Chance of the maximum7.27865098 × 10^-7%≈1 in 137,388,096
Shape of the distribution
1,546 distinct totals, too many to list individually.
1st percentile204≈1.015% of rolls are this or lower
5th percentile347≈5.025% of rolls are this or lower
25th percentile593≈25.009% of rolls are this or lower
50th percentile775≈50% of rolls are this or lower
75th percentile958≈75.112% of rolls are this or lower
95th percentile1,204≈95.019% of rolls are this or lower
99th percentile1,347≈99% of rolls are this or lower
Chance of rolling at least
15899.5395%≈
38992.9688%≈
77650%≈
1,1627.0858%≈
1,3940.4605%≈
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