Recognised as Dice notation
5d316
- 5d316
- 5 to 1580
- mean 792.5
Rolling 5d316 gives a total between 5 and 1,580, with a mean of 792.5 and a standard deviation of 203.9761. There are 3,150,905,752,576 equally likely ordered outcomes, and the most likely total is 792 or 793 at 0.19%.
The roll
Notation5d316
Dice5
Faces per die316
Minimum total5all 5 dice showing 1
Maximum total1,580all 5 dice showing 316
Distinct totals1,576
Mean792.5n(f + 1)/2 + modifier, exact
Variance41,606.25n(f² − 1)/12, exact
Standard deviation203.97610154≈
Counting the outcomes
Ordered outcomes3,150,905,752,576316^5, every die distinguishable
Most likely total792 and 793two totals share the peak
Chance of that total0.189544%≈
Ways to roll it5,972,356,155exact count
Chance of the minimum3.17369061 × 10^-11%≈1 in 3,150,905,752,576
Chance of the maximum3.17369061 × 10^-11%≈1 in 3,150,905,752,576
Shape of the distribution
1,576 distinct totals, too many to list individually.
1st percentile330≈1.004% of rolls are this or lower
5th percentile456≈5.035% of rolls are this or lower
25th percentile651≈25.037% of rolls are this or lower
50th percentile792≈50% of rolls are this or lower
75th percentile934≈75.117% of rolls are this or lower
95th percentile1,129≈95.019% of rolls are this or lower
99th percentile1,255≈99.011% of rolls are this or lower
Chance of rolling at least
16399.9723%≈
39997.4289%≈
79350%≈
1,1862.6035%≈
1,4230.0277%≈
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