Recognised as Dice notation
3d511
- 3d511
- 3 to 1533
- mean 768
- mode 768
Rolling 3d511 gives a total between 3 and 1,533, with a mean of 768 and a standard deviation of 255.4995. There are 133,432,831 equally likely ordered outcomes, and the most likely total is 768 at 0.147%.
The roll
Notation3d511
Dice3
Faces per die511
Minimum total3all 3 dice showing 1
Maximum total1,533all 3 dice showing 511
Distinct totals1,531
Mean768n(f + 1)/2 + modifier, exact
Variance65,280n(f² − 1)/12, exact
Standard deviation255.49951076≈
Counting the outcomes
Ordered outcomes133,432,831511^3, every die distinguishable
Most likely total768
Chance of that total0.146771%≈
Ways to roll it195,841exact count
Chance of the minimum7.49440743 × 10^-7%≈1 in 133,432,831
Chance of the maximum7.49440743 × 10^-7%≈1 in 133,432,831
Shape of the distribution
1,531 distinct totals, too many to list individually.
1st percentile202≈1.014% of rolls are this or lower
5th percentile344≈5.04% of rolls are this or lower
25th percentile588≈25.099% of rolls are this or lower
50th percentile768≈50.073% of rolls are this or lower
75th percentile948≈75.023% of rolls are this or lower
95th percentile1,192≈95.004% of rolls are this or lower
99th percentile1,334≈99.001% of rolls are this or lower
Chance of rolling at least
15699.5438%≈
38692.9274%≈
76850.0734%≈
1,1517.0726%≈
1,3800.4651%≈
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