Recognised as Dice notation
3d331
- 3d331
- 3 to 993
- mean 498
- mode 498
Rolling 3d331 gives a total between 3 and 993, with a mean of 498 and a standard deviation of 165.4992. There are 36,264,691 equally likely ordered outcomes, and the most likely total is 498 at 0.227%.
The roll
Notation3d331
Dice3
Faces per die331
Minimum total3all 3 dice showing 1
Maximum total993all 3 dice showing 331
Distinct totals991
Mean498n(f + 1)/2 + modifier, exact
Variance27,390n(f² − 1)/12, exact
Standard deviation165.49924471≈
Counting the outcomes
Ordered outcomes36,264,691331^3, every die distinguishable
Most likely total498
Chance of that total0.226587%≈
Ways to roll it82,171exact count
Chance of the minimum0.00000276%≈1 in 36,264,691
Chance of the maximum0.00000276%≈1 in 36,264,691
Shape of the distribution
991 distinct totals, too many to list individually.
1st percentile131≈1.01% of rolls are this or lower
5th percentile223≈5.028% of rolls are this or lower
25th percentile381≈25.056% of rolls are this or lower
50th percentile498≈50.113% of rolls are this or lower
75th percentile615≈75.133% of rolls are this or lower
95th percentile773≈95.039% of rolls are this or lower
99th percentile865≈99.013% of rolls are this or lower
Chance of rolling at least
10299.5405%≈
25192.9049%≈
49850.1133%≈
7467.0951%≈
8940.4735%≈
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