Recognised as Dice notation
3d115
- 3d115
- 3 to 345
- mean 174
- mode 174
Rolling 3d115 gives a total between 3 and 345, with a mean of 174 and a standard deviation of 57.4978. There are 1,520,875 equally likely ordered outcomes, and the most likely total is 174 at 0.652%.
The roll
Notation3d115
Dice3
Faces per die115
Minimum total3all 3 dice showing 1
Maximum total345all 3 dice showing 115
Distinct totals343
Mean174n(f + 1)/2 + modifier, exact
Variance3,306n(f² − 1)/12, exact
Standard deviation57.49782605≈
Counting the outcomes
Ordered outcomes1,520,875115^3, every die distinguishable
Most likely total174
Chance of that total0.65219%≈
Ways to roll it9,919exact count
Chance of the minimum0.00006575%≈1 in 1,520,875
Chance of the maximum0.00006575%≈1 in 1,520,875
Shape of the distribution
343 distinct totals, too many to list individually.
1st percentile47≈1.066% of rolls are this or lower
5th percentile78≈5.002% of rolls are this or lower
25th percentile133≈25.042% of rolls are this or lower
50th percentile174≈50.326% of rolls are this or lower
75th percentile215≈75.5% of rolls are this or lower
95th percentile270≈95.19% of rolls are this or lower
99th percentile301≈99.002% of rolls are this or lower
Chance of rolling at least
3799.5305%≈
8992.7847%≈
17450.3261%≈
2607.2153%≈
3110.5109%≈
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