Recognised as Dice notation
3d400
- 3d400
- 3 to 1200
- mean 601.5
Rolling 3d400 gives a total between 3 and 1,200, with a mean of 601.5 and a standard deviation of 199.9994. There are 64,000,000 equally likely ordered outcomes, and the most likely total is 601 or 602 at 0.188%.
The roll
Notation3d400
Dice3
Faces per die400
Minimum total3all 3 dice showing 1
Maximum total1,200all 3 dice showing 400
Distinct totals1,198
Mean601.5n(f + 1)/2 + modifier, exact
Variance39,999.75n(f² − 1)/12, exact
Standard deviation199.999375≈
Counting the outcomes
Ordered outcomes64,000,000400^3, every die distinguishable
Most likely total601 and 602two totals share the peak
Chance of that total0.1875%≈
Ways to roll it120,000exact count
Chance of the minimum0.00000156%≈1 in 64,000,000
Chance of the maximum0.00000156%≈1 in 64,000,000
Shape of the distribution
1,198 distinct totals, too many to list individually.
1st percentile158≈1.008% of rolls are this or lower
5th percentile269≈5.013% of rolls are this or lower
25th percentile460≈25.022% of rolls are this or lower
50th percentile601≈50% of rolls are this or lower
75th percentile743≈75.134% of rolls are this or lower
95th percentile934≈95.043% of rolls are this or lower
99th percentile1,045≈99.011% of rolls are this or lower
Chance of rolling at least
12399.5387%≈
30292.9688%≈
60250%≈
9017.1017%≈
1,0800.4728%≈
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