Recognised as Dice notation
6d400
- 6d400
- 6 to 2400
- mean 1,203
- mode 1203
Rolling 6d400 gives a total between 6 and 2,400, with a mean of 1,203 and a standard deviation of 282.8418. There are 4,096,000,000,000,000 equally likely ordered outcomes, and the most likely total is 1,203 at 0.138%.
The roll
Notation6d400
Dice6
Faces per die400
Minimum total6all 6 dice showing 1
Maximum total2,400all 6 dice showing 400
Distinct totals2,395
Mean1,203n(f + 1)/2 + modifier, exact
Variance79,999.5n(f² − 1)/12, exact
Standard deviation282.84182859≈
Counting the outcomes
Ordered outcomes4,096,000,000,000,000400^6, every die distinguishable
Most likely total1,203
Chance of that total0.1375%≈
Ways to roll it5,632,016,000,080exact count
Chance of the minimum2.44140625 × 10^-14%≈1 in 4,096,000,000,000,000
Chance of the maximum2.44140625 × 10^-14%≈1 in 4,096,000,000,000,000
Shape of the distribution
2,395 distinct totals, too many to list individually.
1st percentile559≈1.004% of rolls are this or lower
5th percentile736≈5.001% of rolls are this or lower
25th percentile1,008≈25.055% of rolls are this or lower
50th percentile1,203≈50.069% of rolls are this or lower
75th percentile1,398≈75.056% of rolls are this or lower
95th percentile1,670≈95.037% of rolls are this or lower
99th percentile1,847≈99.007% of rolls are this or lower
Chance of rolling at least
24599.9933%≈
60598.4077%≈
1,20350.0688%≈
1,8021.5923%≈
2,1610.0069%≈
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