Recognised as Dice notation
4d204
- 4d204
- 4 to 816
- mean 410
- mode 410
Rolling 4d204 gives a total between 4 and 816, with a mean of 410 and a standard deviation of 117.778. There are 1,731,891,456 equally likely ordered outcomes, and the most likely total is 410 at 0.327%.
The roll
Notation4d204
Dice4
Faces per die204
Minimum total4all 4 dice showing 1
Maximum total816all 4 dice showing 204
Distinct totals813
Mean410n(f + 1)/2 + modifier, exact
Variance13,871.66666667n(f² − 1)/12, exact
Standard deviation117.77803983≈
Counting the outcomes
Ordered outcomes1,731,891,456204^4, every die distinguishable
Most likely total410
Chance of that total0.326801%≈
Ways to roll it5,659,844exact count
Chance of the minimum5.77403391 × 10^-8%≈1 in 1,731,891,456
Chance of the maximum5.77403391 × 10^-8%≈1 in 1,731,891,456
Shape of the distribution
813 distinct totals, too many to list individually.
1st percentile145≈1.02% of rolls are this or lower
5th percentile216≈5.093% of rolls are this or lower
25th percentile328≈25.173% of rolls are this or lower
50th percentile410≈50.163% of rolls are this or lower
75th percentile492≈75.091% of rolls are this or lower
95th percentile604≈95.002% of rolls are this or lower
99th percentile675≈99.008% of rolls are this or lower
Chance of rolling at least
8599.8886%≈
20795.7926%≈
41050.1634%≈
6134.2903%≈
7350.1169%≈
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