Dice notation
4d255
- 4d255
- 4 to 1020
- mean 512
- mode 512
Rolling 4d255 gives a total between 4 and 1,020, with a mean of 512 and a standard deviation of 147.2232. There are 4,228,250,625 equally likely ordered outcomes, and the most likely total is 512 at 0.261%.
The roll
Notation4d255
Dice4
Faces per die255
Minimum total4all 4 dice showing 1
Maximum total1,020all 4 dice showing 255
Distinct totals1,017
Mean512n(f + 1)/2 + modifier, exact
Variance21,674.66666667n(f² − 1)/12, exact
Standard deviation147.22318658≈
Counting the outcomes
Ordered outcomes4,228,250,625255^4, every die distinguishable
Most likely total512
Chance of that total0.26144%≈
Ways to roll it11,054,335exact count
Chance of the minimum2.36504429 × 10^-8%≈1 in 4,228,250,625
Chance of the maximum2.36504429 × 10^-8%≈1 in 4,228,250,625
Shape of the distribution
1,017 distinct totals, too many to list individually.
1st percentile180≈1% of rolls are this or lower
5th percentile269≈5.045% of rolls are this or lower
25th percentile409≈25.041% of rolls are this or lower
50th percentile512≈50.131% of rolls are this or lower
75th percentile615≈75.169% of rolls are this or lower
95th percentile755≈95.03% of rolls are this or lower
99th percentile844≈99.022% of rolls are this or lower
Chance of rolling at least
10699.8869%≈
25895.8007%≈
51250.1307%≈
7664.2654%≈
9180.1175%≈
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