Dice notation
5d643
- 5d643
- 5 to 3215
- mean 1,610
- mode 1610
Rolling 5d643 gives a total between 5 and 3,215, with a mean of 1,610 and a standard deviation of 415.0542. There are 109,914,468,611,443 equally likely ordered outcomes, and the most likely total is 1,610 at 0.093%.
The roll
Notation5d643
Dice5
Faces per die643
Minimum total5all 5 dice showing 1
Maximum total3,215all 5 dice showing 643
Distinct totals3,211
Mean1,610n(f + 1)/2 + modifier, exact
Variance172,270n(f² − 1)/12, exact
Standard deviation415.05421333≈
Counting the outcomes
Ordered outcomes109,914,468,611,443643^5, every die distinguishable
Most likely total1,610
Chance of that total0.093151%≈
Ways to roll it102,386,090,451exact count
Chance of the minimum9.0979833 × 10^-13%≈1 in 109,914,468,611,443
Chance of the maximum9.0979833 × 10^-13%≈1 in 109,914,468,611,443
Shape of the distribution
3,211 distinct totals, too many to list individually.
1st percentile669≈1.001% of rolls are this or lower
5th percentile925≈5.014% of rolls are this or lower
25th percentile1,323≈25.067% of rolls are this or lower
50th percentile1,610≈50.047% of rolls are this or lower
75th percentile1,897≈75.008% of rolls are this or lower
95th percentile2,295≈95.013% of rolls are this or lower
99th percentile2,551≈99.007% of rolls are this or lower
Chance of rolling at least
32699.9733%≈
80897.4413%≈
1,61050.0466%≈
2,4132.5587%≈
2,8940.0271%≈
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