Dice notation
6d729
- 6d729
- 6 to 4374
- mean 2,190
- mode 2190
Rolling 6d729 gives a total between 6 and 4,374, with a mean of 2,190 and a standard deviation of 515.4804. There are 150,094,635,296,999,121 equally likely ordered outcomes, and the most likely total is 2,190 at 0.075%.
The roll
Notation6d729
Dice6
Faces per die729
Minimum total6all 6 dice showing 1
Maximum total4,374all 6 dice showing 729
Distinct totals4,369
Mean2,190n(f + 1)/2 + modifier, exact
Variance265,720n(f² − 1)/12, exact
Standard deviation515.4803585≈
Counting the outcomes
Ordered outcomes150,094,635,296,999,121729^6, every die distinguishable
Most likely total2,190
Chance of that total0.075446%≈
Ways to roll it113,240,219,507,325exact count
Chance of the minimum6.66246331 × 10^-16%≈1 in 150,094,635,296,999,121
Chance of the maximum6.66246331 × 10^-16%≈1 in 150,094,635,296,999,121
Shape of the distribution
4,369 distinct totals, too many to list individually.
1st percentile1,017≈1.006% of rolls are this or lower
5th percentile1,340≈5.016% of rolls are this or lower
25th percentile1,835≈25.053% of rolls are this or lower
50th percentile2,190≈50.038% of rolls are this or lower
75th percentile2,545≈75.007% of rolls are this or lower
95th percentile3,040≈95.005% of rolls are this or lower
99th percentile3,363≈99% of rolls are this or lower
Chance of rolling at least
44399.9933%≈
1,09898.4225%≈
2,19050.0377%≈
3,2821.586%≈
3,9370.0068%≈
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