Recognised as Dice notation
3d681
- 3d681
- 3 to 2043
- mean 1,023
- mode 1023
Rolling 3d681 gives a total between 3 and 2,043, with a mean of 1,023 and a standard deviation of 340.4996. There are 315,821,241 equally likely ordered outcomes, and the most likely total is 1,023 at 0.11%.
The roll
Notation3d681
Dice3
Faces per die681
Minimum total3all 3 dice showing 1
Maximum total2,043all 3 dice showing 681
Distinct totals2,041
Mean1,023n(f + 1)/2 + modifier, exact
Variance115,940n(f² − 1)/12, exact
Standard deviation340.49963289≈
Counting the outcomes
Ordered outcomes315,821,241681^3, every die distinguishable
Most likely total1,023
Chance of that total0.110132%≈
Ways to roll it347,821exact count
Chance of the minimum3.16634814 × 10^-7%≈1 in 315,821,241
Chance of the maximum3.16634814 × 10^-7%≈1 in 315,821,241
Shape of the distribution
2,041 distinct totals, too many to list individually.
1st percentile268≈1.004% of rolls are this or lower
5th percentile457≈5.004% of rolls are this or lower
25th percentile783≈25.073% of rolls are this or lower
50th percentile1,023≈50.055% of rolls are this or lower
75th percentile1,263≈75.019% of rolls are this or lower
95th percentile1,589≈95.029% of rolls are this or lower
99th percentile1,778≈99.007% of rolls are this or lower
Chance of rolling at least
20799.5454%≈
51392.9584%≈
1,02350.0551%≈
1,5337.083%≈
1,8390.4613%≈
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