Recognised as Dice notation
3d820
- 3d820
- 3 to 2460
- mean 1,231.5
Rolling 3d820 gives a total between 3 and 2,460, with a mean of 1,231.5 and a standard deviation of 409.9997. There are 551,368,000 equally likely ordered outcomes, and the most likely total is 1,231 or 1,232 at 0.091%.
The roll
Notation3d820
Dice3
Faces per die820
Minimum total3all 3 dice showing 1
Maximum total2,460all 3 dice showing 820
Distinct totals2,458
Mean1,231.5n(f + 1)/2 + modifier, exact
Variance168,099.75n(f² − 1)/12, exact
Standard deviation409.99969512≈
Counting the outcomes
Ordered outcomes551,368,000820^3, every die distinguishable
Most likely total1,231 and 1,232two totals share the peak
Chance of that total0.091463%≈
Ways to roll it504,300exact count
Chance of the minimum1.81367072 × 10^-7%≈1 in 551,368,000
Chance of the maximum1.81367072 × 10^-7%≈1 in 551,368,000
Shape of the distribution
2,458 distinct totals, too many to list individually.
1st percentile323≈1.009% of rolls are this or lower
5th percentile550≈5.002% of rolls are this or lower
25th percentile942≈25.026% of rolls are this or lower
50th percentile1,231≈50% of rolls are this or lower
75th percentile1,521≈75.05% of rolls are this or lower
95th percentile1,913≈95.026% of rolls are this or lower
99th percentile2,140≈99% of rolls are this or lower
Chance of rolling at least
24999.5445%≈
61792.9688%≈
1,23250%≈
1,8467.0656%≈
2,2140.4611%≈
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