Recognised as Dice notation
3d900
- 3d900
- 3 to 2700
- mean 1,351.5
Rolling 3d900 gives a total between 3 and 2,700, with a mean of 1,351.5 and a standard deviation of 449.9997. There are 729,000,000 equally likely ordered outcomes, and the most likely total is 1,351 or 1,352 at 0.083%.
The roll
Notation3d900
Dice3
Faces per die900
Minimum total3all 3 dice showing 1
Maximum total2,700all 3 dice showing 900
Distinct totals2,698
Mean1,351.5n(f + 1)/2 + modifier, exact
Variance202,499.75n(f² − 1)/12, exact
Standard deviation449.99972222≈
Counting the outcomes
Ordered outcomes729,000,000900^3, every die distinguishable
Most likely total1,351 and 1,352two totals share the peak
Chance of that total0.083333%≈
Ways to roll it607,500exact count
Chance of the minimum1.37174211 × 10^-7%≈1 in 729,000,000
Chance of the maximum1.37174211 × 10^-7%≈1 in 729,000,000
Shape of the distribution
2,698 distinct totals, too many to list individually.
1st percentile354≈1.006% of rolls are this or lower
5th percentile604≈5.013% of rolls are this or lower
25th percentile1,034≈25.04% of rolls are this or lower
50th percentile1,351≈50% of rolls are this or lower
75th percentile1,669≈75.03% of rolls are this or lower
95th percentile2,099≈95.012% of rolls are this or lower
99th percentile2,349≈99.003% of rolls are this or lower
Chance of rolling at least
27399.545%≈
67792.9688%≈
1,35250%≈
2,0267.0625%≈
2,4300.4601%≈
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