Recognised as Dice notation
75d10
- 75d10
- 75 to 750
- mean 412.5
Rolling 75d10 gives a total between 75 and 750, with a mean of 412.5 and a standard deviation of 24.8747. There are 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 equally likely ordered outcomes, and the most likely total is 412 or 413 at 1.6%.
The roll
Notation75d10
Dice75
Faces per die10
Minimum total75all 75 dice showing 1
Maximum total750all 75 dice showing 10
Distinct totals676
Mean412.5n(f + 1)/2 + modifier, exact
Variance618.75n(f² − 1)/12, exact
Standard deviation24.87468593≈
Counting the outcomes
Ordered outcomes1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,00010^75, every die distinguishable
Most likely total412 and 413two totals share the peak
Chance of that total1.600212%≈
Ways to roll it16,002,122,247,148,329,185,744,399,811,242,907,019,731,995,097,001,502,295,350,954,593,788,721,875exact count
Chance of the minimum1 × 10^-73%≈1 in 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
Chance of the maximum1 × 10^-73%≈1 in 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
Shape of the distribution
676 distinct totals, too many to list individually.
1st percentile355≈1.086% of rolls are this or lower
5th percentile372≈5.395% of rolls are this or lower
25th percentile396≈26.039% of rolls are this or lower
50th percentile413≈51.6% of rolls are this or lower
75th percentile429≈75.247% of rolls are this or lower
95th percentile453≈95.033% of rolls are this or lower
99th percentile470≈99.025% of rolls are this or lower
Chance of rolling at least
143100%≈
244100%≈
41350%≈
5811.50526642 × 10^-10%≈
6832.89591719 × 10^-32%≈
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