Dice notation
57d20
- 57d20
- 57 to 1140
- mean 598.5
Rolling 57d20 gives a total between 57 and 1,140, with a mean of 598.5 and a standard deviation of 43.5345. There are 144,115,188,075,855,872,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 equally likely ordered outcomes, and the most likely total is 598 or 599 at 0.914%.
The roll
Notation57d20
Dice57
Faces per die20
Minimum total57all 57 dice showing 1
Maximum total1,140all 57 dice showing 20
Distinct totals1,084
Mean598.5n(f + 1)/2 + modifier, exact
Variance1,895.25n(f² − 1)/12, exact
Standard deviation43.5344691≈
Counting the outcomes
Ordered outcomes144,115,188,075,855,872,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,00020^57, every die distinguishable
Most likely total598 and 599two totals share the peak
Chance of that total0.913896%≈
Ways to roll it1,317,063,127,642,083,427,052,368,436,874,874,531,805,754,673,272,249,640,983,127,955,631,471,360exact count
Chance of the minimum6.9388939 × 10^-73%≈1 in 144,115,188,075,855,872,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
Chance of the maximum6.9388939 × 10^-73%≈1 in 144,115,188,075,855,872,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
Shape of the distribution
1,084 distinct totals, too many to list individually.
1st percentile497≈1.004% of rolls are this or lower
5th percentile527≈5.151% of rolls are this or lower
25th percentile569≈25.314% of rolls are this or lower
50th percentile598≈50% of rolls are this or lower
75th percentile628≈75.414% of rolls are this or lower
95th percentile670≈95.089% of rolls are this or lower
99th percentile700≈99.057% of rolls are this or lower
Chance of rolling at least
165100%≈
328100%≈
59950%≈
8696.56475978 × 10^-9%≈
1,0326.96836502 × 10^-28%≈
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