Dice notation
33d61
- 33d61
- 33 to 2013
- mean 1,023
- mode 1023
Rolling 33d61 gives a total between 33 and 2,013, with a mean of 1,023 and a standard deviation of 101.1435. There are 82,391,907,081,252,241,482,446,054,994,858,845,541,258,598,700,475,465,198,781 equally likely ordered outcomes, and the most likely total is 1,023 at 0.393%.
The roll
Notation33d61
Dice33
Faces per die61
Minimum total33all 33 dice showing 1
Maximum total2,013all 33 dice showing 61
Distinct totals1,981
Mean1,023n(f + 1)/2 + modifier, exact
Variance10,230n(f² − 1)/12, exact
Standard deviation101.14346247≈
Counting the outcomes
Ordered outcomes82,391,907,081,252,241,482,446,054,994,858,845,541,258,598,700,475,465,198,78161^33, every die distinguishable
Most likely total1,023
Chance of that total0.392634%≈
Ways to roll it323,498,774,690,493,231,600,139,962,619,628,677,105,821,717,223,872,542,701exact count
Chance of the minimum1.21371144 × 10^-57%≈1 in 82,391,907,081,252,241,482,446,054,994,858,845,541,258,598,700,475,465,198,781
Chance of the maximum1.21371144 × 10^-57%≈1 in 82,391,907,081,252,241,482,446,054,994,858,845,541,258,598,700,475,465,198,781
Shape of the distribution
1,981 distinct totals, too many to list individually.
1st percentile789≈1.025% of rolls are this or lower
5th percentile857≈5.097% of rolls are this or lower
25th percentile955≈25.31% of rolls are this or lower
50th percentile1,023≈50.196% of rolls are this or lower
75th percentile1,091≈75.005% of rolls are this or lower
95th percentile1,189≈95.006% of rolls are this or lower
99th percentile1,257≈99.002% of rolls are this or lower
Chance of rolling at least
231100%≈
528100%≈
1,02350.1963%≈
1,5180%≈
1,8151.26354105 × 10^-17%≈
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