Recognised as Dice notation
45d35
- 45d35
- 45 to 1575
- mean 810
- mode 810
Rolling 45d35 gives a total between 45 and 1,575, with a mean of 810 and a standard deviation of 67.7495. There are 3,041,319,144,574,516,524,140,685,202,864,284,088,008,162,143,523,804,843,425,750,732,421,875 equally likely ordered outcomes, and the most likely total is 810 at 0.587%.
The roll
Notation45d35
Dice45
Faces per die35
Minimum total45all 45 dice showing 1
Maximum total1,575all 45 dice showing 35
Distinct totals1,531
Mean810n(f + 1)/2 + modifier, exact
Variance4,590n(f² − 1)/12, exact
Standard deviation67.74953874≈
Counting the outcomes
Ordered outcomes3,041,319,144,574,516,524,140,685,202,864,284,088,008,162,143,523,804,843,425,750,732,421,87535^45, every die distinguishable
Most likely total810
Chance of that total0.586879%≈
Ways to roll it17,848,874,681,199,248,437,990,694,780,202,578,803,209,626,040,906,651,064,040,486,134,675exact count
Chance of the minimum3.2880469 × 10^-68%≈1 in 3,041,319,144,574,516,524,140,685,202,864,284,088,008,162,143,523,804,843,425,750,732,421,875
Chance of the maximum3.2880469 × 10^-68%≈1 in 3,041,319,144,574,516,524,140,685,202,864,284,088,008,162,143,523,804,843,425,750,732,421,875
Shape of the distribution
1,531 distinct totals, too many to list individually.
1st percentile653≈1.028% of rolls are this or lower
5th percentile699≈5.151% of rolls are this or lower
25th percentile764≈25.153% of rolls are this or lower
50th percentile810≈50.293% of rolls are this or lower
75th percentile856≈75.314% of rolls are this or lower
95th percentile921≈95.004% of rolls are this or lower
99th percentile967≈99.013% of rolls are this or lower
Chance of rolling at least
198100%≈
428100%≈
81050.2934%≈
1,1932.36290475 × 10^-7%≈
1,4222.70943588 × 10^-23%≈
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