Recognised as Dice notation

72d53

72d53
72 to 3816
mean 1,944
mode 1944

Rolling 72d53 gives a total between 72 and 3,816, with a mean of 1,944 and a standard deviation of 129.7998. There are 14,056,027,923,682,352,566,793,320,124,133,007,029,088,368,589,708,072,084,807,135,860,735,846,597,942,852,940,371,722,787,885,521,670,092,971,502,671,368,379,551,841 equally likely ordered outcomes, and the most likely total is 1,944 at 0.307%.

The roll

Notation72d53

Dice72

Faces per die53

Minimum total72all 72 dice showing 1

Maximum total3,816all 72 dice showing 53

Distinct totals3,745

Mean1,944n(f + 1)/2 + modifier, exact

Variance16,848n(f² − 1)/12, exact

Standard deviation129.79984592≈

Counting the outcomes

Ordered outcomes14,056,027,923,682,352,566,793,320,124,133,007,029,088,368,589,708,072,084,807,135,860,735,846,597,942,852,940,371,722,787,885,521,670,092,971,502,671,368,379,551,84153^72, every die distinguishable

Most likely total1,944

Chance of that total0.30671%≈

Ways to roll it43,111,304,959,613,506,569,177,047,991,898,868,441,319,625,995,644,761,503,268,184,467,196,278,332,369,045,164,508,679,152,070,028,269,379,516,532,026,936,446,403exact count

Chance of the minimum7.11438541 × 10^-123%≈1 in 14,056,027,923,682,352,566,793,320,124,133,007,029,088,368,589,708,072,084,807,135,860,735,846,597,942,852,940,371,722,787,885,521,670,092,971,502,671,368,379,551,841

Chance of the maximum7.11438541 × 10^-123%≈1 in 14,056,027,923,682,352,566,793,320,124,133,007,029,088,368,589,708,072,084,807,135,860,735,846,597,942,852,940,371,722,787,885,521,670,092,971,502,671,368,379,551,841

Shape of the distribution

3,745 distinct totals, too many to list individually.

1st percentile1,643≈1.02% of rolls are this or lower

5th percentile1,730≈5.004% of rolls are this or lower

25th percentile1,856≈25.05% of rolls are this or lower

50th percentile1,944≈50.153% of rolls are this or lower

75th percentile2,032≈75.194% of rolls are this or lower

95th percentile2,158≈95.076% of rolls are this or lower

99th percentile2,245≈99.001% of rolls are this or lower

Chance of rolling at least

446100%≈

1,008100%≈

1,94450.1534%≈

2,8803.37609153 × 10^-12%≈

3,4421.52081537 × 10^-38%≈

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