Recognised as Dice notation
51d83
- 51d83
- 51 to 4233
- mean 2,142
- mode 2142
Rolling 51d83 gives a total between 51 and 4,233, with a mean of 2,142 and a standard deviation of 171.0965. There are 74,641,904,363,802,797,266,214,264,251,282,814,828,210,937,723,598,580,648,775,167,654,622,860,253,966,874,545,947,033,752,606,667 equally likely ordered outcomes, and the most likely total is 2,142 at 0.232%.
The roll
Notation51d83
Dice51
Faces per die83
Minimum total51all 51 dice showing 1
Maximum total4,233all 51 dice showing 83
Distinct totals4,183
Mean2,142n(f + 1)/2 + modifier, exact
Variance29,274n(f² − 1)/12, exact
Standard deviation171.09646402≈
Counting the outcomes
Ordered outcomes74,641,904,363,802,797,266,214,264,251,282,814,828,210,937,723,598,580,648,775,167,654,622,860,253,966,874,545,947,033,752,606,66783^51, every die distinguishable
Most likely total2,142
Chance of that total0.232481%≈
Ways to roll it173,528,270,801,234,738,481,850,257,725,697,459,183,196,163,985,658,458,640,409,610,988,206,084,019,437,747,308,883,515,636,137exact count
Chance of the minimum1.33973002 × 10^-96%≈1 in 74,641,904,363,802,797,266,214,264,251,282,814,828,210,937,723,598,580,648,775,167,654,622,860,253,966,874,545,947,033,752,606,667
Chance of the maximum1.33973002 × 10^-96%≈1 in 74,641,904,363,802,797,266,214,264,251,282,814,828,210,937,723,598,580,648,775,167,654,622,860,253,966,874,545,947,033,752,606,667
Shape of the distribution
4,183 distinct totals, too many to list individually.
1st percentile1,745≈1.009% of rolls are this or lower
5th percentile1,860≈5.001% of rolls are this or lower
25th percentile2,026≈25.036% of rolls are this or lower
50th percentile2,142≈50.116% of rolls are this or lower
75th percentile2,258≈75.15% of rolls are this or lower
95th percentile2,424≈95.06% of rolls are this or lower
99th percentile2,539≈99.007% of rolls are this or lower
Chance of rolling at least
469100%≈
1,097100%≈
2,14250.1162%≈
3,1881.07101525 × 10^-8%≈
3,8158.71264877 × 10^-28%≈
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