Dice notation

72d10

72d10
72 to 720
mean 396
mode 396

Rolling 72d10 gives a total between 72 and 720, with a mean of 396 and a standard deviation of 24.3721. There are 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 equally likely ordered outcomes, and the most likely total is 396 at 1.633%.

The roll

Notation72d10

Dice72

Faces per die10

Minimum total72all 72 dice showing 1

Maximum total720all 72 dice showing 10

Distinct totals649

Mean396n(f + 1)/2 + modifier, exact

Variance594n(f² − 1)/12, exact

Standard deviation24.37211521≈

Counting the outcomes

Ordered outcomes1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,00010^72, every die distinguishable

Most likely total396

Chance of that total1.633398%≈

Ways to roll it16,333,976,304,699,214,718,657,221,877,442,624,229,398,621,392,350,520,803,192,093,730,809,000exact count

Chance of the minimum1 × 10^-70%≈1 in 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

Chance of the maximum1 × 10^-70%≈1 in 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

Shape of the distribution

649 distinct totals, too many to list individually.

1st percentile339≈1.011% of rolls are this or lower

5th percentile356≈5.257% of rolls are this or lower

25th percentile380≈26.276% of rolls are this or lower

50th percentile396≈50.817% of rolls are this or lower

75th percentile412≈75.043% of rolls are this or lower

95th percentile436≈95.17% of rolls are this or lower

99th percentile453≈99.096% of rolls are this or lower

Chance of rolling at least

137100%≈

234100%≈

39650.8167%≈

5583.80509046 × 10^-10%≈

6559.64810093 × 10^-31%≈

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