Dice notation

34d20

34d20
34 to 680
mean 357
mode 357

Rolling 34d20 gives a total between 34 and 680, with a mean of 357 and a standard deviation of 33.6229. There are 171,798,691,840,000,000,000,000,000,000,000,000,000,000,000 equally likely ordered outcomes, and the most likely total is 357 at 1.181%.

The roll

Notation34d20

Dice34

Faces per die20

Minimum total34all 34 dice showing 1

Maximum total680all 34 dice showing 20

Distinct totals647

Mean357n(f + 1)/2 + modifier, exact

Variance1,130.5n(f² − 1)/12, exact

Standard deviation33.62290886≈

Counting the outcomes

Ordered outcomes171,798,691,840,000,000,000,000,000,000,000,000,000,000,00020^34, every die distinguishable

Most likely total357

Chance of that total1.181247%≈

Ways to roll it2,029,366,818,891,287,655,488,948,419,024,924,674,052,200exact count

Chance of the minimum5.82076609 × 10^-43%≈1 in 171,798,691,840,000,000,000,000,000,000,000,000,000,000,000

Chance of the maximum5.82076609 × 10^-43%≈1 in 171,798,691,840,000,000,000,000,000,000,000,000,000,000,000

Shape of the distribution

647 distinct totals, too many to list individually.

1st percentile279≈1.036% of rolls are this or lower

5th percentile302≈5.261% of rolls are this or lower

25th percentile334≈25.249% of rolls are this or lower

50th percentile357≈50.591% of rolls are this or lower

75th percentile380≈75.689% of rolls are this or lower

95th percentile412≈95.053% of rolls are this or lower

99th percentile435≈99.045% of rolls are this or lower

Chance of rolling at least

99100%≈

196100%≈

35750.5906%≈

5190%≈

6152.22593225 × 10^-16%≈

Keep nerding

Every link below is a page Nerdulator can generate from what it already knows about this value.

The same dice, different counts

The same count, different dice

Nerdulate something else

Nothing in mind? Surprise me · today’s page