Dice notation

34d10

34d10
34 to 340
mean 187
mode 187

Rolling 34d10 gives a total between 34 and 340, with a mean of 187 and a standard deviation of 16.7481. There are 10,000,000,000,000,000,000,000,000,000,000,000 equally likely ordered outcomes, and the most likely total is 187 at 2.371%.

The roll

Notation34d10

Dice34

Faces per die10

Minimum total34all 34 dice showing 1

Maximum total340all 34 dice showing 10

Distinct totals307

Mean187n(f + 1)/2 + modifier, exact

Variance280.5n(f² − 1)/12, exact

Standard deviation16.74813422≈

Counting the outcomes

Ordered outcomes10,000,000,000,000,000,000,000,000,000,000,00010^34, every die distinguishable

Most likely total187

Chance of that total2.371268%≈

Ways to roll it237,126,779,700,111,728,623,210,793,896,700exact count

Chance of the minimum1 × 10^-32%≈1 in 10,000,000,000,000,000,000,000,000,000,000,000

Chance of the maximum1 × 10^-32%≈1 in 10,000,000,000,000,000,000,000,000,000,000,000

Shape of the distribution

307 distinct totals, too many to list individually.

1st percentile148≈1.052% of rolls are this or lower

5th percentile159≈5.035% of rolls are this or lower

25th percentile176≈26.613% of rolls are this or lower

50th percentile187≈51.186% of rolls are this or lower

75th percentile198≈75.305% of rolls are this or lower

95th percentile215≈95.559% of rolls are this or lower

99th percentile226≈99.106% of rolls are this or lower

Chance of rolling at least

65100%≈

11199.9999%≈

18751.1856%≈

2640.0001%≈

3093.368765 × 10^-14%≈

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