Dice notation

63d10

63d10
63 to 630
mean 346.5

Rolling 63d10 gives a total between 63 and 630, with a mean of 346.5 and a standard deviation of 22.798. There are 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 equally likely ordered outcomes, and the most likely total is 346 or 347 at 1.745%.

The roll

Notation63d10

Dice63

Faces per die10

Minimum total63all 63 dice showing 1

Maximum total630all 63 dice showing 10

Distinct totals568

Mean346.5n(f + 1)/2 + modifier, exact

Variance519.75n(f² − 1)/12, exact

Standard deviation22.79802623≈

Counting the outcomes

Ordered outcomes1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,00010^63, every die distinguishable

Most likely total346 and 347two totals share the peak

Chance of that total1.745227%≈

Ways to roll it17,452,274,045,523,672,507,042,525,335,393,257,645,495,984,252,293,100,820,754,075exact count

Chance of the minimum1 × 10^-61%≈1 in 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

Chance of the maximum1 × 10^-61%≈1 in 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

Shape of the distribution

568 distinct totals, too many to list individually.

1st percentile294≈1.115% of rolls are this or lower

5th percentile309≈5.234% of rolls are this or lower

25th percentile331≈25.571% of rolls are this or lower

50th percentile347≈51.745% of rolls are this or lower

75th percentile362≈75.817% of rolls are this or lower

95th percentile384≈95.221% of rolls are this or lower

99th percentile399≈99.009% of rolls are this or lower

Chance of rolling at least

120100%≈

205100%≈

34750%≈

4888.49908019 × 10^-9%≈

5738.13108193 × 10^-27%≈

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