Recognised as Dice notation

5d159

5d159
5 to 795
mean 400
mode 400

Rolling 5d159 gives a total between 5 and 795, with a mean of 400 and a standard deviation of 102.632. There are 101,621,504,799 equally likely ordered outcomes, and the most likely total is 400 at 0.377%.

The roll

Notation5d159

Dice5

Faces per die159

Minimum total5all 5 dice showing 1

Maximum total795all 5 dice showing 159

Distinct totals791

Mean400n(f + 1)/2 + modifier, exact

Variance10,533.33333333n(f² − 1)/12, exact

Standard deviation102.63202879≈

Counting the outcomes

Ordered outcomes101,621,504,799159^5, every die distinguishable

Most likely total400

Chance of that total0.37671%≈

Ways to roll it382,818,201exact count

Chance of the minimum9.84043684 × 10^-10%≈1 in 101,621,504,799

Chance of the maximum9.84043684 × 10^-10%≈1 in 101,621,504,799

Shape of the distribution

791 distinct totals, too many to list individually.

1st percentile167≈1.003% of rolls are this or lower

5th percentile231≈5.095% of rolls are this or lower

25th percentile329≈25.172% of rolls are this or lower

50th percentile400≈50.188% of rolls are this or lower

75th percentile471≈75.132% of rolls are this or lower

95th percentile569≈95.012% of rolls are this or lower

99th percentile633≈99.027% of rolls are this or lower

Chance of rolling at least

8499.9714%≈

20397.3809%≈

40050.1884%≈

5982.6191%≈

7160.0304%≈

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