Dice notation

3d312

3d312
3 to 936
mean 469.5

Rolling 3d312 gives a total between 3 and 936, with a mean of 469.5 and a standard deviation of 155.9992. There are 30,371,328 equally likely ordered outcomes, and the most likely total is 469 or 470 at 0.24%.

The roll

Notation3d312

Dice3

Faces per die312

Minimum total3all 3 dice showing 1

Maximum total936all 3 dice showing 312

Distinct totals934

Mean469.5n(f + 1)/2 + modifier, exact

Variance24,335.75n(f² − 1)/12, exact

Standard deviation155.99919872≈

Counting the outcomes

Ordered outcomes30,371,328312^3, every die distinguishable

Most likely total469 and 470two totals share the peak

Chance of that total0.240385%≈

Ways to roll it73,008exact count

Chance of the minimum0.00000329%≈1 in 30,371,328

Chance of the maximum0.00000329%≈1 in 30,371,328

Shape of the distribution

934 distinct totals, too many to list individually.

1st percentile124≈1.021% of rolls are this or lower

5th percentile210≈5.01% of rolls are this or lower

25th percentile359≈25.018% of rolls are this or lower

50th percentile470≈50.24% of rolls are this or lower

75th percentile580≈75.182% of rolls are this or lower

95th percentile729≈95.062% of rolls are this or lower

99th percentile815≈99.004% of rolls are this or lower

Chance of rolling at least

9699.5443%≈

23692.9689%≈

47050%≈

7037.1217%≈

8430.4704%≈

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