Recognised as Dice notation
4d316
- 4d316
- 4 to 1264
- mean 634
- mode 634
Rolling 4d316 gives a total between 4 and 1,264, with a mean of 634 and a standard deviation of 182.4418. There are 9,971,220,736 equally likely ordered outcomes, and the most likely total is 634 at 0.211%.
The roll
Notation4d316
Dice4
Faces per die316
Minimum total4all 4 dice showing 1
Maximum total1,264all 4 dice showing 316
Distinct totals1,261
Mean634n(f + 1)/2 + modifier, exact
Variance33,285n(f² − 1)/12, exact
Standard deviation182.44177153≈
Counting the outcomes
Ordered outcomes9,971,220,736316^4, every die distinguishable
Most likely total634
Chance of that total0.210972%≈
Ways to roll it21,036,436exact count
Chance of the minimum1.00288623 × 10^-8%≈1 in 9,971,220,736
Chance of the maximum1.00288623 × 10^-8%≈1 in 9,971,220,736
Shape of the distribution
1,261 distinct totals, too many to list individually.
1st percentile223≈1.006% of rolls are this or lower
5th percentile333≈5.046% of rolls are this or lower
25th percentile507≈25.13% of rolls are this or lower
50th percentile634≈50.105% of rolls are this or lower
75th percentile761≈75.041% of rolls are this or lower
95th percentile935≈95.014% of rolls are this or lower
99th percentile1,045≈99.012% of rolls are this or lower
Chance of rolling at least
13099.8896%≈
31995.807%≈
63450.1055%≈
9494.2462%≈
1,1380.1139%≈
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