Dice notation
4d726
- 4d726
- 4 to 2904
- mean 1,454
- mode 1454
Rolling 4d726 gives a total between 4 and 2,904, with a mean of 1,454 and a standard deviation of 419.1559. There are 277,809,109,776 equally likely ordered outcomes, and the most likely total is 1,454 at 0.092%.
The roll
Notation4d726
Dice4
Faces per die726
Minimum total4all 4 dice showing 1
Maximum total2,904all 4 dice showing 726
Distinct totals2,901
Mean1,454n(f + 1)/2 + modifier, exact
Variance175,691.66666667n(f² − 1)/12, exact
Standard deviation419.15589781≈
Counting the outcomes
Ordered outcomes277,809,109,776726^4, every die distinguishable
Most likely total1,454
Chance of that total0.091827%≈
Ways to roll it255,105,026exact count
Chance of the minimum3.59959398 × 10^-10%≈1 in 277,809,109,776
Chance of the maximum3.59959398 × 10^-10%≈1 in 277,809,109,776
Shape of the distribution
2,901 distinct totals, too many to list individually.
1st percentile510≈1.003% of rolls are this or lower
5th percentile762≈5.017% of rolls are this or lower
25th percentile1,162≈25.065% of rolls are this or lower
50th percentile1,454≈50.046% of rolls are this or lower
75th percentile1,746≈75.009% of rolls are this or lower
95th percentile2,146≈95.009% of rolls are this or lower
99th percentile2,398≈99.005% of rolls are this or lower
Chance of rolling at least
29499.8917%≈
72995.8219%≈
1,45450.0459%≈
2,1794.2012%≈
2,6140.1098%≈
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