Dice notation
5d523
- 5d523
- 5 to 2615
- mean 1,310
- mode 1310
Rolling 5d523 gives a total between 5 and 2,615, with a mean of 1,310 and a standard deviation of 337.5944. There are 39,129,873,538,843 equally likely ordered outcomes, and the most likely total is 1,310 at 0.115%.
The roll
Notation5d523
Dice5
Faces per die523
Minimum total5all 5 dice showing 1
Maximum total2,615all 5 dice showing 523
Distinct totals2,611
Mean1,310n(f + 1)/2 + modifier, exact
Variance113,970n(f² − 1)/12, exact
Standard deviation337.59443123≈
Counting the outcomes
Ordered outcomes39,129,873,538,843523^5, every die distinguishable
Most likely total1,310
Chance of that total0.114524%≈
Ways to roll it44,813,004,001exact count
Chance of the minimum2.55559221 × 10^-12%≈1 in 39,129,873,538,843
Chance of the maximum2.55559221 × 10^-12%≈1 in 39,129,873,538,843
Shape of the distribution
2,611 distinct totals, too many to list individually.
1st percentile545≈1.005% of rolls are this or lower
5th percentile753≈5.022% of rolls are this or lower
25th percentile1,076≈25.024% of rolls are this or lower
50th percentile1,310≈50.057% of rolls are this or lower
75th percentile1,544≈75.068% of rolls are this or lower
95th percentile1,867≈95.01% of rolls are this or lower
99th percentile2,075≈99.004% of rolls are this or lower
Chance of rolling at least
26699.9732%≈
65897.4368%≈
1,31050.0573%≈
1,9632.5632%≈
2,3540.0273%≈
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