Recognised as Dice notation
4d688
- 4d688
- 4 to 2752
- mean 1,378
- mode 1378
Rolling 4d688 gives a total between 4 and 2,752, with a mean of 1,378 and a standard deviation of 397.2166. There are 224,054,542,336 equally likely ordered outcomes, and the most likely total is 1,378 at 0.097%.
The roll
Notation4d688
Dice4
Faces per die688
Minimum total4all 4 dice showing 1
Maximum total2,752all 4 dice showing 688
Distinct totals2,749
Mean1,378n(f + 1)/2 + modifier, exact
Variance157,781n(f² − 1)/12, exact
Standard deviation397.21656562≈
Counting the outcomes
Ordered outcomes224,054,542,336688^4, every die distinguishable
Most likely total1,378
Chance of that total0.096899%≈
Ways to roll it217,107,344exact count
Chance of the minimum4.46319896 × 10^-10%≈1 in 224,054,542,336
Chance of the maximum4.46319896 × 10^-10%≈1 in 224,054,542,336
Shape of the distribution
2,749 distinct totals, too many to list individually.
1st percentile484≈1.008% of rolls are this or lower
5th percentile722≈5.011% of rolls are this or lower
25th percentile1,101≈25.045% of rolls are this or lower
50th percentile1,378≈50.048% of rolls are this or lower
75th percentile1,655≈75.033% of rolls are this or lower
95th percentile2,034≈95.016% of rolls are this or lower
99th percentile2,272≈99% of rolls are this or lower
Chance of rolling at least
27999.8913%≈
69195.8212%≈
1,37850.0484%≈
2,0654.2031%≈
2,4770.1103%≈
Keep nerding
Every link below is a page Nerdulator can generate from what it already knows about this value.
Nerdulate something else
Nothing in mind? Surprise me · today’s page