Examples
Examples
Try the starting example
- Fair dice rolled
- 3
- Sides per die
- 6
- Highest dice kept
- 2
- At-least kept-sum query
- 10
- Probability kept sum reaches query
- 0.356481
- Exact kept-sum distribution
- 2: 0.00462962962963; 3: 0.0138888888889; 4: 0.0324074074074; 5: 0.0555555555556; 6: 0.087962962963; 7: 0.125; 8: 0.157407407407; 9: 0.166666666667; 10: 0.157407407407; 11: 0.125; 12: 0.0740740740741
- Expected kept sum
- 8.458333
- Kept-sum variance
- 4.905671
Try another scenario
- Fair dice rolled
- 3
- Sides per die
- 6
- Highest dice kept
- 1
- At-least kept-sum query
- 10
- Probability kept sum reaches query
- 0
- Exact kept-sum distribution
- 1: 0.00462962962963; 2: 0.0324074074074; 3: 0.087962962963; 4: 0.171296296296; 5: 0.282407407407; 6: 0.421296296296
- Expected kept sum
- 4.958333
- Kept-sum variance
- 1.308449
Calculation method
Calculation method
Probability kept sum reaches query
Sum exact histogram-weighted outcomes with retained sum≥query.
Exact kept-sum distribution
Enumerate face-count histograms, weighting each by n!/product(face-count factorials); retain the highest specified count.
Expected kept sum
First moment of the exact integer-count distribution.
Kept-sum variance
Second central moment from exact integer weighted sums.
Symbols and units
- a
- Fair dice rolled
- b
- Sides per die
- c
- Highest dice kept
- d
- At-least kept-sum query
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Assumptions & limits
Assumptions & limits
- Independent fair dice with highest-face retention. Count-histogram enumeration is bounded to 100,000 histograms and reports an input error above that bound; keep-zero is a deterministic zero sum.
Are these inputs private?
These calculations run in your browser. A shared link contains the values you choose to share. Only questions submitted to the separate AI finder are sent to OpenAI.
Further reading
Background reading; this does not imply endorsement or independent review of SumFizz.