Examples
Examples
Try the starting example
- Equally likely collectible types
- 5
- Distinct types already owned
- 2
- Additional independent draws to query
- 3
- Expected additional draws to complete collection
- 9.166667
- Completion probability within queried additional draws
- 0.048
- Distinct missing types
- 3
- Probability next draw is a currently missing type
- 0.6
Try another scenario
- Equally likely collectible types
- 5
- Distinct types already owned
- 3
- Additional independent draws to query
- 3
- Expected additional draws to complete collection
- 7.5
- Completion probability within queried additional draws
- 0.192
- Distinct missing types
- 2
- Probability next draw is a currently missing type
- 0.4
Calculation method
Calculation method
Expected additional draws to complete collection
Types×(1+1/2+...+1/missing), zero when complete.
Completion probability within queried additional draws
Exact inclusion–exclusion sum sum((-1)^j×choose(missing,j)×(types−j)^draws)/types^draws.
Distinct missing types
Types−already owned; duplicate owned copies do not change this count.
Probability next draw is a currently missing type
Missing/types before making the next draw; later discovery chances decline as types are found.
Symbols and units
- a
- Equally likely collectible types
- b
- Distinct types already owned
- c
- Additional independent draws to query
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Calculation steps and notation
sum(list) adds all entries in the list.
Assumptions & limits
Assumptions & limits
- Uniform independent draws with replacement, starting with a supplied number of distinct owned types. At most 50 missing types and 500 queried draws; rarity weights, trading and guaranteed-new mechanics are outside this model.
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.