Examples
Examples
Try the starting example
- Remaining deck/population size
- 10
- Target cards remaining
- 3
- Cards drawn without replacement
- 4
- At-least target count to query
- 2
- Probability of at least queried target count
- 0.333333
- Target-card-count distribution
- 0: 0.166666666667; 1: 0.5; 2: 0.3; 3: 0.0333333333333; 4: 0
- Expected target-card count
- 1.2
- Target-card-count variance
- 0.56
Try another scenario
- Remaining deck/population size
- 10
- Target cards remaining
- 3
- Cards drawn without replacement
- 4
- At-least target count to query
- 3
- Probability of at least queried target count
- 0.033333
- Target-card-count distribution
- 0: 0.166666666667; 1: 0.5; 2: 0.3; 3: 0.0333333333333; 4: 0
- Expected target-card count
- 1.2
- Target-card-count variance
- 0.56
Calculation method
Calculation method
Probability of at least queried target count
Sum hypergeometric counts at/above the queried count.
Target-card-count distribution
choose(targets,k)×choose(nontargets,draw−k)/choose(population,draw), including zero-probability counts.
Expected target-card count
draw×targets/population.
Target-card-count variance
Finite-population variance, obtained from exact first and second count moments.
Symbols and units
- a
- Remaining deck/population size
- b
- Target cards remaining
- c
- Cards drawn without replacement
- d
- At-least target count 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”.
Assumptions & limits
Assumptions & limits
- A uniform unordered draw without replacement from a supplied finite population. It does not infer card identities, shuffle quality, betting choices or an actual game’s hidden state.
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.