Examples
Examples
Try the starting example
- Pool size
- 10
- Main numbers drawn without replacement
- 4
- Unique ticket selections
- 3
- Bonus numbers drawn from remaining pool
- 1
- Minimum main matches for queried event
- 2
- Minimum bonus matches for queried event
- 1
- Probability both supplied match thresholds are met
- 0.05
- Expected main matches
- 1.2
- Expected bonus matches
- 0.3
- Joint main/bonus match distribution
- main=0/bonus=0: 0.0833333333333; main=0/bonus=1: 0.0833333333333; main=1/bonus=0: 0.333333333333; main=1/bonus=1: 0.166666666667; main=2/bonus=0: 0.25; main=2/bonus=1: 0.05; main=3/bonus=0: 0.0333333333333; main=3/bonus=1: 0
Try another scenario
- Pool size
- 10
- Main numbers drawn without replacement
- 4
- Unique ticket selections
- 3
- Bonus numbers drawn from remaining pool
- 1
- Minimum main matches for queried event
- 3
- Minimum bonus matches for queried event
- 0
- Probability both supplied match thresholds are met
- 0.033333
- Expected main matches
- 1.2
- Expected bonus matches
- 0.3
- Joint main/bonus match distribution
- main=0/bonus=0: 0.0833333333333; main=0/bonus=1: 0.0833333333333; main=1/bonus=0: 0.333333333333; main=1/bonus=1: 0.166666666667; main=2/bonus=0: 0.25; main=2/bonus=1: 0.05; main=3/bonus=0: 0.0333333333333; main=3/bonus=1: 0
Calculation method
Calculation method
Probability both supplied match thresholds are met
Sum exact disjoint main/bonus match-cell counts meeting both supplied thresholds.
Expected main matches
Main draw count×ticket selections/pool.
Expected bonus matches
Bonus draw count×ticket selections/pool; bonus is sampled from numbers not in main draw.
Joint main/bonus match distribution
For each main match count, draw remaining ticket/non-ticket bonus choices from the remaining pool and divide by choose(pool,main)×choose(pool−main,bonus).
Symbols and units
- a
- Pool size
- b
- Main numbers drawn without replacement
- c
- Unique ticket selections
- d
- Bonus numbers drawn from remaining pool
- e
- Minimum main matches for queried event
- f
- Minimum bonus matches for queried event
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 finite-pool main draw followed by disjoint bonus draws, not a named lottery’s prize rules. Ticket uniqueness and thresholds are supplied; no payouts, tickets or future draws are predicted.
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.