Examples
Examples
Try the starting example
- Available deck: standard, or unique card codes separated by commas
- standard
- Known removed cards, comma-separated, or none
- none
- Exact target traditional category
- straight-flush
- Exact-category probability
- 0.000015
- Five-card combinations in selected category
- 40
- All equally likely remaining five-card combinations
- 2598960
- Hand-category combination counts
- high-card: 1302540; one-pair: 1098240; two-pair: 123552; three-of-a-kind: 54912; straight: 10200; flush: 5108; full-house: 3744; four-of-a-kind: 624; straight-flush: 40
Try another scenario
- Available deck: standard, or unique card codes separated by commas
- standard
- Known removed cards, comma-separated, or none
- AS
- Exact target traditional category
- straight-flush
- Exact-category probability
- 0.000016
- Five-card combinations in selected category
- 38
- All equally likely remaining five-card combinations
- 2349060
- Hand-category combination counts
- high-card: 1176825; one-pair: 992640; two-pair: 111672; three-of-a-kind: 49632; straight: 9690; flush: 4615; full-house: 3384; four-of-a-kind: 564; straight-flush: 38
Calculation method
Calculation method
Exact-category probability
Category combinations/choose(remaining cards,5), using exact integer rank/suit counting.
Five-card combinations in selected category
Count rank-multiplicity patterns, straight windows and suit combinations; royal flush is included in straight-flush.
All equally likely remaining five-card combinations
Choose remaining-card count five, unordered without replacement.
Hand-category combination counts
Mutually exclusive traditional categories sum to all five-card subsets; ace is low only in A-2-3-4-5.
Symbols and units
- a
- Available deck: standard, or unique card codes separated by commas
- b
- Known removed cards, comma-separated, or none
- c
- Exact target traditional category
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
- Uniform five-card subsets of a supplied subset of the standard unique 52-card deck, under traditional high-hand ranks. Royal flush is a straight-flush subtype here. No betting, player behavior, short-deck ranking changes or seven-card best-hand rules are modeled.
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.