Examples
Examples
Try the starting example
- Equally likely wheel pockets
- 37
- Selected winning pockets
- 1
- Stake per independent spin ($)
- 10
- Net win payout per stake unit, excluding returned stake
- 35
- Independent spins in scenario
- 100
- Single-spin win probability
- 0.027027
- Expected net result per spin ($)
- -$0.27027
- Single-spin net-result variance ($ squared)
- 3,408.035062
- Expected net result across supplied spins ($)
- -$27.03
- Standard deviation across independent spins ($)
- $583.78
Try another scenario
- Equally likely wheel pockets
- 38
- Selected winning pockets
- 1
- Stake per independent spin ($)
- 10
- Net win payout per stake unit, excluding returned stake
- 35
- Independent spins in scenario
- 100
- Single-spin win probability
- 0.026316
- Expected net result per spin ($)
- -$0.526316
- Single-spin net-result variance ($ squared)
- 3,320.775623
- Expected net result across supplied spins ($)
- -$52.63
- Standard deviation across independent spins ($)
- $576.26
Calculation method
Calculation method
Single-spin win probability
Winning pockets/total pockets.
Expected net result per spin ($)
Stake×(p×net-win-multiple−(1−p)).
Single-spin net-result variance ($ squared)
Stake²×(net-win-multiple+1)²×p×(1−p), preserving square-dollar units.
Expected net result across supplied spins ($)
Spins×single-spin expectation.
Standard deviation across independent spins ($)
sqrt(spins×single-spin variance), assuming independent identical spins.
Symbols and units
- a
- Equally likely wheel pockets
- b
- Selected winning pockets
- c
- Stake per independent spin ($)
- d
- Net win payout per stake unit, excluding returned stake
- e
- Independent spins in scenario
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 supplied uniform-wheel/payout mathematical model, not actual casino terms, a profit forecast or a recommendation to gamble. Net payout excludes returned stake; loss is the stake. Variance uses squared currency units.
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.