Examples
Examples
Try the starting example
- Success payoff before upfront cost ($)
- 100
- Failure payoff before upfront cost ($)
- -20
- Upfront cost paid in either outcome ($)
- 10
- Required alternative net payoff ($)
- 0
- Algebraic break-even success probability (%)
- 25
- Net payoff at the algebraic crossing (USD)
- $0.00
- Success-probability requirement
- At or above threshold
Try another scenario
- Success payoff before upfront cost ($)
- 10
- Failure payoff before upfront cost ($)
- -20
- Upfront cost paid in either outcome ($)
- 10
- Required alternative net payoff ($)
- 0
- Algebraic break-even success probability (%)
- 100
- Net payoff at the algebraic crossing (USD)
- $0.00
- Success-probability requirement
- At or above threshold
Calculation method
Calculation method
Algebraic break-even success probability (%)
Solve p×success+(1−p)×failure−cost=alternative, giving p=(alternative+cost−failure)/(success−failure).
Net payoff at the algebraic crossing (USD)
Substitute the unrounded crossing into the net-payoff formula.
Success-probability requirement
Describe whether feasible probabilities lie above or below the crossing, or whether no/all probabilities can meet the alternative.
Symbols and units
- a
- Success payoff before upfront cost ($)
- b
- Failure payoff before upfront cost ($)
- c
- Upfront cost paid in either outcome ($)
- d
- Required alternative net payoff ($)
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
- Explicit two-outcome expected-payoff arithmetic. The upfront cost is charged in both outcomes and payoffs exclude that cost. Algebraic probabilities outside 0–1 remain visible instead of being silently clipped.
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
OpenStax: arithmetic and geometry ↗
Background reading; this does not imply endorsement or independent review of SumFizz.