For a mutually exclusive win-or-lose wager with no pushes.
Probability first
A 20% event occurs one time in five on average. Its fair net payout is four units because one four-unit win offsets four one-unit losses.
Probability and payout must describe the same event, rule set, and time horizon.
Net odds versus return
Four-to-one means four units of profit plus return of the stake. Five-for-one often means five units returned in total and therefore only four units of profit.
Convert all schedules to net profit before comparing them.
Implied probability
Offered net odds b:1 imply a break-even probability of 1 ÷ (b + 1). A 3:1 offer implies 25% before pushes or commissions.
An event can win frequently and still be expensive when the payout is too small.
Pushes and multiple prizes
Pushes return the stake and need their own probability branch. Multi-category wagers require a complete outcome table rather than one headline price.
Use the fair-odds calculator only for the simple binary case it states.
Working checklist
- Use net payouts
- Match event and probability
- Include pushes separately
- Convert implied probability
- Use a full outcome table for multiple prizes
Fair odds and payout conversion, explained. uses rounded teaching examples. Apply a number to a live game only after matching its rules, pay table, strategy and denominator.