Derive the single-zero straight-bet expectation
Count all possible pockets, including zero, and distinguish the winning profit from the returned stake.
The distinction that matters
Assume 37 equally likely pockets and a one-unit bet on one number paying 35 units of profit when it wins. There is one winning outcome and 36 losing outcomes. Net expectation is 35/37 − 36/37 = −1/37, approximately −0.027027 units per unit staked.
A worked example
At a fictional fixed turnover of C$370, that model has expected cost C$10. It does not predict ten dollars of loss in a particular sequence, and it does not imply that exactly one of every 37 consecutive spins must land on your number.
Your next steps
- State the equal-probability assumption.
- Include zero in the outcome count.
- Use profit, not gross returned amount, for the net formula.
- Show the fractional result before rounding.
Where this answer stops
This is a self-contained derivation for a specified hypothetical ruleset. It does not establish real-world fairness or availability. If a game pays a different amount, this formula must be recalculated rather than copied.
Sources & reading
Primary references support the factual context below. Explanations, worked examples and calculations are original Northline analysis. Read how we handle evidence.
- OLG PlaySmart — European roulette
Background comparison of wheel variants. Northline articles independently derive stated mathematical models and do not infer table availability. Accessed .
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