Calculate a five-number wager from its own payout
A broader group of winning numbers can still have a worse expected return if the payout is reduced.
The distinction that matters
Assume 38 equally likely pockets and a bet covering five outcomes that pays six units of profit on a win. There are five winning and 33 losing outcomes. Expected net result is (5 × 6 − 33) / 38 = −3/38, approximately −7.8947% of the stake.
A worked example
For hypothetical C$380 turnover under these rules, expected cost is C$30. Borrowing the −2/38 expectation from a 35-to-1 single-number bet would be wrong because the payout and coverage differ. The correct calculation starts again from the stated outcomes.
Your next steps
- Count the covered outcomes exactly.
- Read the profit payout for that particular bet.
- Include uncovered outcomes as losses.
- Compare net expectation rather than the apparent size of the covered area.
Where this answer stops
This is a derivation for a specified model, not a catalogue of available bets. A bet with more winning outcomes does not automatically have a lower expected cost or a better chance of session profit.
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 — roulette rules brochure
Primary educational description of 38 pockets and the five-number top-line bet. Used for the stated rules context, not a claim that an online operator offers it. Accessed .
- BCLC — double-zero roulette payout schedule
Primary British Columbia rules document: section 1.0, payout schedule. Cited only as a documented mathematical rules example, not as Ontario law, operator terms or evidence of availability in Ontario. Accessed .
An editorial review date is not a new policy effective date. Always check the current source for operator-specific conditions.
Suggest a correction