House edge and expected loss: calculate the exposure
A worked explanation of turnover, theoretical return and why an average is not a session forecast.
House edge is a rate, not a bill
House edge is the expected net loss per dollar wagered under a specified model. If h is the house edge and T is total turnover, expected net loss is T × h. The word expected describes a probability-weighted average. It does not mean the player will lose that amount in an individual session.
Deposit, bankroll and turnover differ
A deposit describes money added to an account. A bankroll describes money available at a point in time. Turnover is the sum of stakes actually wagered. Winnings can be wagered again, so turnover can exceed the initial deposit. Conversely, the available balance can run out before a proposed session or bonus target is completed.
Imagine placing one hundred $5 wagers under unchanged rules. Turnover is $500. At a 1/37 house edge, expected net loss is $500/37, approximately $13.51. This calculation does not establish that the bankroll can support all one hundred wagers or that the resulting balance will be close to its expectation.
Deriving the rate from outcomes
For a two-outcome bet, let p be the winning probability and b the net payout to 1. Expected net return per dollar is p × b − (1 − p). House edge is the negative of that expression. For one number on a 37-pocket wheel with a 35:1 net payout, expected net return is (35 − 36)/37 = −1/37.
When a game includes pushes or multiple prizes, sum probability × net return for every outcome instead. A push has net return zero. Do not force a game with complex outcomes into the two-outcome formula unless the categories and their net returns remain accurate.
Variable stakes and rules
If stake i is si and its house edge is hi, expected loss across the planned wagers is the sum of si × hi. If the rate is constant, that reduces to turnover × h. Merely averaging the rates can be misleading when more money is wagered on the higher-edge bet; use the stake-weighted result.
What the estimate cannot tell you
Expected loss does not identify the largest possible loss, a safe bankroll, the chance of an early balance depletion, or the likely path of a session. Those questions require a complete outcome distribution and an explicit stopping rule. A plan to double stakes after losses changes exposure; it does not change the underlying expectation of a fixed game rule.
Likewise, theoretical return is not a promise that a short session returns a particular percentage. Results can be far above or below an average. The model also assumes the specified rules are correct and the outcome probabilities match the game.
A bonus target is not a spending target
A promotion can require much more turnover than its headline amount suggests. A simple turnover estimate can show that exposure, but it cannot establish the chance of clearing a bonus, eligibility or withdrawable winnings. Read the wagering requirements guide before interpreting that number.
Use the tools with their assumptions visible
The roulette calculator reports expected net result for entered stakes and rounds. It assumes equally likely wheel pockets and independent rounds. Do not use it for special-rule games without checking whether that model still applies. Choosing not to wager has no gambling turnover and no exposure under this model.
Sources and checks
- Nevada Gaming Control Board: Live Roulette rules and paytable · Checked 2026-10-02
- Loto-Québec: roulette game rules · Checked 2026-10-02