Casino game odds: probability, payout and house edge
Understand why the chance of a winning bet is different from its expected return, with reproducible roulette examples.
What do you mean by the best odds?
A game can offer frequent small wins and still return less than the total money wagered in the long run. Before comparing games, specify the measure: probability of a winning round, net payout on a win, theoretical return per dollar, or probability of a profitable session. Those are different questions. A single label such as “best odds” hides the distinction.
This guide uses a simple roulette model because its assumptions are visible. It does not claim one universal ranking across blackjack, slots and every casino game. Rules, strategy and the exact payout table can change the calculation. A number without those conditions is not a useful comparison.
A reproducible roulette example
Consider a fair single-zero wheel with 37 pockets and a straight-up bet covering one number. The win probability is 1/37, approximately 2.7027%. If the net payout is 35 to 1, a winning $10 stake produces $350 profit and returns $360 including the stake. A losing round loses the $10 stake.
The expected net result is (1/37 × $350) + (36/37 × −$10) = −$10/37, approximately −$0.27 per $10 wagered. Dividing the expected loss by the stake gives a house edge of 1/37, approximately 2.7027%. This is an average under the model, not the outcome of any particular round.
More frequent wins need not improve expected return
A standard red bet covers 18 of the 37 pockets and pays 1 to 1 net. Its probability of winning is 18/37, approximately 48.6486%, much higher than a straight-up bet. Its expected net per dollar is 18/37 − 19/37 = −1/37. Under these stated rules, the house edge is the same even though the win frequencies are very different.
| Single-zero example | Win probability | Net payout | House edge |
|---|---|---|---|
| Straight-up | 1/37 = 2.7027% | 35:1 | 1/37 = 2.7027% |
| Red | 18/37 = 48.6486% | 1:1 | 1/37 = 2.7027% |
Changing the wheel changes the calculation
On a double-zero wheel with 38 pockets, the same straight-up payout gives expected net per dollar of (35 − 37)/38 = −2/38. The house edge is approximately 5.2632%. Holding the payout constant while adding an extra losing outcome changes the expected return. These examples do not cover special zero rules, bonus multipliers or side bets.
Why session results are another question
For n independent rounds with a fixed win probability p, the chance of at least one winning round is 1 − (1 − p)n. That is not the probability of being profitable. If a win returns less profit than the accumulated losing stakes, the session still ends behind. To calculate a session profit probability, you must model the stake schedule, payouts and number of wins required.
How to compare an unfamiliar game
- Read the exact rules and payout convention. Check whether a quoted return includes the stake.
- Identify the winning outcomes and the assumptions about their probabilities.
- Calculate expected net return across all outcomes, including losses and pushes.
- Record any strategy assumption rather than treating it as universal.
- Keep short-session uncertainty separate from long-run expectation.
If the probability distribution is unavailable, do not manufacture it from a marketing claim or a short sample of spins. A payout table alone may not reveal how often each outcome occurs.
Explore the model
The roulette odds calculator exposes coverage, pockets, net payout, stake and rounds. The expected-loss guide explains turnover. Neither predicts the next result or provides a strategy that removes a negative expectation.
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