Roulette

Identify the wheel and rules

Names such as European, American or French are useful labels, but the actual pockets and settlement rules determine the calculation. Other wheels, bonus games and altered payouts need their own analysis.

On these examples, 18 of the numbered pockets are red and 18 are black. Zero and double zero are separate outcomes; they do not win red/black, odd/even or high/low wagers under the ordinary full-loss-on-zero rules.

Reference: roulette rules, payout tables and zero-rule variants.

Follow a round

1. Check your stake and selections. One spin can carry several bets. Add their costs rather than treating the chips as one unit wager.
2. Place bets before the cutoff. Follow the dealer’s or game’s betting window; after it closes, the accepted bets stand under the rules.
3. Read the official result. In a ball-and-wheel game, the settled pocket supplies the winning number. Electronic and other versions need their own result rules.
4. Check the payout. A winning chip may return both net winnings and the original stake. Read whether a displayed amount includes that stake.
5. Decide whether to play another round. Previous results do not make a particular pocket due in the independent, uniform model used here.

Net winnings and total return

A payout of 35 to 1 means $35 net winnings for a winning $1 stake, plus that $1 returned: $36 in total. 35 for 1 instead means $35 total, including the stake. Those are different payouts and produce different expected returns. Do not read a large displayed number without its units.

Keep the measure and rule together

For a $1 wager that either wins or loses, expected net return is win probability × net payout − loss probability. House edge is the negative of that expected return, expressed as a percentage of the stake. A push or partial loss adds its own outcome term.

A straight-up wager

On the stated single-zero wheel, a chosen pocket wins once among 37 equally likely outcomes. Winning pays $35 net; the other 36 outcomes lose $1. Expected net return is (35 − 36) / 37 = −1/37 per $1, giving 2.70% house edge.

On the stated double-zero wheel, it is (35 − 37) / 38 = −2/38, giving 5.26%. This is an expected-loss percentage, not the probability that every particular player loses during a visit.

The basket has five winning pockets

The basket’s win probability is 5/38, or 13.16%. With 6:1 net winnings, its expected net return is (5 × 6 − 33) / 38 = −3/38. Its house edge is therefore 7.89%. The win probability and house edge answer different questions.

Red is not a 50% event

On the single-zero example, red wins on 18 of 37 pockets: 48.65%. On double zero it is 18 of 38: 47.37%. Red and black can be equally likely without either having a 50% probability, because the zero outcomes remain.

Under independent spins with unchanged probabilities, a run of black results does not change those next-spin fractions. A short result history does not itself establish that a wheel is biased or that a pattern is useful. This guide does not claim an empirical equipment test of a particular game.

Half back and imprisonment are different rules

For single-zero even-money bets with half back on zero, there are 18 outcomes winning $1, 18 losing $1 and one losing $0.50. Expected net return is (18 − 18 − 0.5) / 37, giving 1.35% house edge.

An imprisonment rule holds a stake instead of immediately returning half. Its result depends on the release and repeat-zero rules. Do not assign every rule called en prison the half-back percentage. Nor does half back improve a straight-up wager that is outside the concession’s scope.

Total amount wagered matters

For a fixed $100 of total wagers in the stated single-zero model, expected loss is about $2.70. For the double-zero model it is about $5.26. These figures concern total action, including money bet again, rather than only the cash brought to the table. Actual results vary.

Betting progressions do not change the expected result per dollar on the same unchanged bet. Doubling after losses changes stake size and exposure. For example, losses on $5, $10, $20, $40, $80 and $160 wagers total $315; the next doubled wager would require another $320. Neither the available funds nor the table limit is unlimited. No promised recovery follows from the sequence.

Compare measures in the game comparison.

• Shackleford: roulette rules, payouts and zero-rule variants. Original published mathematical analysis, used to check the stated payout and settlement examples.
• All displayed probability, edge, spending and progression examples are calculated from their specified inputs. They do not establish the fairness, availability or pace of a particular game.

Checked September 5, 2026. Calculations assume equally likely pockets and independent spins. Check different wheels, altered payouts, multipliers and zero concessions separately.