Roulette Expected Value
Expected value (EV) is the average profit or loss per dollar wagered. For roulette, every standard bet has negative EV. The exact size depends on the wheel - 2.70% loss per dollar on European, 5.26% on American.
Understanding EV is the fastest way to evaluate any 'winning strategy' claim. If the strategy is built on standard bets, its EV is negative by definition.
The EV formula
For a single bet:
EV = (P(win) × profit if win) + (P(loss) × loss if loss)
On a $10 bet on red on European: EV = (18/37 × +$10) + (19/37 × −$10) = −$0.27.
EV per bet type (European)
| Bet | Stake $10 | EV per spin | EV as % of stake |
|---|---|---|---|
| Straight up | $10 | −$0.270 | −2.70% |
| Split | $10 | −$0.270 | −2.70% |
| Street | $10 | −$0.270 | −2.70% |
| Corner | $10 | −$0.270 | −2.70% |
| Six line | $10 | −$0.270 | −2.70% |
| Column / Dozen | $10 | −$0.270 | −2.70% |
| Red / Black / Odd / Even / Low / High | $10 | −$0.270 | −2.70% |
Every standard European bet has the same percentage EV. That is the property of a single-zero wheel.
EV per bet type (American)
On American every standard bet has EV = −5.26% of stake. Exception: the five-number bet (0, 00, 1, 2, 3) which has EV = −7.89% of stake. Avoid the five-number bet.
Why no system has positive EV
Strategies combine bets. EV of combined bets equals the sum of individual EVs. If every component bet has negative EV, the combination also has negative EV.
Doubling stakes after losses (Martingale) multiplies stake size, which multiplies expected loss. It does not flip the sign.
Pressing wins (Paroli) sequences EV-negative bets one after another. The product is still EV-negative.
EV in dollars across sessions
| Total wagered | European EV | American EV |
|---|---|---|
| $1,000 | −$27.03 | −$52.63 |
| $10,000 | −$270.27 | −$526.31 |
| $100,000 | −$2,702.70 | −$5,263.16 |
What positive EV would require
A positive-EV roulette bet would require one of the following:
- A wheel bias detectable across enough spins to overcome variance (extremely rare in modern casinos).
- A dealer signature or wheel-section prediction reliable enough to beat 2.70%.
- A casino offering payouts above the fair odds (does not exist).
- A promo or rule like extended La Partage that flips the math.
Even when these conditions exist, they are not 'strategies' in the betting-system sense. They are physical or rule-based edges, not progression tricks.