Pick a system, a wheel and a bankroll, then run the session. Run it twice — the trajectory changes completely, the expectation does not.
Why no progression beats the wheel
Every even-money spin loses edge × bet in expectation: 2.70% on a European wheel, 5.26% on an American one. A staking system decides how much you wager, so it scales the expected loss — it cannot flip its sign. Martingale mostly ends small wins punctuated by one catastrophic loss; that is a different shape of the same negative number.
Run the same session twice and the trajectory changes completely; the expectation line does not. The only lever that moves it is the wheel — one zero instead of two — and the only winning move on the progression itself is the smaller total wagered.
Methodology
Each spin wins with probability 18/37 (EU) or 18/38 (US) via random_int (CSPRNG); bets follow the chosen progression and are capped by the remaining bankroll. Expected loss is always edge × total wagered — the progression only chooses how much gets wagered.