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.
The two ways a progression ends
Every negative-progression system — Martingale, Labouchère, Fibonacci — ends in one of two states, and the simulator reaches both. Either the session closes while the sequence is complete, which looks like a small steady profit, or the sequence runs into the bankroll or the table maximum, which erases every earlier win at once. The first happens most evenings; the second decides the average.
The arithmetic is unforgiving. A Martingale from £10 needs £1,270 to survive seven consecutive losses, an event that occurs roughly once in every 150 attempts on a colour bet. Seven losses in a row are not unlucky, they are scheduled; the only question is whether they arrive before or after you stop. Flat betting removes the cliff without changing the expected cost, which is why it is the honest baseline the tool compares against.
FAQ
Which system performs best here?
None of them, in expectation. Martingale, d'Alembert, Fibonacci and flat betting all end at edge × turnover; what differs is how the loss arrives — in many small pieces or one large one.
Why does Martingale look profitable for a while?
Because it converts a few large losses into many small wins. Run it until the bankroll or the table limit stops a doubling sequence, and the accumulated wins go back in a single hand.
Does a bigger bankroll make a system work?
It postpones the failure rather than removing it. Every extra step in a progression needs exponentially more money, while the edge keeps charging a fixed percentage of everything staked.
What is worth taking from the simulation?
That session results are mostly variance and the cost is mostly turnover. Lower turnover — smaller stakes, fewer spins — is the only control that reduces the expected loss.