Roulette Strategy Simulator

None of them improves the rate: every even-money bet on a single-zero wheel costs 2.70% of what is on it, whatever pattern put it there. They are not equally expensive, though, and the usual answer stops one step too early. Because each system stakes a different amount to play the same 200 spins, the expected cost of a session at this page's opening settings varies several-fold across the six, from flat betting at the cheap end to Labouchère at the dear one; the comparison table on this page has the exact figures. If the question is which one loses the least money, the answer is the one that turns over the least, which is flat betting.

Flat betting, and by a wide margin, because expected loss is turnover times the wheel edge and flat betting has the lowest turnover of the six. The comparison table on this page runs all six over 5,000 sessions each at the opening settings and orders them by turnover, so the size of the gap between flat betting and Labouchère (the dearest of the six) is a row you can read rather than a set of figures to remember. The ordering is stable across seeds. It is not stable across settings: give an escalating system a deeper bankroll or a higher table limit and it stakes far more before anything stops it, which widens the gap rather than closing it. Labouchère's place at the expensive end also rests on a stopping rule this page does not use. It rewrites the crossed-off line and plays your full spin count, where the system is usually taught to finish the moment the line clears; stop there and it stakes about $354 rather than the several thousand it reaches by playing on. That is a shorter evening rather than a cheaper way to bet, though, because it ends after about seven spins instead of 200. The rate is 2.70% either way, and the methodology note below has the figures.

Six consecutive losses end it at the opening settings, and it is your bankroll rather than the table limit that does the ending. The progression is 5, 10, 20, 40, 80, 160, so six losses have taken $315 and leave $185, and the seventh bet asks for $320. The $500 table limit would not have refused anything until the eighth bet at $640, so the received idea that Martingale dies at the table limit is not what happens at an ordinary bankroll. Six losses in a row is (19/37) to the sixth power, or 1.83% per attempt, which over a few hundred spins comes up far more often than people expect, and when it lands it gives back every prior small win at once.

It depends entirely on how long you sit there, and the simulator will show you the crossover. Over 25 spins at the opening settings about 77% of Martingale sessions finish in profit against 45% flat. By 100 spins it is 49% against 36%, and by 200 spins the ordering has inverted: 31% against 33%. Every extra spin is another chance to meet the six-loss run, and one of those gives back every small win at once. The high win rate is real and it is temporary, which is a different thing from an edge.

No. As long as each individual spin is negative expectation, every finite combination of those spins is also negative expectation. Only a biased wheel or dealer signature (not a staking pattern) can change that.