Betting System Myth Tester

Martingale, Fibonacci and d’Alembert change how your results are spread. They cannot change the house edge. Run the simulator to check that for yourself.

Edited by Greg Parsons, editor · Last updated 2026-10-15

The systems

Martingale: double the bet after each loss and go back to one unit after a win. Each run of losses is recovered with a one-unit profit, until you hit the table maximum or run out of money.
Fibonacci: bet along 1, 1, 2, 3, 5, 8… units. Move one step up after a loss and two steps back after a win.
d’Alembert: add one unit after a loss and take one away after a win, never going below one unit.

Why the expected value doesn’t move

Every spin is a separate bet with the same odds. On European roulette a $1 red bet wins $1 with probability 18/37 and loses $1 with probability 19/37, so its expected value is 18/37 − 19/37 = −1/37 ≈ −2.70% of the stake. On a double-zero wheel it is −2/38 ≈ −5.26%. A system only decides how much you put on each spin, and each of those amounts has the same −2.70% expectation. Add them up and the total expected loss is still 2.70% of everything you bet, whatever order the bets come in. Mathematicians call this the optional stopping theorem; the plain version is that no pattern of bet sizes can turn a negative-expectation bet positive.

What a system does change is the shape of the results. Martingale wins small amounts most of the time and occasionally loses a lot in one go. Run the simulator and you will usually see more winning sessions than with flat betting, a bigger share of sessions that go broke, and a result per dollar wagered close to −2.70% every time. Choose the fair coin flip and it lands close to 0%, which shows the systems aren’t adding anything of their own.

A Martingale losing streak, step by step

With the default settings you start at $5 and double after each loss: $5, $10, $20, $40, $80, $160, $320. After seven losses in a row you are down $635, and the next bet should be $640. The table maximum is $500, so you cannot place it. Even a win at $500 leaves you $135 down on the streak, and the system is broken.

Seven reds in a row going against you sounds rare. On a European wheel the chance is (19/37)⁷, a little under 1%. But over a 200-spin session the chance that it happens at least once is roughly 60%. Without a table limit the numbers only get bigger: after ten straight losses the next bet is $5 × 2¹⁰ = $5,120, to win back $5.

What the table maximum does

The table maximum is the reason Martingale cannot work at a real casino, and it is set low on purpose. It caps how far you can double, so a long losing run turns into a large loss you cannot recover. Raise the maximum in the simulator and little changes with a $1,000 bankroll, because your money runs out before the limit does. Either way a long losing run ends the system, and the result per dollar wagered still sits near −2.70%.

Labouchère and other systems

The Labouchère, or cancellation, system is not in the simulator. You write a list of numbers, bet the first plus the last, cross both off after a win and add the lost amount to the end after a loss. It feels organized, but it has the same problem as the others: after a bad run the bets grow quickly, and every bet still carries the house edge. The same reasoning covers any system you can describe, including reverse systems such as Paroli that raise bets after wins.

The fair coin control

The “fair coin flip” option is a test of the tester. With a 50/50 bet there is no house edge, so the result per dollar wagered should land close to 0% for every system. If a system really created an edge, it would show up here as a steady profit. It does not. The systems move results around, and the −2.70% or −5.26% you see on roulette comes from the wheel alone.