Can a Betting System Beat the House?
No. A system can change how often you win a session and how badly you lose the rest, but it cannot change the average.
The myth
Double your bet after every loss and the first win gets everything back plus a profit. It sounds airtight, and in the short run it often seems to work. Versions of the idea, such as Martingale, Fibonacci, d’Alembert and Labouchère, have been sold as ways to turn the odds in your favour for centuries.
Why it can’t work
Each bet on its own has a negative expected value. On a European roulette red/black bet that is −2.70% of the stake. A system only changes how much you put on each bet, and every one of those bets still has the same −2.70% expectation. Add them up and the expected loss is 2.70% of the total you wager, whatever order the bets come in.
The doubling systems also run into hard limits. Ten losses in a row at $5 base means the next Martingale bet is $5,120, and that is beyond many table maximums and most bankrolls. Long losing runs are rare, but over enough sessions they happen, and when they do they wipe out a long series of small wins.
See it for yourself
Our betting system myth tester runs 5,000 sessions of any system on European or American roulette, or on a fair coin. You will usually see Martingale win more sessions than flat betting, go broke more often, and end up close to −2.70% per dollar wagered, the same as flat betting.
What does change your results
Only the bets you choose and how much you bet in total. Pick bets with a lower house edge, bet less overall, and set a loss limit before you start.
Sources
Reviewed by Greg Parsons, editor, against the sources above.