Betting systems are not new: the idea of raising the stake after a loss has been circulating for centuries. The idea stays the same because it matches intuition — and it fails in the same place every time, because it does not match the maths.
Martingale: what happens at the table
The rule is simple: double after every loss, and when a bet finally wins it returns all the previous losses plus one unit of profit. At the table that means this table — starting at ₺10 and losing repeatedly:
| Losing run | Next stake | Lost so far |
|---|---|---|
| 1 | ₺20 | ₺10 |
| 2 | ₺40 | ₺30 |
| 3 | ₺80 | ₺70 |
| 4 | ₺160 | ₺150 |
| 5 | ₺320 | ₺310 |
| 6 | ₺640 | ₺630 |
| 7 | ₺1,280 | ₺1,270 |
| 8 | ₺2,560 | ₺2,550 |
| 9 | ₺5,120 | ₺5,110 |
| 10 | ₺10,240 | ₺10,230 |
On the tenth loss you have to put ₺10,240 on the table having already lost ₺10,230 — and the target profit is still ₺10. On European roulette the chance of red failing ten times in a row is small but not zero; on top of that tables have a maximum stake, so the system stops before the run does. For it to "work" you would need an unlimited budget and an unlimited table, and neither exists.
d’Alembert and Fibonacci: the same wall, approached slower
d’Alembert raises the stake by one unit after a loss and lowers it by one after a win. Fibonacci follows the sequence 1, 1, 2, 3, 5, 8. Both are gentler than Martingale, meaning they drain a balance more slowly — and neither changes the one thing that matters: the expected value of every single bet stays negative by the house edge. The order of your bets does not change their odds.
The number that does not move
| Game | House edge | What it means |
|---|---|---|
| European roulette (single zero) | 2.70% | An expected loss of ₺2.70 for every ₺100 wagered over time |
| American roulette (double zero) | 5.26% | The same bet, at nearly twice the cost |
| Blackjack with basic strategy | about 0.5% | One of the rare games where decision quality affects the result |
| Baccarat, banker | 1.06% | Commission included |
| Baccarat, tie | 14.4% | One of the most expensive bets at the table |
Why the table matters: no system can change that column. The only thing a system changes is the distribution of losses — frequent small wins and a rare large loss. The total arrives at the same place.
The practical conclusion fits in one sentence: choosing the table works where choosing a system does not. Picking single-zero roulette halves the cost of the same bet; no ordering of stakes can do that.
The cultural side of picking numbers at roulette is covered in numbers and the real odds. On the sports side the same arithmetic is called the margin: working out the margin from the odds. The slot equivalent is in slot themes and the maths.
For the history of the system and its place in probability theory, the Wikipedia entry on the Martingale system is a good start.
Frequently asked questions
Does Martingale actually win?
It does not. It makes small wins more frequent and the large loss rarer, but the expected value stays negative by the house edge. Table limits and your own budget also stop you from waiting out the run.
Which system does the least damage?
Keeping the stake flat. Every escalating sequence carries the same expected value, but a flat stake drains a balance most slowly and reduces the risk of one very large loss.
What does the house edge change?
The expected loss on every 100 units wagered over time. On single-zero roulette it is 2.70%, on double-zero 5.26% — the same bet at nearly twice the cost.