What progressions are
A progression is a rule for changing the stake after a win or a loss. The best known are:
- Martingale: after a loss the stake doubles; after a win it goes back to the starting stake.
- Fibonacci: after a loss the stake is the next number in the sequence 1, 1, 2, 3, 5, 8…; after a win it goes two numbers back.
- D'Alembert: after a loss the stake goes up by one unit; after a win it goes down by one.
- Labouchère: you write down the line 1, 2, 3, 4, and the stake is the sum of the two end numbers. A win crosses them out; a loss adds the stake to the end of the line.
What history shows
We played sessions of 100 bets on favourites priced at 1.80–2.20 by an average bookmaker, with a bank of 100 units and a starting stake of 1. There are 13,732 such bets in the database, or 137 sessions. The favourite itself wins 47.8% of the time: slightly worse than a coin toss.
| System | In profit | Went bust | Average result | Per unit staked | Worst session |
|---|---|---|---|---|---|
| Flat stake | 35% | 0% | −4.5 | −4.5% | −30 |
| Martingale | 40% | 59% | −16.2 | −7.6% | −96 |
| Fibonacci | 66% | 31% | −14.3 | −6.6% | −88 |
| D'Alembert | 53% | 30% | −16.7 | −3.5% | −100 |
| Labouchère | 26% | 74% | −29.1 | −4.9% | −100 |
Progressions make winning sessions common: Fibonacci finishes 66% of sessions in profit, against 35% for a flat stake. But the losses are rare and deep: the martingale burned the bank in 59% of sessions. And on average every system loses — from −7.6% to −3.5% per unit staked, roughly the size of the margin.
Why this happens
Each bet on its own is a losing one, however much you put on it. A string of losing bets does not become a winning one because of the order or the size in which you place them. The system only changes the shape of the result: a flat stake loses a little at a time and predictably, while progressions win a little at a time and then lose a lot at once.
There is a practical ceiling too: after a losing run the stake hits the size of the bank or the bookmaker's limit, and there is no longer any way to win it back.