How the systems work
- Martingale. After a loss the stake grows so that the next win recovers all losses of the cycle plus the profit of a base stake; at odds of 2.00 that is doubling. After a win, back to the base stake.
- D’Alembert. After a loss the stake grows by one base stake, after a win it falls by one, but never below the base.
- Fibonacci. Stakes follow the sequence 1, 1, 2, 3, 5, 8… base stakes. After a loss, one step forward; after a win, two steps back.
- Labouchère. The player writes down the line 1-2-3 and stakes the sum of the outer numbers. A win crosses out the outer numbers, a loss adds the stake to the end of the line. An empty line ends the cycle.
- Oscar’s Grind. After a loss the stake stays the same; after a win it grows by one base stake, but never more than needed to finish the cycle one base stake up.
- Paroli. A positive progression: after a win the previous stake is bet again together with the winnings; after three wins in a row or after a loss, back to the base stake.
Why a progression creates no edge
Every bet has its own expected value, and the order of stake sizes does not change it: if one bet has a negative expected value, a sequence of bets of any size has one too. A progression only changes the shape of the result: many small wins and a rare but large loss.
Martingale is especially dangerous: the stake grows exponentially, and just 6–7 losses in a row need a bank of dozens of base stakes. Over hundreds of bets such streaks are not rare, and bookmaker limits can cut the progression off even earlier.
How to read the result
The streak table shows how many losses in a row the bank survives. The simulation shows the long run: the share of runs in which the bank ran out, the share that finished in profit and the median final bank. Compare them with a flat stake of the same base size: with a negative expected value every system ends below the starting bank on average, and a progression only changes how often and how badly the player loses.
Frequently asked questions
Does the Martingale strategy work in betting?
No. It brings frequent small wins, but sooner or later a long losing streak needs a stake larger than the bank or the bookmaker limit. The expected value does not change.
How many losses in a row can a bank survive with Martingale?
At odds of 2.00 the stake doubles, and a bank of 1,000 with a base stake of 10 survives six losses in a row: the seventh stake, 640, is already more than the 370 left. The calculator works this out for any numbers.
How do D’Alembert and Fibonacci differ from Martingale?
Their stake grows more slowly: by one base stake or along the Fibonacci sequence. The bank survives longer streaks, but losses build up for longer, and these systems give no edge either.
Are Paroli and Oscar’s Grind safer?
Their stake does not grow after a loss, so a single streak does not wipe out the bank. But they do not change the expected value either: if it is negative, the bank still shrinks on average.
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