Martingale and progression systems, priced honestly
How long each staking system survives, and what one bad run costs
Every progression trades many small wins for one rare total loss. This works out the exact terms of that trade.
What a progression actually does
Every staking progression rests on the same claim: a win has to come eventually, so raise the stake until it does and you cannot lose. The first half is true. The second does not follow, because you do not have an infinite bankroll and the bookmaker will not take an infinite stake. What a progression really does is reshape the distribution of results. It makes most sessions end slightly up and a rare one end at zero. The average is untouched — it is still turnover multiplied by your edge, exactly as it would be flat staking the same money. What changes is where the losses are stored: a progression takes the losses you would have had spread out and saves them up for one day.
See also: Streak survival probability, Drawdown calculator, Recovery stake calculator
How to use
- 1Pick the system. Martingale raises the stake enough that one win recovers the whole run; Fibonacci and D'Alembert climb more gently and so survive longer.
- 2Enter your bankroll, your opening stake, the odds you bet at and your honest win chance — the real one, not the one the system needs.
- 3Enter the largest stake you can actually place. Account limits are usually what ends a progression, not the bankroll.
- 4Read the longest losing run you survive, how often such a run turns up, and how many winning bets it erases when it does.
Example: €1,000 bank, €10 base, odds 2.00
A near-even bet you win 48.5% of the time, with a €5,000 limit and 500 bets planned. Martingale survives a run of 6: the stakes go 10, 20, 40, 80, 160, 320 and the seventh would need €640 against the €370 you have left. That run costs €630 — sixty-three winning bets at your base stake. And it arrives about once every 108 bets, so over the 500 you planned the chance of meeting it is 99.16%. Fibonacci survives 9 and meets its run every 807 bets: 46.02% over the same plan. D'Alembert survives 13, one run per 11,500 bets, 4.17%. Every one of them has the same −3% edge per bet. They differ only in how long the illusion lasts.
The arithmetic
Nothing here is simulated. Each figure is computed exactly from the stake ladder:
- Martingale stake at step k = (everything lost so far + base × (odds − 1)) ÷ (odds − 1)
- Fibonacci: base × 1, 1, 2, 3, 5, 8, 13 … · D'Alembert: base × 1, 2, 3, 4, 5 …
- The run ends at the first step whose stake exceeds your remaining bankroll or the house limit
- Bets between such runs = (1 − q^n) ÷ (q^n × p), where q is the chance of losing one bet and n the run length
- The chance inside your planned bets is walked forward one bet at a time over the current run length — exact, not approximated
Two assumptions are worth naming. Each bet is treated as independent with a fixed win chance, which is right for a priced market and wrong for anything with momentum. And the profit from completed cycles is not counted as extra ammunition, which makes the figures very slightly pessimistic — a difference of a cycle or two, not of a verdict. A dash under “one such run per” means the run is beyond any number of bets you will place in a lifetime.
The limit kills you before the bankroll does
Raise the bankroll in the example to €100,000 and leave a €200 maximum stake in place: the run you survive drops from 6 to 5, and the chance of ruin over 500 bets rises to 99.99%. More money bought you nothing, because the ladder hit the ceiling instead of the floor. This is not an accident of this example — maximum stakes exist in large part because progressions would otherwise work, and every bookmaker and casino sets them low enough relative to table minimums that no doubling sequence survives long. If you have ever wondered why your account limit fell after a few wins, this is the same mechanism seen from the other side. And none of the above is an argument for picking the gentlest system. A gentler ladder survives longer, which means it takes longer to find out, and the expected loss over that longer time is larger, not smaller, because you have staked more money at the same negative edge.
When to use
- Before trying a system, to see what it costs when it fails rather than what it pays when it works
- To find what your account or table limit does to a progression, which is usually more than the bankroll does
- To understand why a system can feel like it works for months and still be losing money
- When someone is selling you one
Frequently asked questions
What is the Martingale & progression systems calculator?
Every staking progression rests on the same claim: a win has to come eventually, so raise the stake until it does and you cannot lose. The first half is true.
How does the Martingale & progression systems calculator work in practice?
A near-even bet you win 48.5% of the time, with a €5,000 limit and 500 bets planned. Martingale survives a run of 6: the stakes go 10, 20, 40, 80, 160, 320 and the seventh would need €640 against the €370 you have left. That run costs €630 — sixty-three winning bets at your base stake. And it arrives about once every…
What is the most common mistake with the Martingale & progression systems calculator?
Raise the bankroll in the example to €100,000 and leave a €200 maximum stake in place: the run you survive drops from 6 to 5, and the chance of ruin over 500 bets rises to 99.99%. More money bought you nothing, because the ladder hit the ceiling instead of the floor. This is not an accident of this example — maximum…
When should I use the Martingale & progression systems calculator?
Before trying a system, to see what it costs when it fails rather than what it pays when it works. To find what your account or table limit does to a progression, which is usually more than the bankroll does. To understand why a system can feel like it works for months and still be losing money.