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Next: find your ladder limit
The martingale calculator shows the bet at each step and the margin needed, so you can see where your own account runs out.
What is included
- What it is, in plain words
- The formula or mechanism, with exact arithmetic
- How it hits grid, martingale and DCA bots
- A check you can run before you switch a bot on
Who it is for
- People who run or plan to run a trading bot
- Anyone reading a backtest or a bot sales page
- Readers who want the numbers, not the pitch
- Not advice, and not a signal service
Key facts
- The martingale strategy doubles the bet after every loss, so a single win recovers all earlier losses and leaves a profit equal to the first bet.
- The bankroll sets a hard limit. With a $10 first bet and a $1000 bankroll, 6 losses in a row cost $630.00, and the next bet of $640.00 cannot be paid for (calculated by us on 28 Oct 2026, exact).
- On a fair 50 percent bet the expected result of each round is exactly $0.00. The small wins are paid for by the rare large loss.
- On a bet with an edge against you the expected result is negative: -$1.74 a round at a win chance of 18 in 37 (made-up example).
- A bot that uses this ladder wins often and loses rarely and large. A high win rate is the sign of the strategy, not of an edge.
How the strategy works
Place a bet. If it loses, bet twice as much on the next. If that loses, double again. The first win pays back every earlier loss and adds the size of the first bet. On an even-money bet, bet one pays back $10.00, bet two pays $20.00 against $10.00 lost, bet three pays $40.00 against $30.00 lost, and so on. The profit is always $10.00 per completed round.
The idea looks sound, because a long losing run is unlikely. On a fair bet the chance of losing 6 in a row is 0.5 to the power 6, which is 1.56%. Rare, but not impossible, and the cost of it is large.
The bankroll limit, with numbers
The ladder needs a bigger bet each step. After 6 losses at a first bet of $10.00 the total staked is $10.00 x (2^6 - 1) = $630.00. The next bet would be $640.00, which takes the total to $1,270.00, above the $1,000.00 bankroll. The ladder ends there with a loss of $630.00, whatever happens next.
Chance the ladder fails in a round = (1 - win chance)^n
Expected result per round = (1 - fail chance) x first bet - fail chance x loss at failure
Expected value, exactly
On a fair bet the fail chance per round is 1.56%. The expected result is 0.984 x $10.00 - 0.016 x $630.00 = $0.00. The pile of small wins and the one large loss cancel exactly. A fair bet cannot be turned into a profit by changing the size of the bets.
Now take a bet with a win chance of 18 in 37, which is 48.65%. The fail chance per round rises to 1.83%, and the expected result becomes -$1.74 per round. The average round loses. Every real market has costs such as spread and fees that put the odds below fair, so this is the usual case.
How long does it last?
The chance that the ladder has not yet failed after n rounds is (1 - fail chance)^n. On the fair bet that is 85.4 percent after 10 rounds, 45.5 percent after 50 rounds, 20.7 percent after 100 rounds, 0.0 percent after 500 rounds. On the 18 in 37 bet it is 83.1 percent after 10 rounds, 39.6 percent after 50 rounds, 15.7 percent after 100 rounds, 0.0 percent after 500 rounds. A strategy that has run for months and never failed has not shown that it is safe. It has shown that the rare event has not happened yet.
How a trading bot meets this
- Margin takes the place of the bankroll. A bot that doubles its position after a loss runs out of margin or hits a stop-out, not a bankroll. See stop out and margin call.
- Markets trend. A fair coin does not trend. A price can fall for a long time, and a bot that adds on the way down is on a longer ladder than the coin model suggests.
- Costs push the odds below fair. Spread and fees are paid on every step. See spread.
- Backtests hide it. A test that has not met a strong trend shows a smooth line. See survivorship bias and backtesting.
How to check a ladder bot
Count how many losses in a row the account can pay for, using the martingale calculator. Work out the chance of that run on your own win rate, and the loss if it happens. Compare the loss with the profit of one round. The guide on martingale trading covers the bot types, and the risk of ruin calculator simulates the wider picture.
What this page does not tell you
It does not say that a martingale always fails in the short run. It can win for a long time. It shows that the strategy gives no edge, and that the loss when it fails is far larger than the gain from any one round. The numbers are made up and it is not advice.
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FAQ
Frequently Asked Questions
What is the martingale strategy?
Doubling the bet after every loss so that one win recovers all earlier losses and leaves a profit equal to the first bet.
Why does the martingale strategy fail?
The bet grows faster than any bankroll. A run of losses long enough to exhaust it is rare, but when it happens the loss is far larger than the small gain from each completed round.
Is the expected value of a martingale positive?
Not on a fair or an unfair bet. On a fair bet with a bankroll limit it is exactly zero, and with costs or an edge against you it is negative.
Does a long winning run show the strategy is safe?
No. It shows the rare losing run has not happened yet. The chance of surviving many rounds falls with each one.
Does the martingale strategy work in forex?
It can win for a long time, but a price can trend far, margin is limited and costs are paid at each step. Test the ladder against the worst move you could meet.
Are the numbers on this page real?
Example numbers are made up to show how the maths works, and the page says so. A figure only counts as exact when the page says it was calculated on a stated date. Nothing you enter in a calculator leaves your browser.
Can I use this to decide whether to run a bot?
It can show whether a bot's numbers hold together and how much an account can lose. It cannot say what the market will do, and it is not advice. Use it to ask better questions, then read the terms of your own broker or exchange.
Is this financial advice?
No. It is general education about arithmetic. The numbers are made up and it does not consider your situation.
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