Martingale and Anti-Martingale: The Mathematics of Doubling Down

Martingale wins almost every time and loses everything once. This guide shows the arithmetic, then explains the inverted version that professionals actually use.

5 min readIntermediateUpdated September 16, 2026

At a glance

Martingale
Increase size after a loss to recover it
Anti-martingale
Increase size after a win, reduce after a loss
Martingale outcome
Frequent small wins, eventual total loss
Why it fails
Required capital grows exponentially; account size does not

Key takeaways

  • Martingale converts a series of small wins into one catastrophic loss; the expected value does not improve, only the timing of the loss changes.
  • Ten consecutive losses requires 1,024 times the initial stake to continue doubling, which no account and no broker will support.
  • Losing streaks are far more common than intuition suggests: with a 50 percent win rate, ten in a row occurs roughly once per thousand sequences.
  • Anti-martingale, increasing risk after wins and cutting after losses, is the structure behind trend following and pyramiding.
  • Any strategy that responds to losses by increasing exposure is a martingale regardless of what it is called.

The arithmetic, in full

A martingale doubles the stake after each loss so that one win recovers all previous losses plus the original target. On any given sequence it usually works, which is exactly what makes it dangerous.

Loss numberStake requiredCumulative lossCapital needed to continue
1100100200
2200300400
3400700800
51,6003,1003,200
76,40012,70012,800
1051,200102,300102,400
13409,600819,100819,200
Doubling from a 100 USD base stake.

To survive thirteen consecutive losses starting from 100 USD you need over 800,000 USD, and the reward for that entire sequence is 100 USD. The strategy trades a very high probability of a small gain for a small probability of an enormous loss, and because the loss is larger than every accumulated gain, the expected value stays negative once costs are included.

With a 50% win rate, the probability of N consecutive losses
occurring at least once within 1,000 trades is approximately:

   N = 5    ->  ~99.9%
   N = 8    ->  ~98%
   N = 10   ->  ~62%
   N = 12   ->  ~22%
   N = 15   ->  ~3%

A strategy that can survive 10 doublings will still meet
11 eventually.  "Eventually" arrives faster than expected
because trades accumulate quickly.
Probability of hitting a losing streak long enough to break the account.

The disguises martingale wears

Very few traders say they are using a martingale. Many are using one. The defining property is simple: does adverse movement cause exposure to increase? If yes, it is a martingale, whatever the label.

  • Averaging down without a cap. Adding at each new low to improve the average price. See trading myths.
  • [Grid trading](/library/strategy-styles/grid-trading-strategy) without boundaries. A ladder of orders that fills further into a trend is a martingale with extra steps.
  • Removing or widening a stop. Converting a bounded loss into an unbounded one is functionally the same decision.
  • Increasing size to recover a drawdown. "I need a bigger position to get back to even" is the same reasoning with the same outcome.
  • Selling options against a losing position to reduce the cost basis. The exposure grows precisely as the thesis deteriorates.
  • Adding to a losing position at "better technical levels". The levels are not the problem; the growth of exposure during disconfirmation is.

When adding to a position is legitimate

Not all scaling in is martingale. The distinction is whether the total risk was planned in advance and capped.

PropertyPlanned scale-inMartingale
Total riskFixed before the first entryGrows with each addition
Number of additionsDefined in advanceContinues until recovery or ruin
Stop levelSingle stop for the whole position, set at entryMoved or absent
Size progressionEqual or decreasingIncreasing, often doubling
Trigger for addingRules-based, often on confirmationThe loss itself
Worst caseKnown and survivableUnbounded

A legitimate scale-in example: risk 1 percent of equity total, entered as three equal tranches at defined levels, with one stop below all three. If the stop is hit after all three fill, the loss is 1 percent, exactly as planned. The position grew, but the risk never did.

Anti-martingale: what professionals actually do

The inverted structure increases exposure after wins and decreases it after losses. It produces a lower win rate and a much better survival profile, because size is largest when the strategy is performing and smallest when it is not.

  • Pyramiding. Adding to a winning position as it moves in your favour, with the stop raised so that total risk stays constant or falls. This is standard practice in trend following.
  • Fixed fractional sizing. Risking a constant percentage of equity means position sizes shrink automatically during a drawdown and grow during a recovery. This is anti-martingale by construction.
  • Drawdown-based de-risking. Halving risk after a defined drawdown, then restoring it after recovery. It extends survival at a modest cost in recovery speed.
  • Volatility targeting. Reducing exposure when volatility rises, which typically coincides with adverse conditions. See volatility targeting.
  • The Kelly framework. Optimal growth sizing is proportional to edge and inversely proportional to variance, which also implies smaller size when the edge is uncertain. See Kelly criterion.

Frequently asked questions

Does martingale ever work?

It produces profits in most sequences, which is why it attracts people, and it fails catastrophically in the remainder. Because the loss when it fails exceeds all accumulated gains, the long-run expectation is negative once costs are included. No amount of capital removes this, because the required stake grows exponentially while any account is finite.

What about martingale with a stop loss?

Adding a maximum number of doublings and a hard stop converts it into a bounded strategy, which is an improvement. But then it is simply a strategy with a large, rare loss and many small wins, and it must be evaluated on expectancy like any other. The doubling adds nothing except concentrating the loss into a single event.

Is averaging down always wrong?

No. Scaling into a position at planned levels within a fixed total risk budget and a single stop is a legitimate execution technique. The failure mode is adding without a cap, without a stop, or in response to the loss itself rather than to a rule defined before entry.

Why do martingale bots show such good results?

Because the test period was shorter than the interval between ruin events, or because the equity curve shown counts only closed trades while the losing position remains open. Ask for total equity including open positions, over a period containing a sustained trend, and the picture changes completely.

What should I use instead?

Fixed fractional risk, typically 0.25 to 1 percent of equity per trade, with position size derived from the stop distance. It is anti-martingale automatically, it makes losing streaks survivable, and it is the basis of essentially every professional risk framework. See position sizing.

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Referenced by

Educational use only. This guide explains how a strategy works. It is not investment advice, not a recommendation, and no result described here is a forecast. Test any approach on historical and out-of-sample data, size positions conservatively, and never risk money you cannot afford to lose.