What is a Martingale Strategy? Definition, Formula, and Example
A martingale strategy is a position-sizing method that doubles the bet after every loss so that the first win recovers all prior losses plus one unit of profit.
What is a Martingale Strategy?
A martingale strategy is a betting and position-sizing system in which the trader doubles the size of the position after every loss. The logic is that a single win recovers all previous losses plus a profit equal to the original stake. The strategy originates in 18th-century French gambling and requires an unlimited bankroll and no position-size ceiling to work with certainty. In real markets, both constraints exist, so martingale converts a high probability of small steady gains into a small probability of total account loss.
How the Sizing Is Calculated
Starting with base stake B, the position size after n consecutive losses is:
Size(n) = B x 2^n
Cumulative capital committed after n losses, assuming each position is fully lost, is:
Cumulative Risk = B x (2^(n+1) − 1)
The required bankroll grows exponentially. After 10 consecutive losses starting at $100, the next position must be $102,400 and total capital at risk is $204,700, all to net $100 of profit on the eventual win. The probability of ruin depends on the per-trade win probability p: with p = 0.5, the chance of 10 straight losses is 0.5^10, about 0.098%, which sounds rare until the strategy is repeated hundreds of times, at which point the losing streak becomes a near certainty.
Worked Example
A trader applies martingale to short-term mean-reversion longs in SPY, buying $1,000 on each dip with a $10 profit target and doubling after each stopped-out loss. Sequence: trade 1 loses $1,000, trade 2 risks $2,000 and loses, trade 3 risks $4,000 and loses, trade 4 risks $8,000 and wins $80 gross. Net result across four trades: −$1,000 − $2,000 − $4,000 + $8,080 scaled profit on the final position, roughly breakeven plus the base unit. Now extend the losing streak to eight trades. Trade 9 requires $256,000 of buying power. A retail margin account hits its limit long before that, and the realized loss of $255,000 is unrecoverable.
When Traders Use It
Martingale appears most often in grid trading systems, forex scalping bots, and averaging-down approaches on range-bound instruments. Some traders apply a capped variant, doubling only two or three times before resetting, which bounds the loss but also breaks the mathematical recovery guarantee. Anti-martingale, the reverse system that doubles after wins and cuts after losses, is the version that survives contact with trending markets and aligns with sound position sizing. If you want to observe how quickly martingale sizing destroys a simulated account, run it in the paper trading simulator with real market data.
Limitations and Common Misconceptions
The core misconception is that martingale has a positive expectancy. It does not. Doubling the stake changes the distribution of outcomes, not the expected value, which remains negative whenever the underlying trade has negative or zero edge after costs. The strategy also assumes losses are independent and bounded; markets deliver correlated gaps, halts, and slippage that can exceed the planned loss on a single leg. Commissions and borrow costs compound the bleed. Martingale is a risk-of-ruin machine dressed as a recovery system, and any backtest showing smooth equity curves from it is one tail event away from zero.