Definition
Martingale strategy
Martingale doubles the stake after every loss so that one win recovers it all. The arithmetic of a losing streak, gambler's ruin, and why a 95% win rate is not an edge.
The martingale strategy is a position-sizing rule that doubles the stake after every losing trade so that the first winning trade recovers all prior losses plus one base unit. The win rate it produces looks spectacular, often above 95%, because most losing sequences end before the capital does. The arithmetic is the problem: nine straight losses at a $10 base have cost $5,110 and demand a $5,120 tenth stake, $10,230 of capital in total, and against a finite bankroll the gambler's-ruin result puts the long-run probability of ruin at 1 for any fair or negative-edge game.
- Also known as
- doubling-down strategy · grid martingale · martingale money management
How it is calculated
stake_n = base × 2^(n−1) (n = position in the losing run)
capital needed to survive n losses = base × (2^n − 1)
P(n straight losses) = (1 − p)^n
base = $10: nine losses cost 10 × (2^9 − 1) = $5,110; tenth stake = 10 × 2^9 = $5,120; total = $10,230
p = 0.5, n = 10 → 0.5^10 = 0.098% per ten-trade window, ≈1 such run expected over 1,000 trades
Worked example: At a $10 base the stakes run 10, 20, 40, 80, 160, 320, 640, 1,280, 2,560, 5,120: the tenth trade risks $5,120 to win back $5,110 and earn $10.
The streak arrives on schedule
Each stake is the base times 2 to the power of the losses so far, so the capital needed to survive n straight losses is base × (2ⁿ − 1): it doubles with every extra loss the rule is asked to absorb. With a 50% win rate, ten straight losses occur in 0.098% of any given ten-trade window, which sounds remote until the window is slid across 1,000 trades, where the expected number of such runs is roughly one. Grinstead and Snell's treatment of gambler's ruin gives the general result: a player with finite capital facing a fair or unfavourable game is ruined with probability 1 in the long run, and the martingale only changes how fast.
Kelly says bet less after a loss, not more
Kelly sizing stakes a fixed fraction of current capital, so a loss shrinks the next bet in absolute terms. MacLean, Thorp and Ziemba show that betting above the Kelly fraction lowers growth and raises the chance of large losses, and the martingale bets above it by construction. The retail crypto form is the grid bot in martingale mode, which enlarges each successive buy as price falls and so carries the same exposure in a different wrapper. The mirror image is the anti-martingale: pyramiding or Kelly-style sizing that adds after wins and cuts after losses. None of QANTERION's four managed strategies scale into a losing position; each runs under a hard maximum-drawdown cap instead, which is the opposite design choice.
How it gets misread
The martingale is misread as an edge because its equity curve is a long, smooth staircase of small wins and its win rate sits above 95%. Win rate and edge are different quantities: the rule does not change the expected value of a single trade, it only changes the shape of the loss, converting many small losses into one catastrophic loss whose timing is unknown and whose arrival is certain given enough trades. A 95% win rate paired with a loss 19 times the average win is exactly break-even before fees.
Sources
- Grinstead and Snell's Introduction to Probability — American Mathematical Society (CHANCE Project edition)
- A New Interpretation of Information Rate — J. L. Kelly, Jr., Bell System Technical Journal (hosted by Princeton University)
- Good and bad properties of the Kelly criterion — MacLean, Thorp & Ziemba, hosted by the UC Berkeley Department of Statistics
Definitions are educational. Nothing here is investment advice, and no metric described on this page predicts future results.
Definitions are the easy part
Knowing what drawdown means is not the same as having a system that halts on it. QANTERION applies these limits while a strategy runs.