Why martingale fails: the maths of doubling after a loss

Martingale is the idea that you can never lose if you double your stake after every loss, because the first win recovers everything plus a small profit. It feels airtight, and on paper it works on every round except the one that matters: the long losing streak that eventually arrives and asks for a stake you cannot place. With payouts below 100%, the system is worse than its classic casino version, because doubling is not even enough to break even.

The system in one paragraph

Start with a base stake, say $10. If the trade wins, take the profit and start again at $10. If it loses, double: $20. Lose again: $40, then $80, and so on. When a win finally comes, it is supposed to cover all previous losses and leave you with the original small profit. The system comes from gambling, long before electronic trading; see the martingale glossary entry for a short definition.

Problem one: losing streaks are longer than you think

Assume, generously, a 50/50 chance per trade, ignoring ties. The chance that any particular sequence of trades loses n times in a row is 0.5 to the power n. That looks tiny. But you do not trade once; you trade hundreds of times, and each trade can start a streak.

These are calculated probabilities for a 50/50 process, not observed statistics. Read the 500-trade column: an active short-expiry trader can reach 500 trades in a couple of weeks, and by then an eight-loss streak is more likely than not. If you trade with an edge below 50%, streaks come even sooner.

Problem two: at payouts below 100%, doubling does not recover

In the casino version, an even-money bet pays 100%, so doubling recovers your losses plus one base unit. Here the payout is less than 100%. Look at pure doubling with a $1 base at 80% payout, where the win finally comes on trade n:

After three losses, a win at double the stake still leaves you down. Plain doubling stops being a recovery system at all.

To actually recover all losses plus the original profit at payout p, each stake must be multiplied not by 2 but by (1 + p) / p. At 80% payout that is 2.25. With a $10 base:

Every one of those rows, if the next trade wins, earns you exactly $8, the profit of your first $10 trade. After nine losses you are placing $6,568 to win $8.

Problem three: the wall at the end of the table

Every progression hits a limit: your balance, or the platform's maximum stake. On Sky Trade the default maximum stake per trade is $50,000. In the table above, the twelfth stake would be about $74,818, which is not allowed. By then you would already have lost $59,846 across eleven trades. Most people hit their balance limit long before that: someone with $1,000 who loses five times in a row has $546.68 left and cannot place the sixth stake of $576.65.

So martingale converts many small wins into a rare but enormous loss. Here is the trade it offers, in round numbers: in the long run, you collect a long series of $8 wins and then give back hundreds or thousands of them in one streak.

Problem four: it does not change the expected value

Stake progressions rearrange losses in time; they cannot turn a negative expected value positive. If each trade at 80% payout and 50% wins is worth −10% of its stake, then a $10,000 stake late in a streak is worth −$1,000 on average, just like every other trade. Martingale makes you put the largest amounts on trades that are no better than the rest, which is why the eventual risk of ruin climbs so fast.

On Sky Trade OTC instruments this is not even debatable: the price model is itself a mathematical martingale with 50/50 direction, so there is nothing a progression can exploit. A run of losses does not make the next trade more likely to win; believing that it does is the gambler's fallacy, covered in trading psychology.

Conclusion

Martingale does not fail because traders apply it badly; it fails because the arithmetic does not work. Streaks long enough to break it are routine over hundreds of trades, payouts below 100% demand more than doubling, stake and balance limits cut the progression off, and the expected value per trade does not change. Fixed fractional sizing, described in risk per trade, solves the problem martingale pretends to solve: surviving the streak. For what a streak does to a balance, see drawdown and recovery.