Martingale: the math of ruin

Martingale is a position-sizing scheme, not an entry strategy: after every loss you double the size of the next trade, so that one eventual win recovers all prior losses plus a small profit. It comes from casino betting, and it is one of the most dangerous ideas in trading. This lesson is a deliberate warning.

The seductive math

Bet 1 unit and lose. Bet 2 and lose. Bet 4, then 8. The first win recovers everything:

Trade 1: stake 1   -> lose,  running total -1
Trade 2: stake 2   -> lose,  running total -3
Trade 3: stake 4   -> lose,  running total -7
Trade 4: stake 8   -> WIN,   running total +1

You "always" end ahead by your original stake. On paper, it cannot lose.

Why it always eventually blows up

The flaw is that the stake grows exponentially, while your account is finite. A run of losses is not unlikely — it is inevitable given enough trades.

Losing streak:  1   2   3   4    5    6    7     8     9     10
Stake needed:   1   2   4   8   16   32   64   128   256   512

Ten losses in a row demands a stake of 512 to recover a stake of 1 — over a thousand units risked in total. Streaks of ten happen. When the stake exceeds your capital (or the broker's margin limit), the single losing streak you could not fund wipes out every small win you ever banked, and then the account.

The inescapable truth

Martingale does not improve your edge — it only reshapes the distribution of outcomes: a long run of small, reliable-looking wins, terminated by one total loss. Expected value is unchanged at best and worse after costs; what changes is that the catastrophe is hidden until it arrives.

No amount of capital makes it safe, because the stake is unbounded while capital is not. Never trade real money on a martingale. Any system or signal seller advertising a flawless, ever-rising equity curve is almost certainly running a hidden martingale or grid that has simply not met its losing streak yet.