Martingale

A rule imported from wagering rather than from markets. After a loss the next stake is doubled, so a single win returns the sum of everything staked plus one unit, whatever the length of the losing run that preceded it. The arithmetic is correct and that is precisely what makes the scheme durable: it fails on its conditions rather than on its algebra.

There are two conditions and neither is ever available. The first is capital without limit, because the required stake grows geometrically and the sequence needed to exhaust any finite account is short. The second is no ceiling on the stake. Casinos removed the second condition with table limits long ago, and the first condition was never available to anybody at all.

A margined trading account fails both conditions in the same place, and it fails them earlier than a simple count of the sequence suggests. Doubling the size doubles the margin committed while the running loss is reducing the equity available to meet it, so the two move against each other and the account reaches its close out level well before the doubling reaches any theoretical limit. Losses on a leveraged position are not limited to the amount deposited, so the sequence ends in a realised loss rather than in a suspended bet. Schemes described as anti martingale, which increase size after a win instead, are a different rule with different failure modes and share only the name.