The math that always wins (against you)
Martingale's promise is seductive: double after each loss, and the first win recovers everything plus one base unit. The catch is the geometric explosion. Bet 1, lose, bet 2, lose, bet 4, 8, 16, 32… your stake is 2n after n losses, and the total you've risked is 2n−1. Seven losses in a row — which happens roughly once every 128 sequences at even odds, i.e. regularly — needs 255× your base bet. No account is infinite, and exchanges cap position size, so the strategy doesn't reduce risk; it concentrates it into one catastrophic streak.
This is the same trap as averaging down, just faster. The honest fixes are the opposite of martingale: fixed or risk-based sizing, and accepting small losses instead of betting bigger to avoid them. Size from risk with the position size calculator, see your long-run blow-up odds with the risk of ruin calculator, and compare with averaging down on the DCA survival calculator.
FAQ
Does a bigger account make martingale safe? No — it only buys a few more losses. Each extra survivable loss needs roughly double the capital, while the streak that kills you gets only slightly rarer.
What about anti-martingale? Increasing size when winning and cutting when losing is the saner mirror image — it caps downside and lets winners run, the opposite of this calculator's scenario.