The arithmetic seduces: lose 1, bet 2; lose again, bet 4; win at last and you are one unit up overall. The flaw is that stakes grow geometrically while your bankroll and the table limit do not. Seven straight losses on an even-money bet, roughly a 1-in-90 event on a European wheel, require a 128-unit bet to continue, with 127 units already gone.
The system converts a high probability of winning a little into a small probability of losing a great deal. The expected value of the sequence is unchanged, because no arrangement of bets with negative expected value can sum to a positive one: only the shape of the distribution moves. Every variant, d'Alembert, Fibonacci, Labouchère, performs the same trade with different arithmetic.
Why it matters
It is the most sold system in gambling, usually to people who have just discovered the losing side of it feels unlikely. The rare catastrophic loss is not a malfunction of the system; it is the system, priced in from the start.
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