## The Martingale Explained
The Martingale system doubles your stake after every loss. The idea: eventually you win, and the win covers all previous losses plus a small profit.
**Example:** Bet 1 unit. Lose. Bet 2 units. Lose. Bet 4. Lose. Bet 8. Win.
Net result: +1 unit after 4 bets.
This sounds appealing. It fails catastrophically.
## Why Martingale Destroys Bankrolls
**The sequence risk:** A losing run of 10 bets requires a stake of 2^10 = 1,024 units on the 11th bet. Starting from 1 unit, a 10-loss run requires staking 1,023 total units to reach this point. At a £10 unit: you have staked £10,230 to win back £10.
**Losing runs are normal:** Even with a 50% win rate, a 10-loss run has P = (0.5)^10 = 0.1% probability. At 1,000 bets, expected occurrences: 1. At 10,000 bets: 10 occurrences.
**No edge requirement:** Martingale does not address whether your selections have positive EV. It is purely a staking system that assumes infinite bankroll and no stake limits.
## The Fibonacci and D'Alembert Fallacies
Both are variations of progression betting — increasing stakes after losses. All progression systems share the same fatal flaw: they cannot convert negative EV selections into positive EV outcomes. They just change the loss distribution (many small wins, occasional catastrophic loss).
## The Casino's Perspective
Casinos welcome Martingale players. The system is emotionally compelling but mathematically equivalent to flat betting with the same number of units staked in expectation — minus the occasional ruin event.
## The Rule
Never use any staking system that increases stakes after losses without a mathematical basis (like Kelly) connecting the stake increase to a genuine edge calculation.
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