Martingale, Paroli and friends: what they really cost
No system changes the edge. Most raise your average bet, and with it the hourly cost.
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Betting systems change how much you bet based on what just happened. They're fun, they can make a session feel structured, and some have produced memorable wins. None of them can beat the game, because each individual bet still loses 1.06% (on Banker) on average. Sum that over every bet the system makes and the answer is always the same:
Expected cost = house edge × total amount bet
So the honest question about any system is: how much does it make me bet? Here are the common ones, with a $10 unit on Banker:
| System | How it works | Average bet | Cost per hour (72 hands) |
|---|---|---|---|
| Flat | Same bet every hand | $10.00 | $7.62 |
| Follow the shoe | Flat, on whichever side won last | $10.00 | ≈ $8.25 |
| Paroli | Double after a win, up to 3 wins (1-2-4), then back to 1 | $17.13 | $13.05 |
| 1-3-2-6 | After each win, move along 1, 3, 2, 6 units; any loss restarts | $19.98 | $15.22 |
| Fibonacci | After a loss, the next number in 1-1-2-3-5-8…89; after a win, back two | $24.56 | $18.71 |
| Martingale | Double after every loss, back to 1 after a win; at most 7 bets ($10–$640) | $33.24 | $25.32 |
| D'Alembert | +1 unit after a loss, −1 after a win (1 to 20 units) | $45.73 | $34.84 |
| Labouchère | Write 1-2-3-4. Bet first + last; a win crosses them off, a loss adds the bet to the end (bets capped at 100 units) | ≈ $125 | ≈ $95 (≈ simulated) |
(Average bets are for a fresh one-hour session, ties included, with the caps shown and a bankroll that doesn't run out. Auto-play's exact line shows these figures for one system; in a comparison, each system's cost comes from the bets it actually placed, so it lands near them.)
Martingale, up close. It feels unbeatable: keep doubling and one win gets everything back. It usually works. Then, about once every 141 series on Banker, the table produces seven losses in a row, and you've lost $10 + $20 + … + $640 = $1,270 with the table limit or your bankroll in the way. On Banker it's worse than it looks: the commission means a win after five losses pays $304 against $310 lost, so even the "rescue" loses $6. The many small wins and the rare disaster average out to the same 1.06% of everything you bet, and Martingale makes you bet a lot.
Loss-chasing systems (Martingale, Fibonacci, D'Alembert, Labouchère) raise your bet after losses, so your biggest bets come when you're behind. Win-riding systems (Paroli, 1-3-2-6) raise only with money you've just won, so their worst case is a normal losing session. If you enjoy a system, the cheapest feel-good choice is a win-rider at a small unit.
Show the math: How the hourly costs are computed
Each system is a Markov chain over its progression state. Ties leave the state unchanged. Starting from the first step, the exact expected bet on each of the 72 hands is summed and multiplied by the Banker edge 114753351728/10847218479825. Example: Martingale's E[total bet over 72 hands] = 239.30 units, so the cost is 239.30 × $10 × 1.0579% = $25.32. Labouchère has no small state space, so it was simulated (200,000 one-hour sessions). Follow the shoe is ≈ 50.68% × 1.0579% + 49.32% × 1.2351% = 1.1453% of $720. On Player, the costs are higher (flat $8.89, Martingale $31.23).
Quiz
What does a betting system change?
- The house edge
- How much you bet, and so the cost per hour
- The odds of the next hand
- Nothing at all
Show the answer
B: How much you bet, and so the cost per hour. Each bet keeps its edge. A system only changes the amounts, and so the total you put at risk.
Quiz
With $10 Martingale on Banker, capped at seven bets, roughly how often do you lose all seven?
- Never
- About once every 141 series
- Half the time
- Once every 10,000 series
Show the answer
B: About once every 141 series. Seven straight Player wins (ties don't count) happen about 0.71% of the time: $1,270 lost.
Quiz
Which system costs the least per hour?
- Martingale
- Paroli
- Flat betting
- D'Alembert
Show the answer
C: Flat betting. Flat betting at your unit has the smallest average bet, and so the smallest cost.
Quiz
Why is Paroli gentler on your bankroll than Martingale?
- It has a lower edge
- It raises bets only with winnings, not after losses
- It never loses
- It bets Tie
Show the answer
B: It raises bets only with winnings, not after losses. Win-riders risk the money they've just won. Loss-chasers raise when you're behind.