Baccarat Betting Systems Tested: Fibonacci, Paroli, 1-3-2-6 and D'Alembert
No betting system changes the baccarat house edge. I simulated 1 million 100-hand sessions for each of Fibonacci, Paroli, 1-3-2-6 and D'Alembert on the Player bet, and every one lost about 1.24% of the total amount wagered, the same as flat betting. What the systems change is the shape of the results: how often you finish ahead, and how bad the bad nights get.
That shape is why systems feel like they work. Here are the numbers.
How I tested the baccarat betting systems
Each session is 100 hands on Player, starting at 1 unit, with a table maximum of 500 units. Ties push. Hand results use exact 8-deck odds: Player 44.62%, Banker 45.86%, Tie 9.52%.
The four systems, in one line each:
Fibonacci: after a loss, move one step up the sequence 1, 1, 2, 3, 5, 8 and so on. After a win, move back two steps.
Paroli: double after a win, and go back to 1 unit after a loss or after three wins in a row.
1-3-2-6: bet 1, 3, 2, then 6 units as long as you keep winning. Go back to 1 after a loss or after the 6.
D'Alembert: add 1 unit after a loss, take 1 off after a win.
Baccarat betting system results from 1 million sessions
| Finished ahead | Typical session | Worst 1% | Average wagered | Average result | |
|---|---|---|---|---|---|
| Flat 1 unit | 42.7% | -1 | -23 or worse | 100 | -1.24 |
| Paroli | 43.1% | -3 | -42 or worse | 170 | -2.10 |
| 1-3-2-6 | 43.1% | -4 | -50 or worse | 197 | -2.45 |
| D'Alembert | 62.2% | +20 | -291 or worse | 588 | -7.29 |
| Fibonacci | 91.6% | +15 | -378 or worse | 424 | -5.25 |
Average result is 1.24% of the average amount wagered. The simulation matched it within sampling noise.
Why Fibonacci finishes ahead 91.6% of the time and still loses
Fibonacci wins most sessions because a single win after a losing run claws back a lot. But the losing runs that don't end in time are huge. The worst session in my run lost 14,473 units, because the bets hit the 500-unit cap and stayed there.
Add up the many small wins and the few disasters, and you get the same 1.24% of everything wagered. D'Alembert works the same way, just less extreme. It's the Martingale pattern with a gentler slope.
Why Paroli and 1-3-2-6 feel safer
Paroli and 1-3-2-6 raise bets only after wins. Your worst nights are mild, close to flat betting.
The catch is that you bet more in total, so you lose more on average. Paroli wagers about 70% more than flat betting over 100 hands, and loses about 70% more on average.
What a betting system can and can't do
A system decides how much you bet. It doesn't touch the probability of any hand. Every dollar on Player costs 1.24% on average, no matter what pattern of bet sizes it sits in.
The only thing that changes the odds is the cards left in the shoe, and for Banker and Player that change is usually tiny. I showed how tiny in card counting in baccarat.
See the real odds in Baccarator
Baccarator doesn't predict what comes next. It recalculates Banker, Player, Tie and side bet odds from the cards left after each hand you enter. When a bet's expected value turns positive, which is rare and short-lived, it shows a Kelly criterion fraction. That's a long-run average, and the next hand can still lose.
Free on the App Store, 6 or 8 decks, virtual chips only.
Baccarat betting systems FAQ
Do baccarat betting systems work?
No betting system beats the house edge. In 1 million simulated sessions, Fibonacci, Paroli, 1-3-2-6 and D'Alembert all lost about 1.24% of the total wagered on Player, the same as flat betting.
What is the 1-3-2-6 system in baccarat?
You bet 1, 3, 2 and 6 units on consecutive wins, and go back to 1 after a loss or after the fourth bet. It keeps losses small but increases total wagering, so the average loss over 100 hands is about twice that of flat betting.
Is Fibonacci good for baccarat?
It finished ahead in 91.6% of simulated 100-hand sessions, but the losing sessions were very large. On average it lost 1.24% of everything wagered, the same as any other way of betting Player.
Baccarator is a math tool for education. No real-money gambling. 21+ only.
