Fibonacci vs. D’Alembert: which betting system is better?
Neither beats the house: both lose about the house edge on every chip bet. In sessions of a few hundred bets, D’Alembert actually goes bust more often, because it ends up betting more in total.
Over the same simulated sessions, Fibonacci went bust 36.5% of the time and D’Alembert 60.7%. Fibonacci bet 5,272 chips per session on average and D’Alembert 11,131. They lost 2.29% and 2.70% of every chip bet; the house edge on red is 2.70%.
Run these sessions in the simulatorRoulette odds for every bet
The same sessions with each system
| System | Went bust | Finished ahead | Average result | Chips bet per session | Lost per chip bet |
|---|---|---|---|---|---|
| Fibonacci | 36.5% | 60.0% | −120.47 | 5,272 | 2.29% |
| D’Alembert | 60.7% | 35.0% | −300.07 | 11,131 | 2.70% |
| Flat betting | 0.0% | 31.6% | −64.56 | 2,500 | 2.58% |
10,000 sessions of up to 250 bets each, with a 1,000-chip bankroll, a 10-chip base bet and a table maximum of 1,000. Seed “cgs”: the link above replays exactly these sessions.
Why
D’Alembert adds one unit after a loss and takes one off after a win, so its bet tracks how far behind you are: with the house edge pulling you slowly behind, the bet creeps up and stays up. Fibonacci follows 1, 1, 2, 3, 5, 8… and steps back two after every win, so its bet jumps in a losing run but falls back quickly. Over a long session D’Alembert bets more in total, and more money bet at the same edge means bigger losses and more busted bankrolls. Neither changes what each bet is worth.