Monte Carlo
Betting-system simulator
Pick a progression and run ten thousand complete sessions. You will see a high success rate and a negative total at the same time.
Net result at walk-away
Method
Method
Each hand settles on real baccarat probabilities (banker 45.86% / player 44.62% / tie 9.52%, 5% commission on banker). If the bankroll cannot fund the full stake, it bets whatever is left. A session ends at target or bust; ten thousand sessions are then aggregated.
How to read it
Four progressions, one destination
Hitting the target is not the same as winning
Martingale hits the target in 77.2% of sessions against flat betting’s 63.2%. That is real, not an illusion — doubling after a loss genuinely makes a small target easier to reach. In the same runs, though, Martingale’s average result is −36 and it busts 22.8% of the time against flat betting’s 14.9%. It bundles "win small often" together with "occasionally lose everything", and the bundle is priced below zero.
The one column nothing escapes
Look at the rightmost column: loss divided by total amount wagered. The four progressions come in at 1.066%, 1.098%, 1.144% and 1.067%, against a theoretical banker house edge of 1.058%. All four sit inside sampling error (1σ over 100,000 sessions is roughly 0.03–0.10 points). This is not a coincidence but an identity: every hand carries the same −1.058% expectation, and a progression only chooses how much goes on each hand and how many hands there are.
Martingale "loses less" because it plays less
A Martingale session lasts 14.7 hands on average; a flat-betting session lasts 97.6. Total turnover therefore drops from 9,765 to 3,272, and the average result rises from −104 to −36. Martingale appears to lose less because it gets you off the table faster. Per unit wagered the two are identical. If you want to lose less, stake less — changing the shape of the staking will not do it.
| Progression | Hit target | Busted | Avg hands | Avg total wagered | Loss ÷ wagered |
|---|---|---|---|---|---|
| Flat (no progression) | 63.2% | 14.9% | 97.6 | 9,765 | 1.066% |
| Martingale (double after loss) | 77.2% | 22.8% | 14.7 | 3,272 | 1.098% |
| D’Alembert (+1 loss, −1 win) | 76.0% | 24.0% | 14.5 | 3,835 | 1.144% |
| 1-3-2-4 (positive progression) | 73.2% | 26.5% | 32.9 | 6,085 | 1.067% |
Theoretical banker house edge: 1.058%. Measured values are 1.066% ± 0.029, 1.098% ± 0.103, 1.144% ± 0.092 and 1.067% ± 0.055 (bootstrap, 1σ) — every one consistent with theory.
Frequently asked
- Why doesn’t the Martingale work?
- It works; it just does not do what people think it does. It raises the chance of a small win to 77%, and the price is that the remaining 23% is a bust. Cost per unit wagered is 1.098%, statistically identical to flat betting’s 1.066%. A progression redistributes the shape of winning and losing. It cannot change the total.
- Is there any staking system with positive expectation?
- No, and this is provable rather than merely observed. Every hand has negative expectation, any progression is just a weighted sum of those hands, and a weighted sum of negative numbers is negative. Staking can only amplify an edge that already exists per hand — as card counting occasionally creates in blackjack. Baccarat offers no such edge.
- Why do the average hand counts differ so much?
- Because the progression decides how quickly a session ends. Three consecutive Martingale losses puts you at eight units a hand, which a 20-unit bankroll cannot sustain, so sessions resolve fast in one direction or the other — 14.7 hands on average. Flat betting grinds toward the 200-hand cap at 97.6. That difference in hands is exactly where the difference in turnover comes from.
- Can these results be reproduced?
- Yes. Each hand settles on true probabilities (banker 45.8597% paying 0.95, player 44.6247%, tie 9.5156% returning the stake); when the bankroll cannot cover the full bet the remaining balance goes in; a session ends on target or bust. Reseed and rerun, and the cost column still lands near 1.06%. That is convergence, not tuning.