Walk past any eight-deck baccarat pit and you will see players adjusting their chip stacks according to seven recurring blueprints: flat unit sizing, two positive progressions (Paroli and 1-3-2-6), and four negative progressions (D'Alembert, Fibonacci, Labouchere, and Martingale).
Because none of these seven systems can alter the composition of the remaining shoe or change the casino's mathematical advantage (~1.06% on Banker after the 5% commission, ~1.24% on Player, and ~14.36% on Tie at 8:1), ranking them by “expected return” is meaningless—every one of them loses an exact percentage of the total chips put in action. The only mathematically honest way to rank betting progression systems in baccarat is by session survival probability, drawdown speed during a losing run, and average action multiplier. Below, we rank all seven structures from #1 (longest bankroll survival) to #7 (fastest bankroll ruin) and test them against an engine-verified 18-hand shoe you can inspect in our free Baccarat Calculator & Road Decoder.
The 3 structural families of baccarat staking
Before comparing individual progressions, separate them by how they react to the previous hand's result:
- 1. Flat Betting (Constant Stake): You wager the exact same 1-unit stake on every coup regardless of whether the previous hand won, lost, or tied.
- 2. Positive Progressions (Pressing Wins): You keep your stake at 1 unit after every loss and increase your wager only after a winning hand using chips just won from the house, resetting to 1 unit after a short target cycle of 3 or 4 coups.
- 3. Negative Progressions (Escalating After Losses): You increase your stake after every lost hand (linearly, along the Fibonacci sequence, via a split cancellation line, or by geometric doubling) in an effort to offset earlier setbacks when a winning coup eventually lands.
Master ranking: 7 baccarat betting systems compared by survival
Assume a player brings a 100-unit session bankroll (for example, $1,000 divided into $10 base units) to a table with a 500-unit ($5,000) maximum wager. Here is how all seven systems rank when measured by their 10-loss cumulative drawdown, Step 10 required stake, and session survival profile:
| Survival Rank | System & Family | Unit Sequence Rule | 10th Loss Stake | 10-Loss Cumulative Drawdown | 100-Unit Bankroll Status After 10 Losses |
|---|---|---|---|---|---|
| #1 | Flat Betting (Constant) | 1 – 1 – 1 – 1 every hand | 1u | −10u | 90u remaining (intact) |
| #2 | Paroli (Positive, 3-Step) | 1 – 2 – 4 on wins; 1u on loss | 1u | −10u | 90u remaining (intact) |
| #3 | 1-3-2-6 (Positive, 4-Step) | 1 – 3 – 2 – 6 on wins; 1u on loss | 1u | −10u | 90u remaining (intact) |
| #4 | D'Alembert (Linear Neg.) | +1u on loss, −1u on win (min 1u) | 10u | −55u | 45u remaining (heavy drawdown) |
| #5 | Fibonacci (1.618× Neg.) | 1–1–2–3–5–8–13–21–34–55 (+1L / −2W) | 55u | −143u | Busted on Loss #9 (−88u + 55u needed) |
| #6 | Labouchere (1-2-3-4 Line) | Stake = first + last; append lost stake | 14u | −95u | 5u left (cannot cover 15u Hand 11 stake) |
| #7 | Martingale (2.0× Doubling) | 1–2–4–8–16–32–64–128–256–512 | 512u | −1,023u | Busted on Loss #7 (−127u exceeds 100u) |
System-by-system breakdown (#1 to #7)
Rank #1: Flat Betting (1 – 1 – 1 – 1)
How it works: You wager 1 unit on every decided hand you choose to play, never raising after a loss or pressing after a win.
Why it ranks #1 for survival: Because expected loss in baccarat is strictly proportional to total action wagered (Expected Cost = Total Action × House Edge), keeping your wager fixed at the 1-unit table minimum puts the smallest possible volume of chips through the casino's 1.06% (Banker) or 1.24% (Player) edge per hour. Across 100 decided hands at $10 per hand, your total action is $1,000 and your expected mathematical cost is $10.60 on Banker or $12.40 on Player. A 10-hand losing streak costs exactly 10 units—leaving 90% of a 100-unit bankroll untouched.
Rank #2: Paroli System (1 – 2 – 4 Positive Progression)
How it works: You start at 1 unit. If you lose, you stay at 1 unit. If you win, you let the 1-unit payout ride for a 2-unit wager on Hand 2; if Hand 2 wins, you press to a 4-unit wager on Hand 3; and if Hand 3 wins, you collect the +7u even-money cycle gain (or +6.65u before compounding adjustments on Banker) and reset to 1 unit.
Why it ranks #2 for survival: As detailed in our Paroli vs. Martingale breakdown, Paroli never reaches into your reserve bankroll to fund a raised bet—every 2-unit and 4-unit press is funded mostly by the previous hand's winnings. During an adverse 10-loss stretch, your stake stays locked at 1 unit per hand (−10u drawdown). The trade-off is statistical: because completing a 3-hand winning streak happens on only 0.5068³ ≈ 13.02% of three-hand Banker trials (or 0.4932³ ≈ 11.99% on Player), roughly 87% to 88% of Paroli cycles end in a 1-unit net loss before Step 3 completes, and your average wager per hand (~1.73 units) raises your expected hourly cost roughly 1.73× above flat betting.
Rank #3: The 1-3-2-6 System (4-Step Positive Progression)
How it works: You progress through stakes of 1u → 3u → 2u → 6u across four consecutive winning hands, dropping back to 1u after any loss or after completing Step 4.
Why it ranks #3 for survival: Like Paroli, the 1-3-2-6 progression keeps cold-streak drawdowns capped at 1 unit per lost Step 1 hand. Its one extra exposure occurs on Step 2 (3 units): after winning 1 unit on Step 1, you have 2 units on the felt and must add 1 extra unit from your pocket to reach the 3-unit Step 2 stake. Losing at Step 2 therefore costs −2u net (wiping out the Step 1 win plus 1 pocket unit). If Step 2 wins, however, you pull 2 units off the felt so that losing at Step 3 (2u stake) still leaves you ahead +2u for the cycle.
Rank #4: D'Alembert System (Linear Negative Progression)
How it works: Named after 18th-century French mathematician Jean le Rond d'Alembert, this progression adds +1 unit to your wager after every loss and subtracts −1 unit after every win (never dropping below a 1-unit floor): 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
Why it ranks #4 for survival: Among negative progressions, D'Alembert is the slowest to escalate because it grows arithmetically (+1u per loss) rather than exponentially. Across 10 consecutive losses, the cumulative drawdown is 1+2+3+4+5+6+7+8+9+10 = 55 units, which a 100-unit bankroll can survive. Its flaw appears when a shoe chops back and forth after a losing run: if you climb to 8 units and then alternate L – W – L – W – L – W, your stake oscillates between 8u and 9u for dozens of coups, multiplying your average bet size by 8× and bleeding heavy 5% Banker commissions on every winning hand.
Rank #5: Fibonacci System (Golden-Ratio Negative Progression)
How it works: You step one number right along 1 – 1 – 2 – 3 – 5 – 8 – 13 – 21 – 34 – 55 after every loss and step two numbers left after every win.
Why it ranks #5 for survival: As we prove in our deep dive into the Fibonacci betting system in baccarat, the sequence starts gently (1, 1, 2, 3, 5) before its φ ≈ 1.618× exponential growth curve accelerates. By Loss #9, cumulative losses hit 88 units inside a 100-unit bankroll, leaving only 12 units—far short of the 55-unit wager required on Hand 10. Even when the sequence steps back cleanly, the 5% Banker commission leaves a residual deficit on every two-step retreat.
Rank #6: Labouchere / Split-Martingale (Cancellation System)
How it works: You write down a target line of units—for instance, 1 – 2 – 3 – 4 (totalling 10 units). Every wager equals the sum of the first and last numbers on your line (initially 1 + 4 = 5u). When you win, you cross off both outside numbers. When you lose, you append the lost stake to the right end of the line (turning 1 – 2 – 3 – 4 into 1 – 2 – 3 – 4 – 5, making the next wager 1 + 5 = 6u).
Why it ranks #6 for survival: Because each win crosses off two numbers while each loss adds one number, you only need to win more than one-third of your hands to shorten the line. However, starting with a 1 – 2 – 3 – 4 line means your very first wager is already 5 units, and 10 consecutive losses (5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14) consume 95 units of a 100-unit bankroll—leaving only 5 units against a required 15-unit wager on Hand 11.
Rank #7: Martingale System (2.0× Geometric Doubling)
How it works: You double your wager after every lost hand (1, 2, 4, 8, 16, 32, 64, 128, 256, 512) and reset to 1 unit after any win.
Why it ranks #7 (last) for survival: As shown in our mathematical audit of Martingale in baccarat, geometric doubling is the fastest path to bankroll exhaustion or the casino's maximum bet placard. After just seven consecutive losses, a Martingale bettor has lost 1+2+4+8+16+32+64 = 127 units (busting a 100-unit bankroll on Hand 7) and faces a 128-unit wager to chasing a single 1-unit net gain (or even less after 5% Banker commission eats into every prior step).
Worked 18-hand stress test on BBPPBPBPBBPPBBPPBT
To see how these seven systems behave when a real baccarat shoe shifts regimes mid-shoe, inspect this engine-verified 18-hand sequence (BBPPBPBPBBPPBBPPBT—9 Banker wins, 8 Player wins, and 1 Tie on Hand 18):
BBPPBPBPBBPPBBPPBT
Bead Plate
Big Road
Big Eye Boy
Small Road
Cockroach Pig
How the five scoreboards record this 18-hand shoe
Look at the structure of the five casino roads in the diagram above. On the Big Road and Bead Plate, red circles mark Banker wins and blue circles mark Player wins. On the three derived roads (Big Eye Boy, Small Road, Cockroach Pig), red and blue never mean Banker or Player—red means the Big Road pattern repeated and blue means the pattern broke:
- Columns 1 and 2 (Hands 1–4,
BB PP): Column 1 (Banker) and Column 2 (Player) both reach depth 2. When Hand 4 lands at Column 2, Row 2, Big Eye Boy (lookback 1) starts with Rule 2: looking 1 column back at Column 1 (depth 2), Column 1 has a bead at Row 2 too (Case 2A: both drop deeper) → red (=). - Columns 3 to 6 (Hands 5–8,
B P B P): The shoe shifts from pairs into four single-hand chops. On Hand 5 (Column 3, Row 1), Rule 1 compares Column 2 (2 beads) with Column 1 (2 beads) → same depth → red (=). On Hand 6 (Column 4, Row 1), Rule 1 compares Column 3 (1 bead) with Column 2 (2 beads) → different depth → blue (≠). Then on Hands 7, 8, and 9 (Row 1 of Columns 5, 6, and 7), each finished single-bead column matches the single-bead column before it (`1 vs 1`) → three consecutive red (=) marks! - Columns 7 to 10 (Hands 9–16,
BB PP BB PP): On Hand 10 (Column 7, Row 2), Banker extends to Row 2. Big Eye Boy applies Rule 2 looking 1 column back at Column 6 (depth 1): Column 6 stopped at Row 1, one row above (Case 2B: first drop below the match) → blue (≠). (Recall that Rule 2 also has a third case, Case 2C: whenever a streak continues further down so the reference column stopped more than one row above, both cells are empty above the match and the mark turns red.) Once Columns 7, 8, 9, and 10 all finish at depth 2, Big Eye Boy records six straight red (=) marks from Hand 12 through Hand 17! - Hand 18 (Tie) and Hand 19 Preview: Hand 18 is a Tie, drawing a green slash on Column 11, Row 1 without adding any derived-road mark. On Hand 19, if Banker wins (Row 2 of Column 11), all three derived roads will record Red (matching depths of 2 in Columns 10, 9, and 8); if Player wins (starting Column 12 at Row 1 after Column 11's depth of 1), all three derived roads will record Blue.
What happens to a progression bettor during the regime shift?
Imagine a progression player on BBPPBPBPBBPPBBPPBT who uses the classic “follow the last winner” table habit (wagering that each coup will repeat the winner of the previous decided hand, starting on Hand 2 after observing Hand 1's Banker win). Look at the sequence of wins and losses that habit produces from Hand 2 to Hand 9:
- Hand 2 (
BrepeatsB): Win #1 - Hand 3 (
PbreaksB): Loss #1 - Hand 4 (
PrepeatsP): Win #2 - Hands 5, 6, 7, 8, and 9 (
B – P – B – P – B): Because the shoe alternates winners on five consecutive transitions, following the previous winner loses 5 hands in a row! During those five losses, Flat Betting, Paroli, and 1-3-2-6 lose just5 unitstotal (1u per hand), whereas D'Alembert escalates to a 6-unit stake, Fibonacci climbs to Step 6 (8u stake), Labouchere expands its line to 9 numbers, and Martingale escalates to a 32-unit wager on Hand 10 just to chase a 1-unit cycle reset.
How to choose a staking structure if you play recreationally
If you play baccarat for entertainment, keep three rules from this ranking in mind:
- Flat unit sizing maximizes table time per dollar: Keeping your stake constant at 1 unit avoids multiplying your total action during cold stretches and gives your session bankroll the highest mathematical probability of lasting the evening.
- Positive progressions trade win frequency for occasional spikes: Paroli and 1-3-2-6 protect your core bankroll during losing runs because raised bets only happen after wins, though their higher average stake slightly increases expected cost per 100 hands compared to flat betting.
- Negative progressions concentrate risk into catastrophic tail events: D'Alembert, Fibonacci, Labouchere, and Martingale create the illusion of frequent small wins by stacking massive multi-unit exposure onto the inevitable 6-to-10-hand adverse clusters that appear in ordinary fair shoes.
Explore this shoe live in the Road Decoder
Use the interactive road sandbox right below to deal Hand 19 onto BBPPBPBPBBPPBBPPBT and verify how all three derived roads turn Red on a Banker win or Blue on a Player win, or continue exploring our free Road Decoder, how Baccarat Smart works, free Module 1 interactive preview, and full scoreboard mastery course.