The 1-3-2-6 Betting System: Does It Beat Baccarat?

The 1-3-2-6 betting system in baccarat is a four-step positive progression designed around a single structural goal: after two consecutive winning hands, the player pulls enough chips off the felt to lock in a net gain on the cycle even if the third hand loses. Instead of doubling indefinitely or chasing deficits after a loss, you advance through four predetermined unit multiples—1 unit, 3 units, 2 units, and 6 units—only while winning, and reset immediately to 1 unit after any loss or after completing Step 4.

Because it caps exposure and banks chips mid-sequence, the 1-3-2-6 progression is often marketed alongside Paroli and Martingale progressions as a disciplined way to ride streaks on the baccarat scoreboards. Below, we walk through all four stages of the sequence, compute the exact probability tree and expected value for both Player (1:1) and Banker (0.95:1 after 5% commission) wagers, and trace an 18-hand shoe (BBBBPPBBBBPPBPBBPT) you can inspect hand by hand in our free Baccarat Calculator & Road Decoder.

How the 4-step 1-3-2-6 progression works in baccarat

Before starting a 1-3-2-6 sequence, you define a fixed base unit (for example, $10 or $25) that stays constant for the entire session. Every cycle begins at Step 1 with a single base unit. You only move forward when your chosen side wins; the moment a hand loses, the cycle ends and the next hand restarts at Step 1.

To see how chips move between your stack and the betting circle, look at each step on an even-money (1:1) payout first, followed by the exact adjustment required when paying the standard 5% commission on winning Banker hands:

• Step 1 — Stake 1 unit: If the hand loses, the cycle ends at −1 unit and you wager 1 unit again on the next hand. If the hand wins at 1:1, you now hold 2 units on the felt (your 1-unit stake plus 1 unit of winnings). To prepare for Step 2, you add 1 additional unit from your stack so the next wager totals 3 units.
• Step 2 — Stake 3 units: This is the highest out-of-pocket exposure of the entire cycle because 2 units of your own starting bankroll are now at risk (1 unit from Step 1 plus the 1 extra unit added for Step 2). If Step 2 loses, the cycle finishes at −2 units net and resets to Step 1. If Step 2 wins at 1:1, there are now 6 units on the table (representing a +4-unit cumulative gain across Steps 1 and 2). You pull 4 units back into your stack and leave 2 units in the betting circle for Step 3.
• Step 3 — Stake 2 units: Because you already locked 4 units into your stack after Step 2, Step 3 is played entirely with chips won earlier in the cycle. If Step 3 loses, you still walk away from the cycle with a +2-unit net gain (+4 units from Steps 1–2 minus the 2-unit loss on Step 3) and reset to Step 1. If Step 3 wins at 1:1, the 2-unit stake becomes 4 units on the felt, and you add 2 of your previously banked units to place a 6-unit wager for Step 4.
• Step 4 — Stake 6 units: After three consecutive wins (+1, +3, and +2 units), your cumulative gain entering Step 4 is exactly +6 units, and all 6 of those won units are staked on the fourth hand. If Step 4 loses on an even-money wager, the 6-unit loss cancels the 6 units won across Steps 1–3, ending the cycle at 0 units (break-even). If Step 4 wins, you collect +12 units net (+1 + 3 + 2 + 6) and immediately reset to Step 1 on the next hand.

What happens when a hand ends in a Tie?

In standard 8-deck baccarat, 9.5156% of all hands end in a Tie (roughly 1 in every 10.5 coups). Unless you placed a separate Tie bet, a Tie hand is a push on both Banker and Player: your chips are neither won nor lost. In a 1-3-2-6 progression, a Tie simply pauses the sequence at its current step—if you were on Step 3 with 2 units in the circle, those 2 units stay in place for the next hand. This mirrors how the Big Road handles a Tie, marking a green diagonal slash on the most recent circle without advancing the column or adding an entry to any derived road.

Probability tree and expected value of one 1-3-2-6 cycle

Every finite progression is a branching tree of resolved (non-tie) coups. Once Ties are pushed and replayed, an 8-deck baccarat shoe has two conditional non-tie probabilities:

• Resolved Player win probability: 44.6247% / (45.8597% + 44.6247%) = 49.3175% (with 50.6825% probability of losing to Banker), paying 1:1.
• Resolved Banker win probability: 45.8597% / (45.8597% + 44.6247%) = 50.6825% (with 49.3175% probability of losing to Player), paying 0.95:1 after the 5% house commission.

A single 1-3-2-6 cycle has exactly five possible endings: losing immediately on Step 1, losing on Step 2 after one win, losing on Step 3 after two wins, losing on Step 4 after three wins, or winning all four steps in a row. Multiplying the probability of each branch by its net unit outcome reveals the exact distribution of the system:

3 mathematical lessons hidden inside this table

1. 75.68% of Player cycles (and 80.73% of Banker cycles) lose chips: Because both Branch 1 (L) and Branch 2 (WL) end in the red (75.68% on Player and 74.31% on Banker)—and Banker's Branch 4 (WWWL, 6.42%) also finishes at −0.30 units after the 5% commission—more than three out of every four cycles reduce your bankroll. You only finish a cycle ahead when you win at least two hands in a row and then either stop on Step 3 (WWL, ~12.3%–12.7%) or sweep all four hands (WWWW, ~5.9%–6.6%).
2. The 5% Banker commission breaks the Step 4 break-even promise: On an even-money Player bet, winning Steps 1, 2, and 3 yields +1u + 3u + 2u = +6.00u, so losing the 6-unit Step 4 wager leaves you at 0.00u. On Banker, however, the 5% commission shaves 0.05u off Step 1, 0.15u off Step 2, and 0.10u off Step 3—leaving you with only +5.70u after three wins. If you stake 6 full units on Step 4 and lose, the cycle finishes at −0.30 units instead of breaking even.
3. Expected loss equals total action multiplied by the house edge: Across an average Player cycle, you put 3.6857 units into action across resolved hands, and your expected loss of −0.050305 units is −0.050305 / 3.6857 = −1.3649% per non-tie unit staked (which equals the standard −1.2351% Player house edge when the 9.5156% Tie push rate is included). On Banker, −0.044595 / 3.8153 = −1.1688% per non-tie unit staked (the exact −1.0579% Banker house edge across all hands). Changing bet sizes from 1 to 3 to 2 to 6 simply scales your average wager by ~3.7x to 3.8x per cycle.

Worked 18-hand shoe walkthrough: BBBBPPBBBBPPBPBBPT

To see how a 1-3-2-6 progression interacts with real scoreboard geometry, examine this engine-verified 18-hand sequence (BBBBPPBBBBPPBPBBPT—11 Banker wins, 6 Player wins, and 1 Tie at the end):

BBBBPPBBBBPPBPBBPT

Tracing the Big Road and derived roads alongside the 4-step cycle

Remember the core rule of baccarat scoreboards: on the Bead Plate and Big Road, red circles represent Banker wins and blue circles represent Player wins. On the three derived roads (Big Eye Boy, Small Road, and Cockroach Pig), red and blue have nothing to do with Banker or Player—red means a pattern repeated and blue means a pattern broke. Here is how the 18 hands of BBBBPPBBBBPPBPBBPT unfold across the boards and the 1-3-2-6 progression:

1. Hands 1–4 (Column 1: BBBB, depth 4): Banker opens the shoe with four consecutive wins, filling Column 1 of the Big Road down to Row 4. A player backing Banker completes all four steps of a 1-3-2-6 cycle (1u → 3u → 2u → 6u) right out of the gate. Notice that all three derived roads remain completely blank during Hands 1–4 because Big Eye Boy cannot record its first entry until the hand after Column 2, Row 1.
2. Hands 5–6 (Column 2: PP, depth 2 — The Step 2 Cliff): Hand 5 switches to Player, starting Column 2 at Row 1. On Hand 6, Player wins a second time (Column 2, Row 2). Because Column 2 is moving downward, Rule 2 fires on Big Eye Boy (lookback 1): this bead is at Row 2, and Column 1 has a bead at Row 2 too → red (=) (Mark #1). Meanwhile, anyone who started a 1-3-2-6 cycle on Player at Hand 5 won Step 1 (+1u) and Step 2 (+3u), advancing to Step 3 for Hand 7.
3. Hands 7–10 (Column 3: BBBB, depth 4 — All 3 Cases of Rule 2): Hand 7 flips back to Banker at Column 3, Row 1 (winning +2u net for the Player progression that stopped at Step 3, or completing a new 4-hand Banker sweep through Hand 10). Watch how Big Eye Boy evaluates all four beads of Column 3 against Column 2 (which has 2 beads):
   • Hand 7 (Column 3, Row 1 · Rule 1): Column 2 has 2 beads and Column 1 has 4 beads. Different depth → blue (≠) (Mark #2).
   • Hand 8 (Column 3, Row 2 · Rule 2, Case 2A): This bead is at Row 2. Column 2 has a bead at Row 2 too → red (=) (Mark #3).
   • Hand 9 (Column 3, Row 3 · Rule 2, Case 2B): This bead is at Row 3. Column 2 stopped at Row 2, one row above → blue (≠) (Mark #4).
   • Hand 10 (Column 3, Row 4 · Rule 2, Case 2C): This bead is at Row 4. Column 2 stopped at Row 2, more than one row above → red (=) (Mark #5).
4. Hands 11–12 (Column 4: PP, depth 2 — Small Road Symmetry): Player wins twice in Column 4. Because the first four Big Road columns formed a repeating 4, 2, 4, 2 depth rhythm—where each column matched the depth of the column two steps to its left—Small Road (lookback 2) recorded six consecutive red (=) entries through Column 5, Row 1 (Marks #1–#6). Yet a 1-3-2-6 player backing Player on Column 4 only reached Step 2 before Banker cut the streak off on Hand 13.
5. Hands 13–18 (Columns 5–8: B, P, BB, PT — Chop and Step 2 Traps): Over the final six hands, no column exceeds depth 2: Column 5 has 1 bead (B), Column 6 has 1 bead (P), Column 7 has 2 beads (BB), and Column 8 has 1 bead plus a Tie slash (PT). Every 1-3-2-6 cycle started during this stretch either loses 1 unit on Step 1 (when a column stops at 1 bead) or loses 2 units on Step 2 (when Column 7 stops at 2 beads and loses the 3-unit press on Hand 17). On Hand 18, the Tie places a green slash on Column 8, Row 1 and leaves all three derived roads unchanged.

Check your understanding: what happens on Hand 19?

Before tapping the interactive sandbox at the bottom of this page, trace what Hand 19 will record on the three derived roads:

• If Hand 19 is Banker (starts Column 9 at Row 1 · Rule 1): Every derived road compares Column 8 (which finished with 1 bead) against its lookback column. Big Eye Boy compares Column 8 (1 bead) with Column 7 (2 beads): different depth → blue (≠). Small Road compares Column 8 (1 bead) with Column 6 (1 bead): same depth → red (=). Cockroach Pig compares Column 8 (1 bead) with Column 5 (1 bead): same depth → red (=).
• If Hand 19 is Player (moves down Column 8 to Row 2 · Rule 2): Every derived road inspects Row 2 of its lookback column. Big Eye Boy looks 1 column back at Column 7 (2 beads): Column 7 has a bead at Row 2 too → red (=). Small Road looks 2 columns back at Column 6 (1 bead): Column 6 stopped at Row 1, one row above → blue (≠). Cockroach Pig looks 3 columns back at Column 5 (1 bead): Column 5 stopped at Row 1, one row above → blue (≠).

Where the 1-3-2-6 progression bleeds bankroll in real shoes

When players test the 1-3-2-6 progression over a short session, the root cause of drawdowns is almost never a long losing streak—in fact, a string of consecutive single losses only costs 1 unit per hand, identical to flat betting. Instead, the system is vulnerable to two-hand chop sequences (Big Road columns of depth 1 or depth 2):

• The Step 2 vulnerability (WL): Whenever your chosen side wins once and immediately loses on the next hand, Step 1 wins +1.00u (or +0.95u on Banker) and Step 2 loses −3.00u, resulting in a −2.00u (or −2.05u) net drop across two coups—even though you won 50% of the hands played! Because WL occurs on 24.995% of all cycles, one out of every four cycles costs double your base unit.
• How 1-3-2-6 compares with other classic progressions: Compared with a 3-step Paroli (1-2-4), the 1-3-2-6 system requires four consecutive wins instead of three to hit its top payout, and risks an extra unit out of pocket on Step 2, in exchange for turning a Step 3 loss into a +2u gain. Compared with Martingale negative doubling, 1-3-2-6 never threatens your stack with exponential table-limit wipeouts—yet as shown in our house-edge mathematics guide and baccarat strategy breakdown, neither system alters the negative expectation attached to every wager.

Test this shoe in the free Road Decoder & interactive course

Use the interactive road sandbox directly below to deal additional Banker, Player, and Tie hands onto BBBBPPBBBBPPBPBBPT, or open the full eight-road board in our free Baccarat Calculator. To master third-card rules, Big Road geometry, and all three derived roads without risking a cent, explore how Baccarat Smart works, try our free interactive lesson preview, or browse the complete Baccarat Smart curriculum.