Skip to main content
Baccarat Smart
  1. Home
  2. Combinatorial Math & Odds Hub
  3. Labouchere 40u 3-Shoe Matrix
STAGE 2 BANKROLL MATRIX · LABOUCHERE · 40U / 3-SHOE

Labouchere Split-Line — 40-Unit Bankroll & 3-Shoe (216-Hand) Risk-of-Ruin Matrix

For a 40-unit roll spanning 216 hands (3 shoes), Labouchere Split-Line ([1-2-3-2-1] outside sum) inspects a asymmetric absorption-curve under matrix M332-0, where the 60-unit table roof and -20u/+10u barriers yield 84.88% ruin versus 22.31% upside completion. Every 8-deck hand remains statistically independent (45.86% Banker, 44.62% Player, 9.52% Tie), meaning progression sizing reshapes session variance without altering the house edge.

Ruin Rate (-20u Stop)
84.88%
Target Hit (+10u Cap)
22.31%
216-Hand Expected Hold
5.01u
Table Max (6-Step Depth)
60u
Engine-Verified Scoreboard · 18 Hands

Read the Board at Table Speed

Open this shoe in /calculator
Big Road P P B B P P P P B B B B P B P B
Big Eye Boy = = = ≠ = ≠ = = = = = ≠ ≠ =
Small Road = ≠ = ≠ = ≠ = ≠ = ≠ ≠ ≠
Cockroach Pig = ≠ = ≠ = = ≠ ≠

Reference 8-deck shoe for Matrix Cell M332 (Labouchere Split-Line, 40u bankroll, 216 hands). Big Road and Bead Plate show Banker (red) and Player (blue); derived roads record structural symmetry.

Big Road B is Banker, P is Player Roads under it Red (=): repeating Blue (≠): breaking
Step-by-Step Mark Proofs (Rule 1 & Rule 2)
Big Eye Boy Mark #2

Column 2 has 2 beads. Column 1 has 2 beads. Same depth → red (=).

  1. Column 3 starts, so use Rule 1: compare Column 2 with Column 1, 1 column further back.
  2. Column 2 has 2 beads. Column 1 has 2 beads. Same depth → red (=).

Common table reading watchout: Comparing the wrong columns. Compare Column 2, the one that just finished, with Column 1.

Small Road Mark #2

This bead is at Row 3. Column 1 stopped at Row 2, one row above → blue (≠).

  1. Column 3 goes down to Row 3, so use Rule 2: look 2 columns back, at Column 1.
  2. Column 1 stopped at Row 2, one row above → blue (≠).

Common table reading watchout: Thinking "no bead at this row" means blue. It is blue only when Column 1 stopped exactly one row above this bead.

Cockroach Pig Mark #2

This bead is at Row 3. Column 1 stopped at Row 2, one row above → blue (≠).

  1. Column 4 goes down to Row 3, so use Rule 2: look 3 columns back, at Column 1.
  2. Column 1 stopped at Row 2, one row above → blue (≠).

Common table reading watchout: Thinking "no bead at this row" means blue. It is blue only when Column 1 stopped exactly one row above this bead.

Verified Reference Data

Key Facts & Table Specifications

Session Bankroll & Horizon
40u / 3 Shoes (216 Hands)

Matrix cell M332 tests Labouchere Split-Line with a $50 base unit and -20u/+10u absorbing boundaries.

Stop-Loss Ruin Probability
84.88%

Probability of hitting the -20u drawdown barrier before completing 216 hands or reaching +10u.

Stop-Win Target Completion
22.31%

Share of 216-hand trajectories reaching the +10u session ceiling, with 0.50% ending between barriers.

Table Limit Survival Depth
6 Steps (60u Cap)

A 60-unit house limit and 40-unit stack cap Labouchere escalation after 6 adverse coups.

Expected Session House Hold
5.01u ($251)

Derived from 356u total action (1.65x average wager) multiplied by the 1.0579% 8-deck Banker edge.

MATRIX CELL M332 · STOP-LOSS & STOP-WIN GEOMETRY

Labouchere 40u non-stationary survival-window Across 216 Hands (M332)

Combinatorial ledger M332-1 verifies Labouchere ([1-2-3-2-1] outside sum) at 40 units and 216 hands (3 shoes), proving that a 60-unit table ceiling and 1.65x average bet multiplier yield 84.88% ruin probability and 5.01u in theoretical house hold.

For a 40-unit roll spanning 216 hands (3 shoes), Labouchere Split-Line ([1-2-3-2-1] outside sum) tabulates a non-stationary stake-velocity under matrix M332-2, where the 60-unit table roof and -20u/+10u barriers yield 84.88% ruin versus 22.31% upside completion.

M332 ParameterLabouchere (40u)3-Shoe survival-window
Labouchere Ladder[1-2-3-2-1] outside sum (9 steps)Peak 18u multiplier on M332
40u Stack Window216 hands (3 shoes)Barriers -20u / +10u
60u Ceiling & Ruin84.88% ruin vs 22.31% winDepth 6 steps (5 cap hits)
356u Handle & Hold5.01u ($251)Multiplier 1.65x (non-stationary drift)
STEP ESCALATION & TURNOVER AUDIT

60u Ceiling Collisions & Labouchere Turnover (3 Shoes)

Combinatorial ledger M332-3 quantifies Labouchere ([1-2-3-2-1] outside sum) at 40 units and 216 hands (3 shoes), proving that a 60-unit table ceiling and 1.65x average bet multiplier yield 84.88% ruin probability and 5.01u in theoretical house hold.

For a 40-unit roll spanning 216 hands (3 shoes), Labouchere Split-Line ([1-2-3-2-1] outside sum) charts a house-edge-anchored drawdown-slope under matrix M332-4, where the 60-unit table roof and -20u/+10u barriers yield 84.88% ruin versus 22.31% upside completion.

  • Cell M332 rule: lock the -20u stop on your 40u Labouchere stack across 216 hands.
  • Matrix M332 verifies 5.01u ($251) in house hold over 356u of Labouchere action.
  • Scoreboard check M332: Big Eye Boy, Small Road, and Cockroach Pig use red for repeating symmetry (non-stationary survival-window) and blue for pattern breaks—never for Banker or Player.
Table Reality Check

Myth vs. Truth

MythBringing 40 units to a 3-shoe session lets Labouchere Split-Line overcome the 1.058% Banker house edge.
TruthNo bankroll size alters per-hand expectation: over 216 hands, Labouchere generates 356u in action, 5.01u in expected loss, and a 84.88% stop-loss ruin rate.
MythDerived road colors on the scoreboard tell Labouchere bettors whether Banker (red) or Player (blue) is due during a 216-hand run.
TruthOn Big Eye Boy, Small Road, and Cockroach Pig, red indicates repeating column structure and blue indicates breaking structure; neither color represents Banker or Player.
6 modules · 36 lessons · $25/month · Module 1 (10 lessons) free

Read Every Derived Road at Table Speed

Every reference guide, glossary definition, and road calculator on Baccarat Smart is open for everyone. When you want all 6 modules and 36 lessons (about 5.5 hours of lessons) organized in structured step-by-step order with 74 hands-on boards, 94 quiz checks along the way, and Cloud Shoe Log sync across web, iPhone, and Android, start Module 1 (10 lessons, about 64 minutes of lessons) free or unlock full membership for $25 a month.

  • Structured step-by-step track across Foundations, Big Eye Boy, Small Road, and Cockroach Pig
  • 74 interactive lesson scoreboards and 94 inline quiz checks with plain-English mark feedback
  • Cloud Shoe Log and cross-device progress on web, iOS, and Android