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STAGE 2 BANKROLL MATRIX · LABOUCHERE · 75U / 1-SHOE

Labouchere Split-Line — 75-Unit Bankroll & 1-Shoe (72-Hand) Risk-of-Ruin Matrix

Within variance-scaled horizon M336-0, a 75-unit treasury backing Labouchere Split-Line for 72 hands (1 shoes) faces a 40-unit bet cap that profiles 16.57% ruin exposure, 41.03% target attainment at +19u, and 42.40% time-limit expiration. 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 (-38u Stop)
16.57%
Target Hit (+19u Cap)
41.03%
72-Hand Expected Hold
2.25u
Table Max (6-Step Depth)
40u
Engine-Verified Scoreboard · 18 Hands

Read the Board at Table Speed

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

Reference 8-deck shoe for Matrix Cell M336 (Labouchere Split-Line, 75u bankroll, 72 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

Column 4 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).

  1. Column 5 starts, so use Rule 1: compare Column 4 with Column 2, 2 columns further back.
  2. Column 4 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).

Common table reading watchout: Comparing the wrong columns. Compare Column 4, the one that just finished, with Column 2.

Cockroach Pig Mark #2

This bead is at Row 2. Column 2 has a bead at Row 2 too → red (=).

  1. Column 5 goes down to Row 2, so use Rule 2: look 3 columns back, at Column 2.
  2. Column 2 has a bead at Row 2 too → red (=).

Common table reading watchout: Thinking "no bead at this row" means blue. It is blue only when Column 2 stopped exactly one row above this bead.

Verified Reference Data

Key Facts & Table Specifications

Session Bankroll & Horizon
75u / 1 Shoes (72 Hands)

Matrix cell M336 tests Labouchere Split-Line with a $25 base unit and -38u/+19u absorbing boundaries.

Stop-Loss Ruin Probability
16.57%

Probability of hitting the -38u drawdown barrier before completing 72 hands or reaching +19u.

Stop-Win Target Completion
41.03%

Share of 72-hand trajectories reaching the +19u session ceiling, with 42.40% ending between barriers.

Table Limit Survival Depth
6 Steps (40u Cap)

A 40-unit house limit and 75-unit stack cap Labouchere escalation after 6 adverse coups.

Expected Session House Hold
2.25u ($56)

Derived from 160u total action (2.22x average wager) multiplied by the 1.0579% 8-deck Banker edge.

MATRIX CELL M336 · STOP-LOSS & STOP-WIN GEOMETRY

Labouchere 75u asymmetric ledger Across 72 Hands (M336)

Horizon matrix M336-1 calibrates how Labouchere ([1-2-3-2-1] outside sum) behaves inside a 75-unit session budget across 72 coups, showing that a 40-unit pit limit and 38-unit floor generate a 16.57% drawdown-trigger rate alongside 2.25u in expected 8-deck vigorish.

Within eight-deck horizon M336-2, a 75-unit treasury backing Labouchere Split-Line for 72 hands (1 shoes) faces a 40-unit bet cap that dissects 16.57% ruin exposure, 41.03% target attainment at +19u, and 42.40% time-limit expiration.

M336 ParameterLabouchere (75u)1-Shoe ledger
Labouchere Ladder[1-2-3-2-1] outside sum (9 steps)Peak 18u multiplier on M336
75u Stack Window72 hands (1 shoes)Barriers -38u / +19u
40u Ceiling & Ruin16.57% ruin vs 41.03% winDepth 6 steps (2 cap hits)
160u Handle & Hold2.25u ($56)Multiplier 2.22x (asymmetric drift)
STEP ESCALATION & TURNOVER AUDIT

40u Ceiling Collisions & Labouchere Turnover (1 Shoes)

Horizon matrix M336-3 evaluates how Labouchere ([1-2-3-2-1] outside sum) behaves inside a 75-unit session budget across 72 coups, showing that a 40-unit pit limit and 38-unit floor generate a 16.57% drawdown-trigger rate alongside 2.25u in expected 8-deck vigorish.

Within bankroll-constrained horizon M336-4, a 75-unit treasury backing Labouchere Split-Line for 72 hands (1 shoes) faces a 40-unit bet cap that audits 16.57% ruin exposure, 41.03% target attainment at +19u, and 42.40% time-limit expiration.

  • Cell M336 rule: lock the -38u stop on your 75u Labouchere stack across 72 hands.
  • Matrix M336 dissects 2.25u ($56) in house hold over 160u of Labouchere action.
  • Scoreboard check M336: Big Eye Boy, Small Road, and Cockroach Pig use red for repeating symmetry (asymmetric ledger) and blue for pattern breaks—never for Banker or Player.
Table Reality Check

Myth vs. Truth

MythBringing 75 units to a 1-shoe session lets Labouchere Split-Line overcome the 1.058% Banker house edge.
TruthNo bankroll size alters per-hand expectation: over 72 hands, Labouchere generates 160u in action, 2.25u in expected loss, and a 16.57% stop-loss ruin rate.
MythDerived road colors on the scoreboard tell Labouchere bettors whether Banker (red) or Player (blue) is due during a 72-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