In multi-coup comparative trial S238-0, running Labouchere against Flat Betting for 210 hands of Player High-Tie (high-tie) on 130 units dissects 8.21u vs 2.70u in expected toll and 31.99% vs 8.79% ruin under a 85-unit pit limit. Because every 8-deck coup is statistically independent under Even-Money Player Side (1.235% edge) (1.2351% edge), progression rules alter drawdown speed and table-cap collisions without changing per-hand expectation.
Reference 8-deck shoe for Stress Cell S238 (Labouchere vs Flat Betting, Three-Shoe 15% Tie Density on Even-Money Player Wagers). Big Road shows Banker (red) and Player (blue); derived roads track symmetry.
This bead is at Row 3. 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.
This bead is at Row 3. 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.
Column 4 has 2 beads. Column 1 has 2 beads. Same depth → red (=).
Common table reading watchout: Comparing the wrong columns. Compare Column 4, the one that just finished, with Column 1.
Stress cell S238 compares [1-2-3-2-1] outside sum against 1-1-1-1 constant unit over 210 hands.
Probability of exhausting the 130-unit bankroll under a 85-unit house bet limit.
Theoretical erosion under Even-Money Player Side (1.235% edge) (1.2351% house edge) across 210 coups.
Deepest unit trough triggered by a 4-hand run inside the high-tie shoe profile.
Reflects 15.24% tie frequency (32 pushes) and 3.94u in vigorish friction.
Under Player High-Tie (1.2351% effective edge), discrete-time stress run S238-1 over 210 hands and a 130-unit treasury quantifies a -32u drawdown (31.99% ruin) for Labouchere Split-Line against -14u (8.79% ruin) for Flat 1-Unit Baseline inside a 85-unit cap.
In drawdown-weighted comparative trial S238-2, running Labouchere against Flat Betting for 210 hands of Player High-Tie (high-tie) on 130 units computes 8.21u vs 2.70u in expected toll and 31.99% vs 8.79% ruin under a 85-unit pit limit.
| S238 progression-curve | Labouchere | Flat Betting |
|---|---|---|
| Labouchere / Flat Betting Rule | [1-2-3-2-1] outside sum | 1-1-1-1 constant unit |
| 210-Hand Ruin (130u) | 31.99% | 8.79% |
| Player High-Tie Hold (1.2351%) | 8.21u | 2.70u |
| 4-Run Trough (85u Cap) | -32u | -14u |
Under Player High-Tie (1.2351% effective edge), capital-bounded stress run S238-3 over 210 hands and a 130-unit treasury maps a -32u drawdown (31.99% ruin) for Labouchere Split-Line against -14u (8.79% ruin) for Flat 1-Unit Baseline inside a 85-unit cap.
In sequential comparative trial S238-4, running Labouchere against Flat Betting for 210 hands of Player High-Tie (high-tie) on 130 units evaluates 8.21u vs 2.70u in expected toll and 31.99% vs 8.79% ruin under a 85-unit pit limit.
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