In sequential comparative trial S231-0, running Labouchere against Flat Betting for 74 hands of No-Comm Streak (streak) on 90 units evaluates 3.41u vs 1.12u in expected toll and 13.40% vs 4.92% ruin under a 65-unit pit limit. Because every 8-deck coup is statistically independent under No-Commission Banker 6 (0.50:1 on 6) (1.4579% edge), progression rules alter drawdown speed and table-cap collisions without changing per-hand expectation.
Reference 8-deck shoe for Stress Cell S231 (Labouchere vs Flat Betting, 11-Hand Banker Run under No-Commission Banker 6 Half-Pay). Big Road shows Banker (red) and Player (blue); derived roads track symmetry.
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.
Column 3 has 2 beads. Column 1 has 2 beads. Same depth → red (=).
Common table reading watchout: Comparing the wrong columns. Compare Column 3, the one that just finished, with Column 1.
Column 5 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).
Common table reading watchout: Comparing the wrong columns. Compare Column 5, the one that just finished, with Column 2.
Stress cell S231 compares [1-2-3-2-1] outside sum against 1-1-1-1 constant unit over 74 hands.
Probability of exhausting the 90-unit bankroll under a 65-unit house bet limit.
Theoretical erosion under No-Commission Banker 6 (0.50:1 on 6) (1.4579% house edge) across 74 coups.
Deepest unit trough triggered by a 11-hand run inside the streak shoe profile.
Reflects 8.11% tie frequency (6 pushes) and 2.11u in vigorish friction.
Under No-Comm Streak (1.4579% effective edge), bankroll-constrained stress run S231-1 over 74 hands and a 90-unit treasury charts a -58u drawdown (13.40% ruin) for Labouchere Split-Line against -20u (4.92% ruin) for Flat 1-Unit Baseline inside a 65-unit cap.
In stochastic comparative trial S231-2, running Labouchere against Flat Betting for 74 hands of No-Comm Streak (streak) on 90 units inspects 3.41u vs 1.12u in expected toll and 13.40% vs 4.92% ruin under a 65-unit pit limit.
| S231 boundary | Labouchere | Flat Betting |
|---|---|---|
| Labouchere / Flat Betting Rule | [1-2-3-2-1] outside sum | 1-1-1-1 constant unit |
| 74-Hand Ruin (90u) | 13.40% | 4.92% |
| No-Comm Streak Hold (1.4579%) | 3.41u | 1.12u |
| 11-Run Trough (65u Cap) | -58u | -20u |
Under No-Comm Streak (1.4579% effective edge), absorbing-barrier stress run S231-3 over 74 hands and a 90-unit treasury documents a -58u drawdown (13.40% ruin) for Labouchere Split-Line against -20u (4.92% ruin) for Flat 1-Unit Baseline inside a 65-unit cap.
In house-edge-anchored comparative trial S231-4, running Labouchere against Flat Betting for 74 hands of No-Comm Streak (streak) on 90 units audits 3.41u vs 1.12u in expected toll and 13.40% vs 4.92% ruin under a 65-unit pit limit.
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Verify 8-deck combinatorial probabilities, Banker/Player house edge, and commission rules.
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Plain-English answers on independent trials, progression variance, and scoreboard reading.