Evaluating D'Alembert vs Flat Betting in scenario S199-0 (72 hands, 60u stack, 50u table limit) documents how 7 tie stalls (9.52%) and a 2-coup run shape eight-deck envelope, yielding 15.34% vs 5.84% ruin. Because every 8-deck coup is statistically independent under 5% Banker Commission (0.95:1) (1.0579% edge), progression rules alter drawdown speed and table-cap collisions without changing per-hand expectation.
Reference 8-deck shoe for Stress Cell S199 (D'Alembert vs Flat Betting, Single-Alternating Chop under 5% Banker Commission). 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 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.
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 S199 compares +1 on loss / -1 on win against 1-1-1-1 constant unit over 72 hands.
Probability of exhausting the 60-unit bankroll under a 50-unit house bet limit.
Theoretical erosion under 5% Banker Commission (0.95:1) (1.0579% house edge) across 72 coups.
Deepest unit trough triggered by a 2-hand run inside the chop shoe profile.
Reflects 9.52% tie frequency (7 pushes) and 0.73u in vigorish friction.
Stress test S199-1 audits D'Alembert Pyramid (+1 on loss / -1 on win) against Flat 1-Unit Baseline (1-1-1-1 constant unit) inside a 60-unit bankroll over 72 hands (5% Comm Chop, chop), where a 50-unit table ceiling produces 15.34% vs 5.84% ruin rates and charts 0.73u in table-capped vigorish drag.
Evaluating D'Alembert vs Flat Betting in scenario S199-2 (72 hands, 60u stack, 50u table limit) profiles how 7 tie stalls (9.52%) and a 2-coup run shape step-indexed trajectory, yielding 15.34% vs 5.84% ruin.
| S199 absorption-curve | D'Alembert | Flat Betting |
|---|---|---|
| D'Alembert / Flat Betting Rule | +1 on loss / -1 on win | 1-1-1-1 constant unit |
| 72-Hand Ruin (60u) | 15.34% | 5.84% |
| 5% Comm Chop Hold (1.0579%) | 1.53u | 0.79u |
| 2-Run Trough (50u Cap) | -18u | -12u |
Stress test S199-3 verifies D'Alembert Pyramid (+1 on loss / -1 on win) against Flat 1-Unit Baseline (1-1-1-1 constant unit) inside a 60-unit bankroll over 72 hands (5% Comm Chop, chop), where a 50-unit table ceiling produces 15.34% vs 5.84% ruin rates and calibrates 0.73u in non-stationary vigorish drag.
Evaluating D'Alembert vs Flat Betting in scenario S199-4 (72 hands, 60u stack, 50u table limit) benchmarks how 7 tie stalls (9.52%) and a 2-coup run shape variance-scaled cycle-span, yielding 15.34% vs 5.84% ruin.
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About 64 minutes of lessons covering outcomes, the Bead Plate, Big Road columns, and dragon tails.
Train Third-Card Rule decisions, depth counting, lookback column references, and derived-road speed recognition.
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Macau Cantonese, French, and mathematical table terms explained in plain English with road diagrams.
Direct answers to real student questions on dragon tails, tie handling, lookback rules, and table variants.
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Plain-English answers on independent trials, progression variance, and scoreboard reading.
Practical bankroll boundaries, stop-loss discipline, and 18+/21+ support resources.
Verify 8-deck combinatorial probabilities, Banker/Player house edge, and commission rules.
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Step-by-step lookback rules for Big Eye Boy (1), Small Road (2), and Cockroach Pig (3).