Benchmark S210-0 audits the multi-coup capital-runway between D'Alembert and Flat Betting over 210 hands of Player High-Tie: with 130 units, a 85-unit cap, and 1.2351% house edge, ruin settles at 22.20% vs 8.79% while step-indexed decay-rate reaches -23u. 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 S210 (D'Alembert 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 S210 compares +1 on loss / -1 on win 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 2.50u in vigorish friction.
When Player High-Tie (high-tie) injects a 4-hand extreme run and 32 tie pushes (15.24% Tie density) over 210 coups, discrete-time audit S210-1 profiles D'Alembert Pyramid at 5.21u expected erosion (22.20% ruin) compared with 2.70u (8.79% ruin) for Flat 1-Unit Baseline on 130 units.
Benchmark S210-2 verifies the drawdown-weighted absorption-curve between D'Alembert and Flat Betting over 210 hands of Player High-Tie: with 130 units, a 85-unit cap, and 1.2351% house edge, ruin settles at 22.20% vs 8.79% while absorbing-barrier distribution reaches -23u.
| S210 decay-rate | D'Alembert | Flat Betting |
|---|---|---|
| D'Alembert / Flat Betting Rule | +1 on loss / -1 on win | 1-1-1-1 constant unit |
| 210-Hand Ruin (130u) | 22.20% | 8.79% |
| Player High-Tie Hold (1.2351%) | 5.21u | 2.70u |
| 4-Run Trough (85u Cap) | -23u | -16u |
When Player High-Tie (high-tie) injects a 4-hand extreme run and 32 tie pushes (15.24% Tie density) over 210 coups, capital-bounded audit S210-3 benchmarks D'Alembert Pyramid at 5.21u expected erosion (22.20% ruin) compared with 2.70u (8.79% ruin) for Flat 1-Unit Baseline on 130 units.
Benchmark S210-4 tracks the sequential stake-velocity between D'Alembert and Flat Betting over 210 hands of Player High-Tie: with 130 units, a 85-unit cap, and 1.2351% house edge, ruin settles at 22.20% vs 8.79% while capital-bounded survival-window reaches -23u.
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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.
Visual step-by-step breakdowns with closed captions, chapter markers, and full searchable transcripts.
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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Definitions for progression ladders, absorbing barriers, commission formats, and shoe terms.
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.
Inspect Big Road, Bead Plate, Big Eye Boy, Small Road, and Cockroach Pig marks interactively.