In head-to-head trial S201-0 across 78 deals (5% Comm High-Tie, 1.0579% edge), D'Alembert records a -26u peak excursion and 14.40% ruin probability on a 75-unit stack, whereas Flat Betting logs a -12u trough and 5.52% ruin under the 50-unit limit. 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 S201 (D'Alembert vs Flat Betting, 16% High-Tie Cluster Shoe 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.
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.
Stress cell S201 compares +1 on loss / -1 on win against 1-1-1-1 constant unit over 78 hands.
Probability of exhausting the 75-unit bankroll under a 50-unit house bet limit.
Theoretical erosion under 5% Banker Commission (0.95:1) (1.0579% house edge) across 78 coups.
Deepest unit trough triggered by a 4-hand run inside the high-tie shoe profile.
Reflects 16.67% tie frequency (13 pushes) and 0.80u in vigorish friction.
Within finite-shoe testbed S201-1, a 75-unit bankroll facing 78 coups of 5% Comm High-Tie (high-tie) and a 50-unit maximum wager computes 14.40% ruin (1.66u expected loss) on D'Alembert Pyramid versus 5.52% ruin (0.86u expected loss) on Flat 1-Unit Baseline.
In head-to-head trial S201-2 across 78 deals (5% Comm High-Tie, 1.0579% edge), D'Alembert records a -26u peak turnover and 14.40% ruin probability on a 75-unit stack, whereas Flat Betting logs a -12u trough and 5.52% ruin under the 50-unit limit.
| S201 threshold | D'Alembert | Flat Betting |
|---|---|---|
| D'Alembert / Flat Betting Rule | +1 on loss / -1 on win | 1-1-1-1 constant unit |
| 78-Hand Ruin (75u) | 14.40% | 5.52% |
| 5% Comm High-Tie Hold (1.0579%) | 1.66u | 0.86u |
| 4-Run Trough (50u Cap) | -26u | -12u |
Within multi-coup testbed S201-3, a 75-unit bankroll facing 78 coups of 5% Comm High-Tie (high-tie) and a 50-unit maximum wager evaluates 14.40% ruin (1.66u expected loss) on D'Alembert Pyramid versus 5.52% ruin (0.86u expected loss) on Flat 1-Unit Baseline.
In head-to-head trial S201-4 across 78 deals (5% Comm High-Tie, 1.0579% edge), D'Alembert records a -26u peak decay-rate and 14.40% ruin probability on a 75-unit stack, whereas Flat Betting logs a -12u trough and 5.52% ruin under the 50-unit limit.
Enter any sequence to inspect the Big Road, Big Eye Boy, Small Road, Cockroach Pig, and next-hand previews.
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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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.
Step-by-step lookback rules for Big Eye Boy (1), Small Road (2), and Cockroach Pig (3).
Definitions for progression ladders, absorbing barriers, commission formats, and shoe terms.
Plain-English answers on independent trials, progression variance, and scoreboard reading.