Within discrete-time horizon M286-0, a 75-unit treasury backing D'Alembert Pyramid for 72 hands (1 shoes) faces a 40-unit bet cap that computes 11.64% ruin exposure, 42.41% target attainment at +19u, and 45.96% time-limit expiration. Every 8-deck hand remains statistically independent (45.86% Banker, 44.62% Player, 9.52% Tie), meaning progression sizing reshapes session variance without altering the house edge.
Reference 8-deck shoe for Matrix Cell M286 (D'Alembert Pyramid, 75u bankroll, 72 hands). Big Road and Bead Plate show Banker (red) and Player (blue); derived roads record structural 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.
Matrix cell M286 tests D'Alembert Pyramid with a $25 base unit and -38u/+19u absorbing boundaries.
Probability of hitting the -38u drawdown barrier before completing 72 hands or reaching +19u.
Share of 72-hand trajectories reaching the +19u session ceiling, with 45.96% ending between barriers.
A 40-unit house limit and 75-unit stack cap D'Alembert escalation after 6 adverse coups.
Derived from 114u total action (1.58x average wager) multiplied by the 1.0579% 8-deck Banker edge.
Horizon matrix M286-1 inspects how D'Alembert (+1 on loss / -1 on win) behaves inside a 75-unit session budget across 72 coups, showing that a 40-unit pit limit and 38-unit floor generate a 11.64% drawdown-trigger rate alongside 1.46u in expected 8-deck vigorish.
Within asymmetric horizon M286-2, a 75-unit treasury backing D'Alembert Pyramid for 72 hands (1 shoes) faces a 40-unit bet cap that verifies 11.64% ruin exposure, 42.41% target attainment at +19u, and 45.96% time-limit expiration.
| M286 Parameter | D'Alembert (75u) | 1-Shoe survival-window |
|---|---|---|
| D'Alembert Ladder | +1 on loss / -1 on win (10 steps) | Peak 12u multiplier on M286 |
| 75u Stack Window | 72 hands (1 shoes) | Barriers -38u / +19u |
| 40u Ceiling & Ruin | 11.64% ruin vs 42.41% win | Depth 6 steps (2 cap hits) |
| 114u Handle & Hold | 1.46u ($37) | Multiplier 1.58x (sequential drift) |
Horizon matrix M286-3 tabulates how D'Alembert (+1 on loss / -1 on win) behaves inside a 75-unit session budget across 72 coups, showing that a 40-unit pit limit and 38-unit floor generate a 11.64% drawdown-trigger rate alongside 1.46u in expected 8-deck vigorish.
Within non-stationary horizon M286-4, a 75-unit treasury backing D'Alembert Pyramid for 72 hands (1 shoes) faces a 40-unit bet cap that quantifies 11.64% ruin exposure, 42.41% target attainment at +19u, and 45.96% time-limit expiration.
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.
Every reference guide, glossary definition, and road calculator on Baccarat Smart is open for everyone. When you want all 6 modules and 36 lessons (about 5.5 hours of lessons) organized in structured step-by-step order with 74 hands-on boards, 94 quiz checks along the way, and Cloud Shoe Log sync across web, iPhone, and Android, start Module 1 (10 lessons, about 64 minutes of lessons) free or unlock full membership for $25 a month.
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.
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.