Within multi-coup horizon M300-0, a 500-unit treasury backing D'Alembert Pyramid for 360 hands (5 shoes) faces a 80-unit bet cap that evaluates 9.00% ruin exposure, 44.79% target attainment at +125u, and 46.21% 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 M300 (D'Alembert Pyramid, 500u bankroll, 360 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 M300 tests D'Alembert Pyramid with a $50 base unit and -250u/+125u absorbing boundaries.
Probability of hitting the -250u drawdown barrier before completing 360 hands or reaching +125u.
Share of 360-hand trajectories reaching the +125u session ceiling, with 46.21% ending between barriers.
A 80-unit house limit and 500-unit stack cap D'Alembert escalation after 7 adverse coups.
Derived from 788u total action (2.19x average wager) multiplied by the 1.0579% 8-deck Banker edge.
Horizon matrix M300-1 audits how D'Alembert (+1 on loss / -1 on win) behaves inside a 500-unit session budget across 360 coups, showing that a 80-unit pit limit and 250-unit floor generate a 9.00% drawdown-trigger rate alongside 10.09u in expected 8-deck vigorish.
Within session-bounded horizon M300-2, a 500-unit treasury backing D'Alembert Pyramid for 360 hands (5 shoes) faces a 80-unit bet cap that tracks 9.00% ruin exposure, 44.79% target attainment at +125u, and 46.21% time-limit expiration.
| M300 Parameter | D'Alembert (500u) | 5-Shoe footprint |
|---|---|---|
| D'Alembert Ladder | +1 on loss / -1 on win (10 steps) | Peak 12u multiplier on M300 |
| 500u Stack Window | 360 hands (5 shoes) | Barriers -250u / +125u |
| 80u Ceiling & Ruin | 9.00% ruin vs 44.79% win | Depth 7 steps (4 cap hits) |
| 788u Handle & Hold | 10.09u ($505) | Multiplier 2.19x (commission-adjusted drift) |
Horizon matrix M300-3 measures how D'Alembert (+1 on loss / -1 on win) behaves inside a 500-unit session budget across 360 coups, showing that a 80-unit pit limit and 250-unit floor generate a 9.00% drawdown-trigger rate alongside 10.09u in expected 8-deck vigorish.
Within step-indexed horizon M300-4, a 500-unit treasury backing D'Alembert Pyramid for 360 hands (5 shoes) faces a 80-unit bet cap that maps 9.00% ruin exposure, 44.79% target attainment at +125u, and 46.21% 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.
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.
Practical bankroll boundaries, stop-loss discipline, and 18+/21+ support resources.