Across 216 eight-deck hands (3 shoes), bankroll-constrained simulation M287-0 for D'Alembert Pyramid on a 75-unit bankroll documents a 33.06% risk-of-ruin figure, verifies 3 ceiling-collision events against the 60-unit cap and a 30.12% mid-corridor finish rate. 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 M287 (D'Alembert Pyramid, 75u bankroll, 216 hands). Big Road and Bead Plate show Banker (red) and Player (blue); derived roads record structural 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.
Matrix cell M287 tests D'Alembert Pyramid with a $50 base unit and -38u/+19u absorbing boundaries.
Probability of hitting the -38u drawdown barrier before completing 216 hands or reaching +19u.
Share of 216-hand trajectories reaching the +19u session ceiling, with 30.12% ending between barriers.
A 60-unit house limit and 75-unit stack cap D'Alembert escalation after 6 adverse coups.
Derived from 341u total action (1.58x average wager) multiplied by the 1.0579% 8-deck Banker edge.
Cell M287-1 benchmarks the capital-bounded dispersion of a 75-unit D'Alembert plan over 216 hands: because each hand remains independent at 1.058% Banker edge, scaling stakes toward the 60-unit ceiling elevates total turnover to 341u and sets ruin at 33.06%.
Across 216 eight-deck hands (3 shoes), discrete-time simulation M287-2 for D'Alembert Pyramid on a 75-unit bankroll models a 33.06% risk-of-ruin figure, tracks 3 ceiling-collision events against the 60-unit cap and a 30.12% mid-corridor finish rate.
| M287 Parameter | D'Alembert (75u) | 3-Shoe boundary |
|---|---|---|
| D'Alembert Ladder | +1 on loss / -1 on win (10 steps) | Peak 12u multiplier on M287 |
| 75u Stack Window | 216 hands (3 shoes) | Barriers -38u / +19u |
| 60u Ceiling & Ruin | 33.06% ruin vs 36.82% win | Depth 6 steps (3 cap hits) |
| 341u Handle & Hold | 4.37u ($219) | Multiplier 1.58x (bankroll-constrained drift) |
Cell M287-3 computes the commission-adjusted distribution of a 75-unit D'Alembert plan over 216 hands: because each hand remains independent at 1.058% Banker edge, scaling stakes toward the 60-unit ceiling elevates total turnover to 341u and sets ruin at 33.06%.
Across 216 eight-deck hands (3 shoes), asymmetric simulation M287-4 for D'Alembert Pyramid on a 75-unit bankroll inspects a 33.06% risk-of-ruin figure, tabulates 3 ceiling-collision events against the 60-unit cap and a 30.12% mid-corridor finish rate.
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.
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.