Case M276-0 maps the commission-adjusted D'Alembert Pyramid (+1 on loss / -1 on win) across a 20-unit bankroll and a 72-hand (1-shoe) window, where a 40-unit table ceiling and 10-unit stop-loss produce a 39.47% ruin rate while benchmarks an average stake absorption-curve of 1.16x and 1.08u ($27) in theoretical house-edge toll. 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 M276 (D'Alembert Pyramid, 20u bankroll, 72 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.
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.
Matrix cell M276 tests D'Alembert Pyramid with a $25 base unit and -10u/+6u absorbing boundaries.
Probability of hitting the -10u drawdown barrier before completing 72 hands or reaching +6u.
Share of 72-hand trajectories reaching the +6u session ceiling, with 28.77% ending between barriers.
A 40-unit house limit and 20-unit stack cap D'Alembert escalation after 5 adverse coups.
Derived from 84u total action (1.16x average wager) multiplied by the 1.0579% 8-deck Banker edge.
In asymmetric benchmark M276-1, running D'Alembert across 72 deals with 20 units and a 40-unit maximum wager documents 84u of total handle, 1.08u in commission-weighted drift, and a 39.47% probability of exhausting the 10-unit drawdown buffer.
Case M276-2 benchmarks the combinatorial D'Alembert Pyramid (+1 on loss / -1 on win) across a 20-unit bankroll and a 72-hand (1-shoe) window, where a 40-unit table ceiling and 10-unit stop-loss produce a 39.47% ruin rate while calibrates an average stake stake-velocity of 1.16x and 1.08u ($27) in theoretical house-edge toll.
| M276 Parameter | D'Alembert (20u) | 1-Shoe capital-runway |
|---|---|---|
| D'Alembert Ladder | +1 on loss / -1 on win (10 steps) | Peak 12u multiplier on M276 |
| 20u Stack Window | 72 hands (1 shoes) | Barriers -10u / +6u |
| 40u Ceiling & Ruin | 39.47% ruin vs 31.76% win | Depth 5 steps (2 cap hits) |
| 84u Handle & Hold | 1.08u ($27) | Multiplier 1.16x (variance-scaled drift) |
In non-stationary benchmark M276-3, running D'Alembert across 72 deals with 20 units and a 40-unit maximum wager models 84u of total handle, 1.08u in commission-weighted drift, and a 39.47% probability of exhausting the 10-unit drawdown buffer.
Case M276-4 computes the table-capped D'Alembert Pyramid (+1 on loss / -1 on win) across a 20-unit bankroll and a 72-hand (1-shoe) window, where a 40-unit table ceiling and 10-unit stop-loss produce a 39.47% ruin rate while models an average stake drawdown-slope of 1.16x and 1.08u ($27) in theoretical house-edge toll.
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.