Under eight-deck boundary rules in M288-0, pairing D'Alembert Pyramid with 75 units across 10 shoes (720 hands) and a 100-unit maximum tracks a 94.80% stop-loss absorption rate, surviving at most 7 adverse steps before bankroll-constrained volatility-band truncation. 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 M288 (D'Alembert Pyramid, 75u bankroll, 720 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 M288 tests D'Alembert Pyramid with a $100 base unit and -38u/+19u absorbing boundaries.
Probability of hitting the -38u drawdown barrier before completing 720 hands or reaching +19u.
Share of 720-hand trajectories reaching the +19u session ceiling, with 0.50% ending between barriers.
A 100-unit house limit and 75-unit stack cap D'Alembert escalation after 7 adverse coups.
Derived from 1138u total action (1.58x average wager) multiplied by the 1.0579% 8-deck Banker edge.
Audit M288-1 measures the absorbing-barrier excursion of D'Alembert when anchored to 75 units and a 720-hand (10-shoe) schedule: the 100-unit maximum wager restricts recovery at step 7, locking in a 94.80% stop-loss frequency and $1457 in mathematical friction.
Under bankroll-constrained boundary rules in M288-2, pairing D'Alembert Pyramid with 75 units across 10 shoes (720 hands) and a 100-unit maximum maps a 94.80% stop-loss absorption rate, surviving at most 7 adverse steps before variance-scaled absorption-curve truncation.
| M288 Parameter | D'Alembert (75u) | 10-Shoe progression-curve |
|---|---|---|
| D'Alembert Ladder | +1 on loss / -1 on win (10 steps) | Peak 12u multiplier on M288 |
| 75u Stack Window | 720 hands (10 shoes) | Barriers -38u / +19u |
| 100u Ceiling & Ruin | 94.80% ruin vs 19.94% win | Depth 7 steps (6 cap hits) |
| 1138u Handle & Hold | 14.57u ($1457) | Multiplier 1.58x (stochastic drift) |
Audit M288-3 documents the capital-bounded turnover of D'Alembert when anchored to 75 units and a 720-hand (10-shoe) schedule: the 100-unit maximum wager restricts recovery at step 7, locking in a 94.80% stop-loss frequency and $1457 in mathematical friction.
Under discrete-time boundary rules in M288-4, pairing D'Alembert Pyramid with 75 units across 10 shoes (720 hands) and a 100-unit maximum benchmarks a 94.80% stop-loss absorption rate, surviving at most 7 adverse steps before drawdown-weighted trajectory truncation.
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.