Under discrete-time boundary rules in M145-0, pairing Grand Martingale (2x+1) with 200 units across 5 shoes (360 hands) and a 80-unit maximum profiles a 46.51% stop-loss absorption rate, surviving at most 7 adverse steps before commission-adjusted progression-curve 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 M145 (Grand Martingale (2x+1), 200u 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 M145 tests Grand Martingale (2x+1) with a $50 base unit and -100u/+50u absorbing boundaries.
Probability of hitting the -100u drawdown barrier before completing 360 hands or reaching +50u.
Share of 360-hand trajectories reaching the +50u session ceiling, with 19.21% ending between barriers.
A 80-unit house limit and 200-unit stack cap Grand Martingale escalation after 7 adverse coups.
Derived from 2207u total action (6.13x average wager) multiplied by the 1.0579% 8-deck Banker edge.
Audit M145-1 calibrates the commission-adjusted threshold of Grand Martingale when anchored to 200 units and a 360-hand (5-shoe) schedule: the 80-unit maximum wager restricts recovery at step 7, locking in a 46.51% stop-loss frequency and $1961 in mathematical friction.
Under asymmetric boundary rules in M145-2, pairing Grand Martingale (2x+1) with 200 units across 5 shoes (360 hands) and a 80-unit maximum dissects a 46.51% stop-loss absorption rate, surviving at most 7 adverse steps before absorbing-barrier drawdown-slope truncation.
| M145 Parameter | Grand Martingale (200u) | 5-Shoe exposure |
|---|---|---|
| Grand Martingale Ladder | 1-3-7-15-31-63-127 (7 steps) | Peak 127u multiplier on M145 |
| 200u Stack Window | 360 hands (5 shoes) | Barriers -100u / +50u |
| 80u Ceiling & Ruin | 46.51% ruin vs 34.28% win | Depth 7 steps (40 cap hits) |
| 2207u Handle & Hold | 39.22u ($1961) | Multiplier 6.13x (session-bounded drift) |
Audit M145-3 evaluates the combinatorial footprint of Grand Martingale when anchored to 200 units and a 360-hand (5-shoe) schedule: the 80-unit maximum wager restricts recovery at step 7, locking in a 46.51% stop-loss frequency and $1961 in mathematical friction.
Under non-stationary boundary rules in M145-4, pairing Grand Martingale (2x+1) with 200 units across 5 shoes (360 hands) and a 80-unit maximum audits a 46.51% stop-loss absorption rate, surviving at most 7 adverse steps before session-bounded capital-runway 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.
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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.
Verify 8-deck combinatorial probabilities, Banker/Player house edge, and commission rules.