Under drawdown-weighted boundary rules in M131-0, pairing Grand Martingale (2x+1) with 40 units across 1 shoes (72 hands) and a 40-unit maximum documents a 46.51% stop-loss absorption rate, surviving at most 6 adverse steps before combinatorial exposure 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 M131 (Grand Martingale (2x+1), 40u bankroll, 72 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 M131 tests Grand Martingale (2x+1) with a $25 base unit and -20u/+10u absorbing boundaries.
Probability of hitting the -20u drawdown barrier before completing 72 hands or reaching +10u.
Share of 72-hand trajectories reaching the +10u session ceiling, with 20.85% ending between barriers.
A 40-unit house limit and 40-unit stack cap Grand Martingale escalation after 6 adverse coups.
Derived from 168u total action (2.34x average wager) multiplied by the 1.0579% 8-deck Banker edge.
Audit M131-1 benchmarks the multi-coup cadence of Grand Martingale when anchored to 40 units and a 72-hand (1-shoe) schedule: the 40-unit maximum wager restricts recovery at step 6, locking in a 46.51% stop-loss frequency and $75 in mathematical friction.
Under finite-shoe boundary rules in M131-2, pairing Grand Martingale (2x+1) with 40 units across 1 shoes (72 hands) and a 40-unit maximum models a 46.51% stop-loss absorption rate, surviving at most 6 adverse steps before capital-bounded footprint truncation.
| M131 Parameter | Grand Martingale (40u) | 1-Shoe excursion |
|---|---|---|
| Grand Martingale Ladder | 1-3-7-15-31-63-127 (7 steps) | Peak 127u multiplier on M131 |
| 40u Stack Window | 72 hands (1 shoes) | Barriers -20u / +10u |
| 40u Ceiling & Ruin | 46.51% ruin vs 32.64% win | Depth 6 steps (16 cap hits) |
| 168u Handle & Hold | 2.99u ($75) | Multiplier 2.34x (discrete-time drift) |
Audit M131-3 computes the session-bounded escalation of Grand Martingale when anchored to 40 units and a 72-hand (1-shoe) schedule: the 40-unit maximum wager restricts recovery at step 6, locking in a 46.51% stop-loss frequency and $75 in mathematical friction.
Under variance-scaled boundary rules in M131-4, pairing Grand Martingale (2x+1) with 40 units across 1 shoes (72 hands) and a 40-unit maximum inspects a 46.51% stop-loss absorption rate, surviving at most 6 adverse steps before step-indexed turnover truncation.
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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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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.