Case M133-0 dissects the table-capped Grand Martingale (2x+1) (1-3-7-15-31-63-127) across a 40-unit bankroll and a 720-hand (10-shoe) window, where a 100-unit table ceiling and 20-unit stop-loss produce a 94.80% ruin rate while measures an average stake volatility-band of 2.34x and 29.95u ($2995) 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 M133 (Grand Martingale (2x+1), 40u 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 M133 tests Grand Martingale (2x+1) with a $100 base unit and -20u/+10u absorbing boundaries.
Probability of hitting the -20u drawdown barrier before completing 720 hands or reaching +10u.
Share of 720-hand trajectories reaching the +10u session ceiling, with 0.50% ending between barriers.
A 100-unit house limit and 40-unit stack cap Grand Martingale escalation after 6 adverse coups.
Derived from 1685u total action (2.34x average wager) multiplied by the 1.0579% 8-deck Banker edge.
In house-edge-anchored benchmark M133-1, running Grand Martingale across 720 deals with 40 units and a 100-unit maximum wager evaluates 1685u of total handle, 29.95u in commission-weighted drift, and a 94.80% probability of exhausting the 20-unit drawdown buffer.
Case M133-2 audits the stochastic Grand Martingale (2x+1) (1-3-7-15-31-63-127) across a 40-unit bankroll and a 720-hand (10-shoe) window, where a 100-unit table ceiling and 20-unit stop-loss produce a 94.80% ruin rate while quantifies an average stake survival-window of 2.34x and 29.95u ($2995) in theoretical house-edge toll.
| M133 Parameter | Grand Martingale (40u) | 10-Shoe turnover |
|---|---|---|
| Grand Martingale Ladder | 1-3-7-15-31-63-127 (7 steps) | Peak 127u multiplier on M133 |
| 40u Stack Window | 720 hands (10 shoes) | Barriers -20u / +10u |
| 100u Ceiling & Ruin | 94.80% ruin vs 19.94% win | Depth 6 steps (64 cap hits) |
| 1685u Handle & Hold | 29.95u ($2995) | Multiplier 2.34x (capital-bounded drift) |
In sequential benchmark M133-3, running Grand Martingale across 720 deals with 40 units and a 100-unit maximum wager tracks 1685u of total handle, 29.95u in commission-weighted drift, and a 94.80% probability of exhausting the 20-unit drawdown buffer.
Case M133-4 measures the drawdown-weighted Grand Martingale (2x+1) (1-3-7-15-31-63-127) across a 40-unit bankroll and a 720-hand (10-shoe) window, where a 100-unit table ceiling and 20-unit stop-loss produce a 94.80% ruin rate while maps an average stake progression-curve of 2.34x and 29.95u ($2995) 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.
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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.