Case M140-0 quantifies the multi-coup Grand Martingale (2x+1) (1-3-7-15-31-63-127) across a 100-unit bankroll and a 360-hand (5-shoe) window, where a 80-unit table ceiling and 50-unit stop-loss produce a 93.02% ruin rate while maps an average stake drawdown-slope of 4.35x and 27.83u ($1392) 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 M140 (Grand Martingale (2x+1), 100u bankroll, 360 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.
This bead is at Row 2. Column 2 has a bead at Row 2 too → red (=).
Common table reading watchout: Thinking "no bead at this row" means blue. It is blue only when Column 2 stopped exactly one row above this bead.
Matrix cell M140 tests Grand Martingale (2x+1) with a $50 base unit and -50u/+25u absorbing boundaries.
Probability of hitting the -50u drawdown barrier before completing 360 hands or reaching +25u.
Share of 360-hand trajectories reaching the +25u session ceiling, with 0.50% ending between barriers.
A 80-unit house limit and 100-unit stack cap Grand Martingale escalation after 7 adverse coups.
Derived from 1566u total action (4.35x average wager) multiplied by the 1.0579% 8-deck Banker edge.
In finite-shoe benchmark M140-1, running Grand Martingale across 360 deals with 100 units and a 80-unit maximum wager charts 1566u of total handle, 27.83u in commission-weighted drift, and a 93.02% probability of exhausting the 50-unit drawdown buffer.
Case M140-2 profiles the session-bounded Grand Martingale (2x+1) (1-3-7-15-31-63-127) across a 100-unit bankroll and a 360-hand (5-shoe) window, where a 80-unit table ceiling and 50-unit stop-loss produce a 93.02% ruin rate while charts an average stake volatility-band of 4.35x and 27.83u ($1392) in theoretical house-edge toll.
| M140 Parameter | Grand Martingale (100u) | 5-Shoe absorption-curve |
|---|---|---|
| Grand Martingale Ladder | 1-3-7-15-31-63-127 (7 steps) | Peak 127u multiplier on M140 |
| 100u Stack Window | 360 hands (5 shoes) | Barriers -50u / +25u |
| 80u Ceiling & Ruin | 93.02% ruin vs 21.26% win | Depth 7 steps (40 cap hits) |
| 1566u Handle & Hold | 27.83u ($1392) | Multiplier 4.35x (table-capped drift) |
In variance-scaled benchmark M140-3, running Grand Martingale across 360 deals with 100 units and a 80-unit maximum wager calibrates 1566u of total handle, 27.83u in commission-weighted drift, and a 93.02% probability of exhausting the 50-unit drawdown buffer.
Case M140-4 dissects the step-indexed Grand Martingale (2x+1) (1-3-7-15-31-63-127) across a 100-unit bankroll and a 360-hand (5-shoe) window, where a 80-unit table ceiling and 50-unit stop-loss produce a 93.02% ruin rate while documents an average stake survival-window of 4.35x and 27.83u ($1392) in theoretical house-edge toll.
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Definitions for progression ladders, absorbing barriers, commission formats, and shoe terms.
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Verify 8-deck combinatorial probabilities, Banker/Player house edge, and commission rules.
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