Case M126-0 measures the discrete-time Grand Martingale (2x+1) (1-3-7-15-31-63-127) across a 20-unit bankroll and a 72-hand (1-shoe) window, where a 40-unit table ceiling and 10-unit stop-loss produce a 93.02% ruin rate while tracks an average stake survival-window of 1.67x and 2.13u ($53) 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 M126 (Grand Martingale (2x+1), 20u bankroll, 72 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 M126 tests Grand Martingale (2x+1) with a $25 base unit and -10u/+6u absorbing boundaries.
Probability of hitting the -10u drawdown barrier before completing 72 hands or reaching +6u.
Share of 72-hand trajectories reaching the +6u session ceiling, with 0.50% ending between barriers.
A 40-unit house limit and 20-unit stack cap Grand Martingale escalation after 5 adverse coups.
Derived from 120u total action (1.67x average wager) multiplied by the 1.0579% 8-deck Banker edge.
In commission-adjusted benchmark M126-1, running Grand Martingale across 72 deals with 20 units and a 40-unit maximum wager maps 120u of total handle, 2.13u in commission-weighted drift, and a 93.02% probability of exhausting the 10-unit drawdown buffer.
Case M126-2 documents the asymmetric Grand Martingale (2x+1) (1-3-7-15-31-63-127) across a 20-unit bankroll and a 72-hand (1-shoe) window, where a 40-unit table ceiling and 10-unit stop-loss produce a 93.02% ruin rate while tabulates an average stake progression-curve of 1.67x and 2.13u ($53) in theoretical house-edge toll.
| M126 Parameter | Grand Martingale (20u) | 1-Shoe boundary |
|---|---|---|
| Grand Martingale Ladder | 1-3-7-15-31-63-127 (7 steps) | Peak 127u multiplier on M126 |
| 20u Stack Window | 72 hands (1 shoes) | Barriers -10u / +6u |
| 40u Ceiling & Ruin | 93.02% ruin vs 16.77% win | Depth 5 steps (16 cap hits) |
| 120u Handle & Hold | 2.13u ($53) | Multiplier 1.67x (session-bounded drift) |
In combinatorial benchmark M126-3, running Grand Martingale across 72 deals with 20 units and a 40-unit maximum wager benchmarks 120u of total handle, 2.13u in commission-weighted drift, and a 93.02% probability of exhausting the 10-unit drawdown buffer.
Case M126-4 models the non-stationary Grand Martingale (2x+1) (1-3-7-15-31-63-127) across a 20-unit bankroll and a 72-hand (1-shoe) window, where a 40-unit table ceiling and 10-unit stop-loss produce a 93.02% ruin rate while measures an average stake ledger of 1.67x and 2.13u ($53) in theoretical house-edge toll.
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