Case M147-0 computes the eight-deck Grand Martingale (2x+1) (1-3-7-15-31-63-127) across a 300-unit bankroll and a 216-hand (3-shoe) window, where a 60-unit table ceiling and 150-unit stop-loss produce a 19.79% ruin rate while documents an average stake stake-velocity of 6.13x and 23.53u ($1177) 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 M147 (Grand Martingale (2x+1), 300u bankroll, 216 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 M147 tests Grand Martingale (2x+1) with a $50 base unit and -150u/+75u absorbing boundaries.
Probability of hitting the -150u drawdown barrier before completing 216 hands or reaching +75u.
Share of 216-hand trajectories reaching the +75u session ceiling, with 39.68% ending between barriers.
A 60-unit house limit and 300-unit stack cap Grand Martingale escalation after 6 adverse coups.
Derived from 1324u total action (6.13x average wager) multiplied by the 1.0579% 8-deck Banker edge.
In absorbing-barrier benchmark M147-1, running Grand Martingale across 216 deals with 300 units and a 60-unit maximum wager inspects 1324u of total handle, 23.53u in commission-weighted drift, and a 19.79% probability of exhausting the 150-unit drawdown buffer.
Case M147-2 verifies the bankroll-constrained Grand Martingale (2x+1) (1-3-7-15-31-63-127) across a 300-unit bankroll and a 216-hand (3-shoe) window, where a 60-unit table ceiling and 150-unit stop-loss produce a 19.79% ruin rate while profiles an average stake drawdown-slope of 6.13x and 23.53u ($1177) in theoretical house-edge toll.
| M147 Parameter | Grand Martingale (300u) | 3-Shoe profile |
|---|---|---|
| Grand Martingale Ladder | 1-3-7-15-31-63-127 (7 steps) | Peak 127u multiplier on M147 |
| 300u Stack Window | 216 hands (3 shoes) | Barriers -150u / +75u |
| 60u Ceiling & Ruin | 19.79% ruin vs 40.54% win | Depth 6 steps (32 cap hits) |
| 1324u Handle & Hold | 23.53u ($1177) | Multiplier 6.13x (finite-shoe drift) |
In capital-bounded benchmark M147-3, running Grand Martingale across 216 deals with 300 units and a 60-unit maximum wager tabulates 1324u of total handle, 23.53u in commission-weighted drift, and a 19.79% probability of exhausting the 150-unit drawdown buffer.
Case M147-4 quantifies the discrete-time Grand Martingale (2x+1) (1-3-7-15-31-63-127) across a 300-unit bankroll and a 216-hand (3-shoe) window, where a 60-unit table ceiling and 150-unit stop-loss produce a 19.79% ruin rate while benchmarks an average stake volatility-band of 6.13x and 23.53u ($1177) in theoretical house-edge toll.
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