Case M122-0 documents the capital-bounded Martingale Doubling (1-2-4-8-16-32-64) 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 14.98% ruin rate while verifies an average stake dispersion of 4.87x and 15.80u ($790) 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 M122 (Martingale Doubling, 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.
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.
Matrix cell M122 tests Martingale Doubling 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 43.14% ending between barriers.
A 60-unit house limit and 300-unit stack cap Martingale escalation after 6 adverse coups.
Derived from 1052u total action (4.87x average wager) multiplied by the 1.0579% 8-deck Banker edge.
In discrete-time benchmark M122-1, running Martingale across 216 deals with 300 units and a 60-unit maximum wager benchmarks 1052u of total handle, 15.80u in commission-weighted drift, and a 14.98% probability of exhausting the 150-unit drawdown buffer.
Case M122-2 models the commission-adjusted Martingale Doubling (1-2-4-8-16-32-64) 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 14.98% ruin rate while tracks an average stake distribution of 4.87x and 15.80u ($790) in theoretical house-edge toll.
| M122 Parameter | Martingale (300u) | 3-Shoe exposure |
|---|---|---|
| Martingale Ladder | 1-2-4-8-16-32-64 (7 steps) | Peak 64u multiplier on M122 |
| 300u Stack Window | 216 hands (3 shoes) | Barriers -150u / +75u |
| 60u Ceiling & Ruin | 14.98% ruin vs 41.88% win | Depth 6 steps (16 cap hits) |
| 1052u Handle & Hold | 15.80u ($790) | Multiplier 4.87x (step-indexed drift) |
In asymmetric benchmark M122-3, running Martingale across 216 deals with 300 units and a 60-unit maximum wager computes 1052u of total handle, 15.80u in commission-weighted drift, and a 14.98% probability of exhausting the 150-unit drawdown buffer.
Case M122-4 inspects the combinatorial Martingale Doubling (1-2-4-8-16-32-64) 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 14.98% ruin rate while tabulates an average stake envelope of 4.87x and 15.80u ($790) in theoretical house-edge toll.
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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.
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