In head-to-head trial S127-0 across 288 deals (4-Shoe Chop, 1.0579% edge), Grand Martingale records a -32u peak trajectory and 47.62% ruin probability on a 160-unit stack, whereas Flat Betting logs a -11u trough and 9.92% ruin under the 100-unit limit. Because every 8-deck coup is statistically independent under 5% Banker Commission (0.95:1) (1.0579% edge), progression rules alter drawdown speed and table-cap collisions without changing per-hand expectation.
Reference 8-deck shoe for Stress Cell S127 (Grand Martingale vs Flat Betting, Four-Shoe Alternating Sawtooth under 5% Banker Commission). Big Road shows Banker (red) and Player (blue); derived roads track symmetry.
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.
Column 4 has 2 beads. Column 1 has 2 beads. Same depth → red (=).
Common table reading watchout: Comparing the wrong columns. Compare Column 4, the one that just finished, with Column 1.
Stress cell S127 compares 1-3-7-15-31-63-127 against 1-1-1-1 constant unit over 288 hands.
Probability of exhausting the 160-unit bankroll under a 100-unit house bet limit.
Theoretical erosion under 5% Banker Commission (0.95:1) (1.0579% house edge) across 288 coups.
Deepest unit trough triggered by a 3-hand run inside the chop shoe profile.
Reflects 9.38% tie frequency (27 pushes) and 9.46u in vigorish friction.
Within combinatorial testbed S127-1, a 160-unit bankroll facing 288 coups of 4-Shoe Chop (chop) and a 100-unit maximum wager calibrates 47.62% ruin (19.71u expected loss) on Grand Martingale (2x+1) versus 9.92% ruin (3.17u expected loss) on Flat 1-Unit Baseline.
In head-to-head trial S127-2 across 288 deals (4-Shoe Chop, 1.0579% edge), Grand Martingale records a -32u peak cycle-span and 47.62% ruin probability on a 160-unit stack, whereas Flat Betting logs a -11u trough and 9.92% ruin under the 100-unit limit.
| S127 volatility-band | Grand Martingale | Flat Betting |
|---|---|---|
| Grand Martingale / Flat Betting Rule | 1-3-7-15-31-63-127 | 1-1-1-1 constant unit |
| 288-Hand Ruin (160u) | 47.62% | 9.92% |
| 4-Shoe Chop Hold (1.0579%) | 19.71u | 3.17u |
| 3-Run Trough (100u Cap) | -32u | -11u |
Within asymmetric testbed S127-3, a 160-unit bankroll facing 288 coups of 4-Shoe Chop (chop) and a 100-unit maximum wager models 47.62% ruin (19.71u expected loss) on Grand Martingale (2x+1) versus 9.92% ruin (3.17u expected loss) on Flat 1-Unit Baseline.
In head-to-head trial S127-4 across 288 deals (4-Shoe Chop, 1.0579% edge), Grand Martingale records a -32u peak capital-runway and 47.62% ruin probability on a 160-unit stack, whereas Flat Betting logs a -11u trough and 9.92% ruin under the 100-unit limit.
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