Pairing a 130-unit bankroll against 210 hands of Player High-Tie (1.2351% edge) in cell S126-0 models Grand Martingale at 52.85% ruin and -37u peak volatility-band, whereas Flat Betting records 8.79% ruin and -12u below the 85-unit ceiling. Because every 8-deck coup is statistically independent under Even-Money Player Side (1.235% edge) (1.2351% edge), progression rules alter drawdown speed and table-cap collisions without changing per-hand expectation.
Reference 8-deck shoe for Stress Cell S126 (Grand Martingale vs Flat Betting, Three-Shoe 15% Tie Density on Even-Money Player Wagers). 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 S126 compares 1-3-7-15-31-63-127 against 1-1-1-1 constant unit over 210 hands.
Probability of exhausting the 130-unit bankroll under a 85-unit house bet limit.
Theoretical erosion under Even-Money Player Side (1.235% edge) (1.2351% house edge) across 210 coups.
Deepest unit trough triggered by a 4-hand run inside the high-tie shoe profile.
Reflects 15.24% tie frequency (32 pushes) and 8.05u in vigorish friction.
Across 210 resolved and tied deals under Player High-Tie (1.2351% edge), discrete-time comparison S126-1 measures Grand Martingale (2x+1) against Flat 1-Unit Baseline on a 130-unit bankroll, showing that 4-hand clusters and a 85-unit ceiling drive 52.85% vs 8.79% stop-loss breaches along the eight-deck drawdown-slope.
Pairing a 130-unit bankroll against 210 hands of Player High-Tie (1.2351% edge) in cell S126-2 dissects Grand Martingale at 52.85% ruin and -37u peak survival-window, whereas Flat Betting records 8.79% ruin and -12u below the 85-unit ceiling.
| S126 cycle-span | Grand Martingale | Flat Betting |
|---|---|---|
| Grand Martingale / Flat Betting Rule | 1-3-7-15-31-63-127 | 1-1-1-1 constant unit |
| 210-Hand Ruin (130u) | 52.85% | 8.79% |
| Player High-Tie Hold (1.2351%) | 16.78u | 2.70u |
| 4-Run Trough (85u Cap) | -37u | -12u |
Across 210 resolved and tied deals under Player High-Tie (1.2351% edge), capital-bounded comparison S126-3 quantifies Grand Martingale (2x+1) against Flat 1-Unit Baseline on a 130-unit bankroll, showing that 4-hand clusters and a 85-unit ceiling drive 52.85% vs 8.79% stop-loss breaches along the bankroll-constrained footprint.
Pairing a 130-unit bankroll against 210 hands of Player High-Tie (1.2351% edge) in cell S126-4 computes Grand Martingale at 52.85% ruin and -37u peak progression-curve, whereas Flat Betting records 8.79% ruin and -12u below the 85-unit ceiling.
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