When Player High-Tie (high-tie) injects a 4-hand extreme run and 32 tie pushes (15.24% Tie density) over 210 coups, multi-coup audit S112-0 computes Martingale Doubling at 11.60u expected erosion (42.16% ruin) compared with 2.70u (8.79% ruin) for Flat 1-Unit Baseline on 130 units. 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 S112 (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 S112 compares 1-2-4-8-16-32-64 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 5.57u in vigorish friction.
Benchmark S112-1 maps the discrete-time turnover between Martingale and Flat Betting over 210 hands of Player High-Tie: with 130 units, a 85-unit cap, and 1.2351% house edge, ruin settles at 42.16% vs 8.79% while eight-deck drawdown-slope reaches -37u.
When Player High-Tie (high-tie) injects a 4-hand extreme run and 32 tie pushes (15.24% Tie density) over 210 coups, drawdown-weighted audit S112-2 evaluates Martingale Doubling at 11.60u expected erosion (42.16% ruin) compared with 2.70u (8.79% ruin) for Flat 1-Unit Baseline on 130 units.
| S112 absorption-curve | Martingale | Flat Betting |
|---|---|---|
| Martingale / Flat Betting Rule | 1-2-4-8-16-32-64 | 1-1-1-1 constant unit |
| 210-Hand Ruin (130u) | 42.16% | 8.79% |
| Player High-Tie Hold (1.2351%) | 11.60u | 2.70u |
| 4-Run Trough (85u Cap) | -37u | -13u |
Benchmark S112-3 charts the capital-bounded decay-rate between Martingale and Flat Betting over 210 hands of Player High-Tie: with 130 units, a 85-unit cap, and 1.2351% house edge, ruin settles at 42.16% vs 8.79% while bankroll-constrained footprint reaches -37u.
When Player High-Tie (high-tie) injects a 4-hand extreme run and 32 tie pushes (15.24% Tie density) over 210 coups, sequential audit S112-4 inspects Martingale Doubling at 11.60u expected erosion (42.16% ruin) compared with 2.70u (8.79% ruin) for Flat 1-Unit Baseline on 130 units.
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About 64 minutes of lessons covering outcomes, the Bead Plate, Big Road columns, and dragon tails.
Train Third-Card Rule decisions, depth counting, lookback column references, and derived-road speed recognition.
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Step-by-step lookback rules for Big Eye Boy (1), Small Road (2), and Cockroach Pig (3).
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.