Benchmark S115-0 tabulates the eight-deck absorption-curve between Grand Martingale and Flat Betting over 72 hands of 5% Comm Chop: with 60 units, a 50-unit cap, and 1.0579% house edge, ruin settles at 31.65% vs 5.84% while commission-adjusted decay-rate reaches -26u. 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 S115 (Grand Martingale vs Flat Betting, Single-Alternating Chop under 5% Banker Commission). Big Road shows Banker (red) and Player (blue); derived roads track 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.
Stress cell S115 compares 1-3-7-15-31-63-127 against 1-1-1-1 constant unit over 72 hands.
Probability of exhausting the 60-unit bankroll under a 50-unit house bet limit.
Theoretical erosion under 5% Banker Commission (0.95:1) (1.0579% house edge) across 72 coups.
Deepest unit trough triggered by a 2-hand run inside the chop shoe profile.
Reflects 9.52% tie frequency (7 pushes) and 2.37u in vigorish friction.
When 5% Comm Chop (chop) injects a 2-hand extreme run and 7 tie pushes (9.52% Tie density) over 72 coups, table-capped audit S115-1 models Grand Martingale (2x+1) at 4.93u expected erosion (31.65% ruin) compared with 0.79u (5.84% ruin) for Flat 1-Unit Baseline on 60 units.
Benchmark S115-2 measures the step-indexed stake-velocity between Grand Martingale and Flat Betting over 72 hands of 5% Comm Chop: with 60 units, a 50-unit cap, and 1.0579% house edge, ruin settles at 31.65% vs 5.84% while combinatorial distribution reaches -26u.
| S115 cadence | Grand Martingale | Flat Betting |
|---|---|---|
| Grand Martingale / Flat Betting Rule | 1-3-7-15-31-63-127 | 1-1-1-1 constant unit |
| 72-Hand Ruin (60u) | 31.65% | 5.84% |
| 5% Comm Chop Hold (1.0579%) | 4.93u | 0.79u |
| 2-Run Trough (50u Cap) | -26u | -13u |
When 5% Comm Chop (chop) injects a 2-hand extreme run and 7 tie pushes (9.52% Tie density) over 72 coups, non-stationary audit S115-3 dissects Grand Martingale (2x+1) at 4.93u expected erosion (31.65% ruin) compared with 0.79u (5.84% ruin) for Flat 1-Unit Baseline on 60 units.
Benchmark S115-4 quantifies the variance-scaled drawdown-slope between Grand Martingale and Flat Betting over 72 hands of 5% Comm Chop: with 60 units, a 50-unit cap, and 1.0579% house edge, ruin settles at 31.65% vs 5.84% while table-capped survival-window reaches -26u.
Enter any sequence to inspect the Big Road, Big Eye Boy, Small Road, Cockroach Pig, and next-hand previews.
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.
Visual step-by-step breakdowns with closed captions, chapter markers, and full searchable transcripts.
Macau Cantonese, French, and mathematical table terms explained in plain English with road diagrams.
Direct answers to real student questions on dragon tails, tie handling, lookback rules, and table variants.
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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.
Inspect Big Road, Bead Plate, Big Eye Boy, Small Road, and Cockroach Pig marks interactively.
Step-by-step lookback rules for Big Eye Boy (1), Small Road (2), and Cockroach Pig (3).