When 5% Comm High-Tie (high-tie) injects a 4-hand extreme run and 13 tie pushes (16.67% Tie density) over 78 coups, asymmetric audit S159-0 calibrates 1-2-3-5 Four-Step Ladder at 1.29u expected erosion (13.14% ruin) compared with 0.86u (5.52% ruin) for Flat 1-Unit Baseline on 75 units. 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 S159 (1-2-3-5 vs Flat Betting, 16% High-Tie Cluster Shoe 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.
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.
Stress cell S159 compares 1-2-3-5 against 1-1-1-1 constant unit over 78 hands.
Probability of exhausting the 75-unit bankroll under a 50-unit house bet limit.
Theoretical erosion under 5% Banker Commission (0.95:1) (1.0579% house edge) across 78 coups.
Deepest unit trough triggered by a 4-hand run inside the high-tie shoe profile.
Reflects 16.67% tie frequency (13 pushes) and 0.62u in vigorish friction.
Benchmark S159-1 tabulates the finite-shoe cycle-span between 1-2-3-5 and Flat Betting over 78 hands of 5% Comm High-Tie: with 75 units, a 50-unit cap, and 1.0579% house edge, ruin settles at 13.14% vs 5.52% while variance-scaled drawdown-slope reaches -24u.
When 5% Comm High-Tie (high-tie) injects a 4-hand extreme run and 13 tie pushes (16.67% Tie density) over 78 coups, commission-adjusted audit S159-2 models 1-2-3-5 Four-Step Ladder at 1.29u expected erosion (13.14% ruin) compared with 0.86u (5.52% ruin) for Flat 1-Unit Baseline on 75 units.
| S159 boundary | 1-2-3-5 | Flat Betting |
|---|---|---|
| 1-2-3-5 / Flat Betting Rule | 1-2-3-5 | 1-1-1-1 constant unit |
| 78-Hand Ruin (75u) | 13.14% | 5.52% |
| 5% Comm High-Tie Hold (1.0579%) | 1.29u | 0.86u |
| 4-Run Trough (50u Cap) | -24u | -15u |
Benchmark S159-3 measures the multi-coup capital-runway between 1-2-3-5 and Flat Betting over 78 hands of 5% Comm High-Tie: with 75 units, a 50-unit cap, and 1.0579% house edge, ruin settles at 13.14% vs 5.52% while eight-deck footprint reaches -24u.
When 5% Comm High-Tie (high-tie) injects a 4-hand extreme run and 13 tie pushes (16.67% Tie density) over 78 coups, discrete-time audit S159-4 dissects 1-2-3-5 Four-Step Ladder at 1.29u expected erosion (13.14% ruin) compared with 0.86u (5.52% ruin) for Flat 1-Unit Baseline on 75 units.
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.
Every reference guide, glossary definition, and road calculator on Baccarat Smart is open for everyone. When you want all 6 modules and 36 lessons (about 5.5 hours of lessons) organized in structured step-by-step order with 74 hands-on boards, 94 quiz checks along the way, and Cloud Shoe Log sync across web, iPhone, and Android, start Module 1 (10 lessons, about 64 minutes of lessons) free or unlock full membership for $25 a month.
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).
Definitions for progression ladders, absorbing barriers, commission formats, and shoe terms.
Plain-English answers on independent trials, progression variance, and scoreboard reading.