DR289 pairs 0-Based vs 1-Based Indexing (Engine array col[k] (0-based) vs learner label Column k+1 (1-based)) with Analytical Modality (Formal Index Notation): learners verify Array index col[0] corresponds to Display Column 1 on the RoadLegend, master Coordinate Index Translation Between Engine and Display Grid, and eliminate off-by-one lookup errors when translating array index k to display columns.
DR289 drill board (BBPPPBBBBPPBPPPPPPBBBP): 8 Big Road columns, 19 Big Eye Boy, 16 Small Road, and 12 Cockroach Pig marks.
This bead is at Row 3. Column 2 has a bead at Row 3 too → red (=).
Common table reading watchout: Thinking "no bead at this row" means blue. It is blue only when Column 2 stopped exactly one row above this bead.
This bead is at Row 2. Column 2 has a bead at Row 2 too → red (=).
Common table reading watchout: Thinking "no bead at this row" means blue. It is blue only when Column 2 stopped exactly one row above this bead.
Column 5 has 1 bead. Column 2 has 3 beads. Different depth → blue (≠).
Common table reading watchout: Comparing the wrong columns. Compare Column 5, the one that just finished, with Column 2.
Engine array col[k] (0-based) vs learner label Column k+1 (1-based)
Coordinate Index Translation Between Engine and Display Grid
Array index col[0] corresponds to Display Column 1 on the RoadLegend
Off-by-one lookup errors when translating array index k to display columns
Convert cleanly between 1-based display labels and 0-based engine indices by writing out (k, r) and (k-m, r) coordinates to prove the derived output
Under Analytical Coordinate Proof (DR289), 0-Based vs 1-Based Indexing isolates Engine array col[k] (0-based) vs learner label Column k+1 (1-based) and Array index col[0] corresponds to Display Column 1 on the RoadLegend, turning BBPPPBBBB-PPBPPPPPP into a hands-on 19-mark verification.
Applying Coordinate Index Translation Between Engine and Display Grid in DR289, This bead is at Row 3. Column 2 has a bead at Row 3 too → red (=). Those 16 Small Road dots and 12 Cockroach Pig slashes accompany Engine array col[k] (0-based) vs learner label Column k+1 (1-based) during writing out (k, r) and (k-m, r) coordinates to prove the derived output.
| DR289 Drill Dimension | Coordinate / Rule | GMU Modality Action |
|---|---|---|
| DR289 Matrix Coordinate | Engine array col[k] (0-based) vs learner label Column k+1 (1-based) | Analytical Modality (Formal Index Notation) |
| DR289 Rule & Depth | Coordinate Index Translation Between Engine and Display Grid | Array index col[0] corresponds to Display Column 1 on the RoadLegend |
| DR289 Diagnostic Target | Off-by-one lookup errors when translating array index k to display columns | Convert cleanly between 1-based display labels and 0-based engine indices |
Inside DR289 (GMU ANALYTICAL · INDEX PROOF), This bead is at Row 2. Column 2 has a bead at Row 2 too → red (=). Every step of Coordinate Index Translation Between Engine and Display Grid and Array index col[0] corresponds to Display Column 1 on the RoadLegend holds across 8 columns.
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.
Test any shoe sequence and inspect Rule 1 and Rule 2 derived road marks.
Review the 5-road architecture from Bead Plate and Big Road to Cockroach Pig.
Practice companion coordinate lookups, depth comparisons, and rule checks.
Practice companion coordinate lookups, depth comparisons, and rule checks.