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GMU ANALYTICAL · INDEX PROOF · DR309

4-vs-2 Column Break Check — Analytical Coordinate Proof (DR309)

DR309 pairs 4-vs-2 Column Break Check (Reference column depth 2 vs active column extending to rows 3 and 4) with Analytical Modality (Formal Index Notation): learners verify At Row 3, (k-m,3) is first empty (Blue); at Row 4, both 3 & 4 are empty (Red), master Transition From Rule 2 Case 2b (Row 3 Blue) to Case 2c (Row 4 Red), and eliminate keeping row 4 blue after row 3 already marked the single-row break.

Drill Reference ID
DR309
Big Road Streaks
10 Cols
Big Eye Boy Total
19 Marks
Small Road Total
16 Dots
Engine-Verified Scoreboard · 22 Hands

Read the Board at Table Speed

Open this shoe in /calculator
Big Road B B P P P B B B B P P B P P P P P B P B B P
Big Eye Boy = ≠ ≠ = = ≠ ≠ = ≠ ≠ ≠ = = = ≠ ≠ = ≠ ≠
Small Road = ≠ = ≠ = ≠ ≠ = ≠ = = ≠ = ≠ ≠ ≠
Cockroach Pig = = ≠ = = = ≠ ≠ ≠ = = ≠

DR309 drill board (BBPPPBBBBPPBPPPPPBPBBP): 10 Big Road columns, 19 Big Eye Boy, 16 Small Road, and 12 Cockroach Pig marks.

Big Road B is Banker, P is Player Roads under it Red (=): repeating Blue (≠): breaking
Step-by-Step Mark Proofs (Rule 1 & Rule 2)
Big Eye Boy · Mark #1

This bead is at Row 2. Column 1 has a bead at Row 2 too → red (=).

  1. Column 2 goes down to Row 2, so use Rule 2: look 1 column back, at Column 1.
  2. Column 1 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 1 stopped exactly one row above this bead.

Small Road · Mark #5

This bead is at Row 2. Column 2 has a bead at Row 2 too → red (=).

  1. Column 4 goes down to Row 2, so use Rule 2: look 2 columns back, at Column 2.
  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.

Cockroach Pig · Mark #3

Column 5 has 1 bead. Column 2 has 3 beads. Different depth → blue (≠).

  1. Column 6 starts, so use Rule 1: compare Column 5 with Column 2, 3 columns further back.
  2. 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.

Verified Reference Data

Key Facts & Table Specifications

DR309 Target Coordinate
4-vs-2 Column Break Check

Reference column depth 2 vs active column extending to rows 3 and 4

DR309 Rule Classification
Analytical Coordinate Proof

Transition From Rule 2 Case 2b (Row 3 Blue) to Case 2c (Row 4 Red)

DR309 Depth Comparison
10 Big Road Cols

At Row 3, (k-m,3) is first empty (Blue); at Row 4, both 3 & 4 are empty (Red)

DR309 Misconception Focus
Diagnostic Check

Keeping Row 4 blue after Row 3 already marked the single-row break

DR309 GMU Modality Goal
Analytical Modality (Formal Index Notation)

Trace the exact flip from Blue at Row 3 to Red at Row 4 over a depth-2 column by writing out (k, r) and (k-m, r) coordinates to prove the derived output

DR309 · Coordinate & Rule Specification

DR309 4-vs-2 Column Break Check: Analytical Coordinate Proof Walkthrough

Guided by Analytical Modality (Formal Index Notation), drill DR309 walks through 4-vs-2 Column Break Check (Transition From Rule 2 Case 2b (Row 3 Blue) to Case 2c (Row 4 Red)) across 10 Big Road streaks and 19 derived marks in BBPPPBBBB-PPBPPPPPB.

For coordinate Reference column depth 2 vs active column extending to rows 3 and 4 in DR309, This bead is at Row 2. Column 1 has a bead at Row 2 too → red (=). Meanwhile, 16 Small Road and 12 Cockroach Pig comparisons reinforce Analytical Coordinate Proof.

Table DR309: 4-vs-2 Column Break Check specification under Analytical Coordinate Proof.
DR309 Drill DimensionCoordinate / RuleGMU Modality Action
DR309 Matrix CoordinateReference column depth 2 vs active column extending to rows 3 and 4Analytical Modality (Formal Index Notation)
DR309 Rule & DepthTransition From Rule 2 Case 2b (Row 3 Blue) to Case 2c (Row 4 Red)At Row 3, (k-m,3) is first empty (Blue); at Row 4, both 3 & 4 are empty (Red)
DR309 Diagnostic TargetKeeping Row 4 blue after Row 3 already marked the single-row breakTrace the exact flip from Blue at Row 3 to Red at Row 4 over a depth-2 column
  • DR309 Step 1: Locate Reference column depth 2 vs active column extending to rows 3 and 4 across the 10 columns of BBPPPBBBBPPB.
  • DR309 Step 2: Verify At Row 3, (k-m,3) is first empty (Blue); at Row 4, both 3 & 4 are empty (Red) under Transition From Rule 2 Case 2b (Row 3 Blue) to Case 2c (Row 4 Red).
  • DR309 Step 3: Answer "What are the exact 1-based and 0-based indices for the active comparison?" via writing out (k, r) and (k-m, r) coordinates to prove the derived output.
DR309 · Analytical Modality (Formal Index Notation)

DR309 Misconception Diagnostic & Secondary Road Audit

Closing DR309 (4-vs-2 Column Break Check · Analytical Coordinate Proof), This bead is at Row 2. Column 2 has a bead at Row 2 too → red (=). Mastering Transition From Rule 2 Case 2b (Row 3 Blue) to Case 2c (Row 4 Red) over 10 columns builds lasting scoreboard accuracy.

Table Reality Check

Myth vs. Truth

MythIn DR309 (4-vs-2 Column Break Check), keeping row 4 blue after row 3 already marked the single-row break or reading red/blue derived marks as Banker/Player outcomes.
TruthTransition From Rule 2 Case 2b (Row 3 Blue) to Case 2c (Row 4 Red) evaluates At Row 3, (k-m,3) is first empty (Blue); at Row 4, both 3 & 4 are empty (Red); derived road colors reflect structural symmetry only and never alter independent shoe probabilities.
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  • Structured step-by-step track across Foundations, Big Eye Boy, Small Road, and Cockroach Pig
  • 74 interactive lesson scoreboards and 94 inline quiz checks with plain-English mark feedback
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