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GMU ANALYTICAL · INDEX PROOF · DR109

Rule 2 Case 2c Over-Depth Red — Analytical Coordinate Proof (DR109)

DR109 pairs Rule 2 Case 2c Over-Depth Red (Continuing column row r >= d_{k-m} + 2 where two reference cells are empty) with Analytical Modality (Formal Index Notation): learners verify Both (k-m, r) and (k-m, r-1) are empty because r exceeds d_{k-m} by 2+, master Rule 2 Case 2c Consecutive Empty Reference Cells returning Red (=), and eliminate forgetting rule 2's third case where two empty reference cells produce red (=).

Drill Reference ID
DR109
Big Road Streaks
8 Cols
Big Eye Boy Total
18 Marks
Small Road Total
15 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 B B P P
Big Eye Boy = ≠ ≠ = = ≠ ≠ = ≠ ≠ ≠ = = = ≠ = ≠ =
Small Road = ≠ = ≠ = ≠ ≠ = ≠ = = ≠ ≠ ≠ =
Cockroach Pig = = ≠ = = = ≠ ≠ = = ≠

DR109 drill board (BBPPPBBBBPPBPPPPPTBBPP): 8 Big Road columns, 18 Big Eye Boy, 15 Small Road, and 11 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 #5

This bead is at Row 3. Column 2 has a bead at Row 3 too → red (=).

  1. Column 3 goes down to Row 3, so use Rule 2: look 1 column back, at Column 2.
  2. 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.

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

DR109 Target Coordinate
Rule 2 Case 2c Over-Depth Red

Continuing column row r >= d_{k-m} + 2 where two reference cells are empty

DR109 Rule Classification
Analytical Coordinate Proof

Rule 2 Case 2c Consecutive Empty Reference Cells returning Red (=)

DR109 Depth Comparison
8 Big Road Cols

Both (k-m, r) and (k-m, r-1) are empty because r exceeds d_{k-m} by 2+

DR109 Misconception Focus
Diagnostic Check

Forgetting Rule 2's third case where two empty reference cells produce red (=)

DR109 GMU Modality Goal
Analytical Modality (Formal Index Notation)

Explain why extending a long streak 2+ rows past d_{k-m} turns red (=) by writing out (k, r) and (k-m, r) coordinates to prove the derived output

DR109 · Coordinate & Rule Specification

DR109 Rule 2 Case 2c Over-Depth Red: Analytical Coordinate Proof Walkthrough

Built around GMU ANALYTICAL · INDEX PROOF, unit DR109 examines Rule 2 Case 2c Over-Depth Red (Continuing column row r >= d_{k-m} + 2 where two reference cells are empty), using 18 Big Eye Boy comparisons in BBPPPBBBB to achieve explain why extending a long streak 2+ rows past d_{k-m} turns red (=).

Checking the first explained mark in DR109 (Rule 2 Case 2c Over-Depth Red), This bead is at Row 3. Column 2 has a bead at Row 3 too → red (=). Simultaneously, Small Road plots 15 marks and Cockroach Pig plots 11 marks while writing out (k, r) and (k-m, r) coordinates to prove the derived output.

Table DR109: Rule 2 Case 2c Over-Depth Red specification under Analytical Coordinate Proof.
DR109 Drill DimensionCoordinate / RuleGMU Modality Action
DR109 Matrix CoordinateContinuing column row r >= d_{k-m} + 2 where two reference cells are emptyAnalytical Modality (Formal Index Notation)
DR109 Rule & DepthRule 2 Case 2c Consecutive Empty Reference Cells returning Red (=)Both (k-m, r) and (k-m, r-1) are empty because r exceeds d_{k-m} by 2+
DR109 Diagnostic TargetForgetting Rule 2's third case where two empty reference cells produce red (=)Explain why extending a long streak 2+ rows past d_{k-m} turns red (=)
  • DR109 Step 1: Locate Continuing column row r >= d_{k-m} + 2 where two reference cells are empty across the 8 columns of BBPPPBBBBPPB.
  • DR109 Step 2: Verify Both (k-m, r) and (k-m, r-1) are empty because r exceeds d_{k-m} by 2+ under Rule 2 Case 2c Consecutive Empty Reference Cells returning Red (=).
  • DR109 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.
DR109 · Analytical Modality (Formal Index Notation)

DR109 Misconception Diagnostic & Secondary Road Audit

On the companion derived road in DR109, This bead is at Row 2. Column 2 has a bead at Row 2 too → red (=). Combining Analytical Coordinate Proof with Rule 2 Case 2c Consecutive Empty Reference Cells returning Red (=) keeps 8-column reading error-free.

Table Reality Check

Myth vs. Truth

MythIn DR109 (Rule 2 Case 2c Over-Depth Red), forgetting rule 2's third case where two empty reference cells produce red (=) or reading red/blue derived marks as Banker/Player outcomes.
TruthRule 2 Case 2c Consecutive Empty Reference Cells returning Red (=) evaluates Both (k-m, r) and (k-m, r-1) are empty because r exceeds d_{k-m} by 2+; 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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