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GMU ANALYTICAL · DEPTH AUDIT · DR110

Rule 2 Case 2c Over-Depth Red — Analytical Depth Audit (DR110)

DR110 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 (Depth Vector Verification): 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
DR110
Big Road Streaks
11 Cols
Big Eye Boy Total
20 Marks
Small Road Total
17 Dots
Engine-Verified Scoreboard · 23 Hands

Read the Board at Table Speed

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

DR110 drill board (PPBBBPPPPBBPBBBBBPBPBBP): 11 Big Road columns, 20 Big Eye Boy, 17 Small Road, and 13 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 #6

This bead is at Row 4. Column 2 stopped at Row 3, one row above → blue (≠).

  1. Column 3 goes down to Row 4, so use Rule 2: look 1 column back, at Column 2.
  2. Column 2 stopped at Row 3, one row above → blue (≠).

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 #1

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

  1. Column 3 goes down to Row 2, so use Rule 2: look 2 columns 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.

Cockroach Pig · Mark #4

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

  1. Column 6 goes down to Row 2, so use Rule 2: look 3 columns back, at Column 3.
  2. Column 3 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 3 stopped exactly one row above this bead.

Verified Reference Data

Key Facts & Table Specifications

DR110 Target Coordinate
Rule 2 Case 2c Over-Depth Red

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

DR110 Rule Classification
Analytical Depth Audit

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

DR110 Depth Comparison
11 Big Road Cols

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

DR110 Misconception Focus
Diagnostic Check

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

DR110 GMU Modality Goal
Analytical Modality (Depth Vector Verification)

Explain why extending a long streak 2+ rows past d_{k-m} turns red (=) by computing the full column-depth vector [d_1, d_2, ..., d_k] across the shoe

DR110 · Coordinate & Rule Specification

DR110 Rule 2 Case 2c Over-Depth Red: Analytical Depth Audit Walkthrough

Drill DR110 pairs Rule 2 Case 2c Over-Depth Red with Analytical Depth Audit (Analytical Modality (Depth Vector Verification)), guiding learners through Continuing column row r >= d_{k-m} + 2 where two reference cells are empty across 11 Big Road columns in shoe PPBBBPPPP-BBPBBBBBP.

As DR110 demonstrates through computing the full column-depth vector [d_1, d_2, ..., d_k] across the shoe, This bead is at Row 4. Column 2 stopped at Row 3, one row above → blue (≠). The board's 17 Small Road and 13 Cockroach Pig symbols confirm Rule 2 Case 2c Consecutive Empty Reference Cells returning Red (=).

Table DR110: Rule 2 Case 2c Over-Depth Red specification under Analytical Depth Audit.
DR110 Drill DimensionCoordinate / RuleGMU Modality Action
DR110 Matrix CoordinateContinuing column row r >= d_{k-m} + 2 where two reference cells are emptyAnalytical Modality (Depth Vector Verification)
DR110 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+
DR110 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 (=)
  • DR110 Step 1: Locate Continuing column row r >= d_{k-m} + 2 where two reference cells are empty across the 11 columns of PPBBBPPPPBBP.
  • DR110 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 (=).
  • DR110 Step 3: Answer "How does the depth vector [d_1..d_k] determine all three derived roads?" via computing the full column-depth vector [d_1, d_2, ..., d_k] across the shoe.
DR110 · Analytical Modality (Depth Vector Verification)

DR110 Misconception Diagnostic & Secondary Road Audit

Follow-up verification DR110 (Analytical Depth Audit) observes: This bead is at Row 2. Column 1 has a bead at Row 2 too → red (=). Learners checking Both (k-m, r) and (k-m, r-1) are empty because r exceeds d_{k-m} by 2+ across 11 columns avoid forgetting rule 2's third case where two empty reference cells produce red (=).

Table Reality Check

Myth vs. Truth

MythIn DR110 (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
  • Cloud Shoe Log and cross-device progress on web, iOS, and Android