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GMU ANALYTICAL · INDEX PROOF · DR069

Rule 1 Equal Depth Red (=) — Analytical Coordinate Proof (DR069)

DR069 pairs Rule 1 Equal Depth Red (=) (New Big Road column row 1 with d_{k-1} == d_{k-1-m}) with Analytical Modality (Formal Index Notation): learners verify Prior column depth d_{k-1} = 2 matches reference depth d_{k-1-m} = 2, master Rule 1 Column-Switch Equality Case returning Red (=), and eliminate reading a red rule 1 mark as a banker win rather than equal column depth.

Drill Reference ID
DR069
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 = = ≠ = = = ≠ ≠ ≠ = = ≠

DR069 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

DR069 Target Coordinate
Rule 1 Equal Depth Red (=)

New Big Road column row 1 with d_{k-1} == d_{k-1-m}

DR069 Rule Classification
Analytical Coordinate Proof

Rule 1 Column-Switch Equality Case returning Red (=)

DR069 Depth Comparison
10 Big Road Cols

Prior column depth d_{k-1} = 2 matches reference depth d_{k-1-m} = 2

DR069 Misconception Focus
Diagnostic Check

Reading a red Rule 1 mark as a Banker win rather than equal column depth

DR069 GMU Modality Goal
Analytical Modality (Formal Index Notation)

Confirm two completed columns share identical depth before marking red by writing out (k, r) and (k-m, r) coordinates to prove the derived output

DR069 · Coordinate & Rule Specification

DR069 Rule 1 Equal Depth Red (=): Analytical Coordinate Proof Walkthrough

Guided by Analytical Modality (Formal Index Notation), drill DR069 walks through Rule 1 Equal Depth Red (=) (Rule 1 Column-Switch Equality Case returning Red (=)) across 10 Big Road streaks and 19 derived marks in BBPPPBBBB-PPBPPPPPB.

For coordinate New Big Road column row 1 with d_{k-1} == d_{k-1-m} in DR069, 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 DR069: Rule 1 Equal Depth Red (=) specification under Analytical Coordinate Proof.
DR069 Drill DimensionCoordinate / RuleGMU Modality Action
DR069 Matrix CoordinateNew Big Road column row 1 with d_{k-1} == d_{k-1-m}Analytical Modality (Formal Index Notation)
DR069 Rule & DepthRule 1 Column-Switch Equality Case returning Red (=)Prior column depth d_{k-1} = 2 matches reference depth d_{k-1-m} = 2
DR069 Diagnostic TargetReading a red Rule 1 mark as a Banker win rather than equal column depthConfirm two completed columns share identical depth before marking red
  • DR069 Step 1: Locate New Big Road column row 1 with d_{k-1} == d_{k-1-m} across the 10 columns of BBPPPBBBBPPB.
  • DR069 Step 2: Verify Prior column depth d_{k-1} = 2 matches reference depth d_{k-1-m} = 2 under Rule 1 Column-Switch Equality Case returning Red (=).
  • DR069 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.
DR069 · Analytical Modality (Formal Index Notation)

DR069 Misconception Diagnostic & Secondary Road Audit

Closing DR069 (Rule 1 Equal Depth Red (=) · Analytical Coordinate Proof), This bead is at Row 2. Column 2 has a bead at Row 2 too → red (=). Mastering Rule 1 Column-Switch Equality Case returning Red (=) over 10 columns builds lasting scoreboard accuracy.

Table Reality Check

Myth vs. Truth

MythIn DR069 (Rule 1 Equal Depth Red (=)), reading a red rule 1 mark as a banker win rather than equal column depth or reading red/blue derived marks as Banker/Player outcomes.
TruthRule 1 Column-Switch Equality Case returning Red (=) evaluates Prior column depth d_{k-1} = 2 matches reference depth d_{k-1-m} = 2; derived road colors reflect structural symmetry only and never alter independent shoe probabilities.
6 modules · 36 lessons · $25/month · Module 1 (10 lessons) free

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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