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GMU ANALYTICAL · INDEX PROOF · DR259

3-2-3-2 Depth Alternation — Analytical Coordinate Proof (DR259)

DR259 pairs 3-2-3-2 Depth Alternation (Big Road depths [3, 2, 3, 2] comparing m=1 vs m=2 lookbacks) with Analytical Modality (Formal Index Notation): learners verify For m=1, d_3=3 != d_2=2 (Blue); for m=2, d_3=3 == d_1=3 (Red), master Lookback Divergence: Big Eye Boy Blue vs Small Road Red, and eliminate assuming all three derived roads must show the same color on a hand.

Drill Reference ID
DR259
Big Road Streaks
10 Cols
Big Eye Boy Total
20 Marks
Small Road Total
17 Dots
Engine-Verified Scoreboard · 24 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 P B B P P
Big Eye Boy = ≠ ≠ = = ≠ ≠ = ≠ ≠ ≠ = = ≠ ≠ = ≠ ≠ = ≠
Small Road = ≠ = ≠ = ≠ ≠ = ≠ = ≠ = ≠ ≠ ≠ ≠ =
Cockroach Pig = = ≠ = = = = ≠ = = ≠ ≠ =

DR259 drill board (BBPPPBBBBPPBPPPPBPBBPPTP): 10 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 #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 #1

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

  1. Column 4 goes down to Row 2, so use Rule 2: look 3 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.

Verified Reference Data

Key Facts & Table Specifications

DR259 Target Coordinate
3-2-3-2 Depth Alternation

Big Road depths [3, 2, 3, 2] comparing m=1 vs m=2 lookbacks

DR259 Rule Classification
Analytical Coordinate Proof

Lookback Divergence: Big Eye Boy Blue vs Small Road Red

DR259 Depth Comparison
10 Big Road Cols

For m=1, d_3=3 != d_2=2 (Blue); for m=2, d_3=3 == d_1=3 (Red)

DR259 Misconception Focus
Diagnostic Check

Assuming all three derived roads must show the same color on a hand

DR259 GMU Modality Goal
Analytical Modality (Formal Index Notation)

Verify why Small Road (m=2) marks red while Big Eye Boy (m=1) marks blue by writing out (k, r) and (k-m, r) coordinates to prove the derived output

DR259 · Coordinate & Rule Specification

DR259 3-2-3-2 Depth Alternation: Analytical Coordinate Proof Walkthrough

Inside Analytical Modality (Formal Index Notation) (DR259), exercise 3-2-3-2 Depth Alternation targets Lookback Divergence: Big Eye Boy Blue vs Small Road Red while writing out (k, r) and (k-m, r) coordinates to prove the derived output produces 20 Big Eye Boy marks over BBPPPBBBB.

Within DR259, Analytical Modality (Formal Index Notation) highlights the primary mark: This bead is at Row 3. Column 2 has a bead at Row 3 too → red (=). Across 17 Small Road and 13 Cockroach Pig entries, For m=1, d_3=3 != d_2=2 (Blue); for m=2, d_3=3 == d_1=3 (Red) remains transparent.

Table DR259: 3-2-3-2 Depth Alternation specification under Analytical Coordinate Proof.
DR259 Drill DimensionCoordinate / RuleGMU Modality Action
DR259 Matrix CoordinateBig Road depths [3, 2, 3, 2] comparing m=1 vs m=2 lookbacksAnalytical Modality (Formal Index Notation)
DR259 Rule & DepthLookback Divergence: Big Eye Boy Blue vs Small Road RedFor m=1, d_3=3 != d_2=2 (Blue); for m=2, d_3=3 == d_1=3 (Red)
DR259 Diagnostic TargetAssuming all three derived roads must show the same color on a handVerify why Small Road (m=2) marks red while Big Eye Boy (m=1) marks blue
  • DR259 Step 1: Locate Big Road depths [3, 2, 3, 2] comparing m=1 vs m=2 lookbacks across the 10 columns of BBPPPBBBBPPB.
  • DR259 Step 2: Verify For m=1, d_3=3 != d_2=2 (Blue); for m=2, d_3=3 == d_1=3 (Red) under Lookback Divergence: Big Eye Boy Blue vs Small Road Red.
  • DR259 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.
DR259 · Analytical Modality (Formal Index Notation)

DR259 Misconception Diagnostic & Secondary Road Audit

Multi-road audit DR259 (3-2-3-2 Depth Alternation) shows: This bead is at Row 2. Column 2 has a bead at Row 2 too → red (=). Grounded in Analytical Modality (Formal Index Notation), readers verify Big Road depths [3, 2, 3, 2] comparing m=1 vs m=2 lookbacks across 10 Big Road columns.

Table Reality Check

Myth vs. Truth

MythIn DR259 (3-2-3-2 Depth Alternation), assuming all three derived roads must show the same color on a hand or reading red/blue derived marks as Banker/Player outcomes.
TruthLookback Divergence: Big Eye Boy Blue vs Small Road Red evaluates For m=1, d_3=3 != d_2=2 (Blue); for m=2, d_3=3 == d_1=3 (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
  • Cloud Shoe Log and cross-device progress on web, iOS, and Android