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GMU ANALYTICAL · INDEX PROOF · DR239

Single-Jump Ping-Pong Run — Analytical Coordinate Proof (DR239)

DR239 pairs Single-Jump Ping-Pong Run (Alternating B-P-B-P columns of depth 1 across Big Road cols 1-6) with Analytical Modality (Formal Index Notation): learners verify Every completed column has d_k = 1, so d_{k-1} == d_{k-1-m} is true, master Rule 1 Depth-1 Parity Producing Red (=) Across Derived Roads, and eliminate expecting alternating b/p hands to produce blue marks on derived roads.

Drill Reference ID
DR239
Big Road Streaks
11 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 B P P B P P B
Big Eye Boy = ≠ ≠ = = ≠ ≠ = ≠ ≠ ≠ = = ≠ ≠ ≠ ≠ ≠ ≠ ≠
Small Road = ≠ = ≠ = ≠ ≠ = ≠ = ≠ = = ≠ = = =
Cockroach Pig = = ≠ = = = = ≠ ≠ ≠ ≠ ≠ ≠

DR239 drill board (BBPPPBBBBPPBPPPPTBPPBPPB): 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 #3

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

  1. Column 3 starts, so use Rule 1: compare Column 2 with Column 1, 1 column further back.
  2. Column 2 has 3 beads. Column 1 has 2 beads. Different depth → blue (≠).

Common table reading watchout: Comparing the wrong columns. Compare Column 2, the one that just finished, with Column 1.

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

DR239 Target Coordinate
Single-Jump Ping-Pong Run

Alternating B-P-B-P columns of depth 1 across Big Road cols 1-6

DR239 Rule Classification
Analytical Coordinate Proof

Rule 1 Depth-1 Parity Producing Red (=) Across Derived Roads

DR239 Depth Comparison
11 Big Road Cols

Every completed column has d_k = 1, so d_{k-1} == d_{k-1-m} is true

DR239 Misconception Focus
Diagnostic Check

Expecting alternating B/P hands to produce blue marks on derived roads

DR239 GMU Modality Goal
Analytical Modality (Formal Index Notation)

Understand why B-P-B-P chop generates solid red (=) derived streaks by writing out (k, r) and (k-m, r) coordinates to prove the derived output

DR239 · Coordinate & Rule Specification

DR239 Single-Jump Ping-Pong Run: Analytical Coordinate Proof Walkthrough

Throughout BBPPPBBBBPPBPPPPTB (11 columns, 20 Big Eye Boy marks), lesson DR239 uses Analytical Coordinate Proof to reinforce Single-Jump Ping-Pong Run and Every completed column has d_k = 1, so d_{k-1} == d_{k-1-m} is true.

In DR239 (Analytical Modality (Formal Index Notation)), mark verification begins: Column 2 has 3 beads. Column 1 has 2 beads. Different depth → blue (≠). Counting 17 Small Road and 13 Cockroach Pig entries prevents expecting alternating b/p hands to produce blue marks on derived roads.

Table DR239: Single-Jump Ping-Pong Run specification under Analytical Coordinate Proof.
DR239 Drill DimensionCoordinate / RuleGMU Modality Action
DR239 Matrix CoordinateAlternating B-P-B-P columns of depth 1 across Big Road cols 1-6Analytical Modality (Formal Index Notation)
DR239 Rule & DepthRule 1 Depth-1 Parity Producing Red (=) Across Derived RoadsEvery completed column has d_k = 1, so d_{k-1} == d_{k-1-m} is true
DR239 Diagnostic TargetExpecting alternating B/P hands to produce blue marks on derived roadsUnderstand why B-P-B-P chop generates solid red (=) derived streaks
  • DR239 Step 1: Locate Alternating B-P-B-P columns of depth 1 across Big Road cols 1-6 across the 11 columns of BBPPPBBBBPPB.
  • DR239 Step 2: Verify Every completed column has d_k = 1, so d_{k-1} == d_{k-1-m} is true under Rule 1 Depth-1 Parity Producing Red (=) Across Derived Roads.
  • DR239 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.
DR239 · Analytical Modality (Formal Index Notation)

DR239 Misconception Diagnostic & Secondary Road Audit

Cross-checking mark #2 in DR239, This bead is at Row 2. Column 2 has a bead at Row 2 too → red (=). With Analytical Modality (Formal Index Notation), Single-Jump Ping-Pong Run connects Alternating B-P-B-P columns of depth 1 across Big Road cols 1-6 to all 11 Big Road columns.

Table Reality Check

Myth vs. Truth

MythIn DR239 (Single-Jump Ping-Pong Run), expecting alternating b/p hands to produce blue marks on derived roads or reading red/blue derived marks as Banker/Player outcomes.
TruthRule 1 Depth-1 Parity Producing Red (=) Across Derived Roads evaluates Every completed column has d_k = 1, so d_{k-1} == d_{k-1-m} is true; 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
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