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GMU ANALYTICAL · INDEX PROOF · DR209

Banker 4 vs 2-7 Third Card — Analytical Coordinate Proof (DR209)

DR209 pairs Banker 4 vs 2-7 Third Card (Banker two-card 4 evaluating Player's third card in [2..7]) with Analytical Modality (Formal Index Notation): learners verify Banker draws on Player third card 2,3,4,5,6,7 and stands on 0,1,8,9, master Banker Total-4 Conditional Tableau Window (Draw on 2-7), and eliminate comparing banker 4 against player's three-card total instead of the third card.

Drill Reference ID
DR209
Big Road Streaks
8 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 P B B B P
Big Eye Boy = ≠ ≠ = = ≠ ≠ = ≠ ≠ ≠ = = = = ≠ = = ≠
Small Road = ≠ = ≠ = ≠ ≠ = ≠ = = = ≠ ≠ = ≠
Cockroach Pig = = ≠ = = = ≠ = ≠ = ≠ ≠

DR209 drill board (BBPPPBBBBPPBPPPPPPBBBP): 8 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 #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 #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

DR209 Target Coordinate
Banker 4 vs 2-7 Third Card

Banker two-card 4 evaluating Player's third card in [2..7]

DR209 Rule Classification
Analytical Coordinate Proof

Banker Total-4 Conditional Tableau Window (Draw on 2-7)

DR209 Depth Comparison
8 Big Road Cols

Banker draws on Player third card 2,3,4,5,6,7 and stands on 0,1,8,9

DR209 Misconception Focus
Diagnostic Check

Comparing Banker 4 against Player's three-card total instead of the third card

DR209 GMU Modality Goal
Analytical Modality (Formal Index Notation)

Evaluate only Player's third card rank when Banker holds two-card 4 by writing out (k, r) and (k-m, r) coordinates to prove the derived output

DR209 · Coordinate & Rule Specification

DR209 Banker 4 vs 2-7 Third Card: Analytical Coordinate Proof Walkthrough

Under Analytical Coordinate Proof (DR209), Banker 4 vs 2-7 Third Card isolates Banker two-card 4 evaluating Player's third card in [2..7] and Banker draws on Player third card 2,3,4,5,6,7 and stands on 0,1,8,9, turning BBPPPBBBB-PPBPPPPPP into a hands-on 19-mark verification.

Applying Banker Total-4 Conditional Tableau Window (Draw on 2-7) in DR209, Column 2 has 3 beads. Column 1 has 2 beads. Different depth → blue (≠). Those 16 Small Road dots and 12 Cockroach Pig slashes accompany Banker two-card 4 evaluating Player's third card in [2..7] during writing out (k, r) and (k-m, r) coordinates to prove the derived output.

Table DR209: Banker 4 vs 2-7 Third Card specification under Analytical Coordinate Proof.
DR209 Drill DimensionCoordinate / RuleGMU Modality Action
DR209 Matrix CoordinateBanker two-card 4 evaluating Player's third card in [2..7]Analytical Modality (Formal Index Notation)
DR209 Rule & DepthBanker Total-4 Conditional Tableau Window (Draw on 2-7)Banker draws on Player third card 2,3,4,5,6,7 and stands on 0,1,8,9
DR209 Diagnostic TargetComparing Banker 4 against Player's three-card total instead of the third cardEvaluate only Player's third card rank when Banker holds two-card 4
  • DR209 Step 1: Locate Banker two-card 4 evaluating Player's third card in [2..7] across the 8 columns of BBPPPBBBBPPB.
  • DR209 Step 2: Verify Banker draws on Player third card 2,3,4,5,6,7 and stands on 0,1,8,9 under Banker Total-4 Conditional Tableau Window (Draw on 2-7).
  • DR209 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.
DR209 · Analytical Modality (Formal Index Notation)

DR209 Misconception Diagnostic & Secondary Road Audit

Inside DR209 (GMU ANALYTICAL · INDEX PROOF), This bead is at Row 2. Column 2 has a bead at Row 2 too → red (=). Every step of Banker Total-4 Conditional Tableau Window (Draw on 2-7) and Banker draws on Player third card 2,3,4,5,6,7 and stands on 0,1,8,9 holds across 8 columns.

Table Reality Check

Myth vs. Truth

MythIn DR209 (Banker 4 vs 2-7 Third Card), comparing banker 4 against player's three-card total instead of the third card or reading red/blue derived marks as Banker/Player outcomes.
TruthBanker Total-4 Conditional Tableau Window (Draw on 2-7) evaluates Banker draws on Player third card 2,3,4,5,6,7 and stands on 0,1,8,9; 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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