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FINAL TOTAL RESOLUTION [RES166] · 6-CARD PROOF

Player 3 + 7 (7) vs. Banker 2 (Draws 7 (7)): 6-Card Resolution #166

In walkthrough RES166, Player opens with 9+4 (3) and draws fifth-card 7 (7) for a modulo-10 total of 0, while Banker opens with 8+4 (2) and draws sixth-card 7 (7) for 9 (6-card B outcome).

RES166 Player Path
P:3->0
RES166 Banker Path
B:2->9
RES166 Deal Length
6 Cards
RES166 Showdown
B (0v9)
Engine-Verified Scoreboard · 20 Hands

Read the Board at Table Speed

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Big Road P P B B P P B P B P P B B B P P P P B B
Big Eye Boy = = = = ≠ = = ≠ ≠ = ≠ ≠ = = ≠ ≠ =
Small Road = = ≠ ≠ = ≠ ≠ ≠ = ≠ = ≠ = ≠ =
Cockroach Pig ≠ ≠ ≠ ≠ ≠ ≠ = ≠ ≠ = = ≠ =

Scoreboard sequence paired with 6-card resolution RES166 (P3+7->0 vs B2->9).

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

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

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

Small Road Mark #3

Column 4 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).

  1. Column 5 starts, so use Rule 1: compare Column 4 with Column 2, 2 columns further back.
  2. Column 4 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).

Common table reading watchout: Comparing the wrong columns. Compare Column 4, the one that just finished, with Column 2.

Cockroach Pig Mark #3

Column 6 has 1 bead. Column 3 has 2 beads. Different depth → blue (≠).

  1. Column 7 starts, so use Rule 1: compare Column 6 with Column 3, 3 columns further back.
  2. Column 6 has 1 bead. Column 3 has 2 beads. Different depth → blue (≠).

Common table reading watchout: Comparing the wrong columns. Compare Column 6, the one that just finished, with Column 3.

Verified Reference Data

Key Facts & Table Specifications

RES166 Four-Card Opening Deal
Player 9+4=3 vs Banker 8+4=2

Verified non-natural start via handTotal([9,4])=3 and handTotal([8,4])=2.

RES166 Fifth-Card Modulo Proof
(3 + 7) mod 10 = 0 via 7

Player draws fifth-card 7 (value 7), transforming two-card 3 into three-card 0.

RES166 Banker Tableau Lookup
BANKER_TABLEAU[2][7] = true

Banker 2 draws sixth-card 7 (7) so (2+7) mod 10 = 9.

RES166 Card Count & Winner
6 Cards -> B (0 vs 9)

Computed directly from resolveHand() with zero discretionary dealer options.

RES166 Derived Road Independence
Red (=) / Blue (≠) Symmetry Only

Big Eye Boy, Small Road, and Cockroach Pig compare Big Road column depths, not B vs P.

MODULO-10 ARITHMETIC · RES166

Step-by-Step Card Arithmetic for RES166: P(9+4)+7 vs B(8+4)

Floor verification [RES166] inspects Player 9+4 (3) versus Banker 8+4 (2); once fifth-card 7 (7) is exposed sideways, 3+7=10 drops the tens digit to three-card 0.

[RES166-B] Because BANKER_TABLEAU[2][7]=true (2-point mandatory draw band) in [RES166], Banker 2 takes sixth-card 7 (7) and 2+7=9 settles at 9.

Complete 6-Card Resolution Trace for RES166
RES166 StageRES166 CardsRES166 Modulo MathRES166 Status
[RES166:Init]P(9+4)=3 vs B(8+4)=2playerShouldDraw(3)=true4-Card Deal
[RES166:5th]Player +7 (7)(3+7) mod 10 = 05th Card Sideways
[RES166:6th]Banker +7 (7)(2+7) mod 10 = 96-Card Final
[RES166:Settle]P=0 vs B=9Winner: BBig Road +B
  • [RES166-1] Confirm [RES166] opening P=3 (9+4) and B=2 (8+4) lack Natural 8/9.
  • [RES166-2] Add [RES166] fifth-card 7 (7) to P=3 for (3+7) mod 10 = 0.
  • [RES166-3] Run [RES166] BANKER_TABLEAU[2][7]=true to settle 0 vs 9 (B).
SETTLEMENT & SCOREBOARD · RES166

Showdown Settlement & Scoreboard Logging for RES166 (0 vs 9)

[RES166-C1] Comparing [RES166] final totals (6c), Player 0 vs Banker 9 awards [RES166] to Banker (B), which pays 0.95:1 on 5%-commission [RES166] layouts (or 0.5:1 on 6 at No-Commission [RES166] tables) and appends B to PPBBPPBPBP.

[RES166-D7] Side-bet & road check for [RES166] (P3+7->0 vs B2->9, 6c): [RES166] leaves [RES166] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=9) and leaves [RES166] Panda 8 inactive (needs winning 3c Player 8, got P=0); on [RES166] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES166, Banker 2 evaluates Player's three-card total (0) before deciding whether to draw.
TruthBanker 2 inspects only Player's fifth card 7 (value 7) via BANKER_TABLEAU[2][7] = true.
MythBecause RES166 resolves as B, the next derived-road mark must match B's colour.
TruthDerived roads record Red (=) when Big Road structure repeats and Blue (≠) when it breaks—never Banker or Player.
6 modules · 36 lessons · $25/month · Module 1 (10 lessons) free

Read Every Derived Road at Table Speed

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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
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