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FINAL TOTAL RESOLUTION [RES168] · 6-CARD PROOF

Player 5 + 7 (7) vs. Banker 2 (Draws 5 (5)): 6-Card Resolution #168

In walkthrough RES168, Player opens with A+4 (5) and draws fifth-card 7 (7) for a modulo-10 total of 2, while Banker opens with 8+4 (2) and draws sixth-card 5 (5) for 7 (6-card B outcome).

RES168 Player Path
P:5->2
RES168 Banker Path
B:2->7
RES168 Deal Length
6 Cards
RES168 Showdown
B (2v7)
Engine-Verified Scoreboard · 20 Hands

Read the Board at Table Speed

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

Scoreboard sequence paired with 6-card resolution RES168 (P5+7->2 vs B2->7).

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

  1. Column 4 starts, so use Rule 1: compare Column 3 with Column 2, 1 column further back.
  2. Column 3 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).

Common table reading watchout: Comparing the wrong columns. Compare Column 3, the one that just finished, with Column 2.

Small Road Mark #3

Column 5 has 1 bead. Column 3 has 1 bead. Same depth → red (=).

  1. Column 6 starts, so use Rule 1: compare Column 5 with Column 3, 2 columns further back.
  2. Column 5 has 1 bead. Column 3 has 1 bead. Same depth → red (=).

Common table reading watchout: Comparing the wrong columns. Compare Column 5, the one that just finished, with Column 3.

Cockroach Pig Mark #3

This bead is at Row 2. Column 3 stopped at Row 1, one row above → blue (≠).

  1. Column 6 goes down to Row 2, so use Rule 2: look 3 columns back, at Column 3.
  2. Column 3 stopped at Row 1, one row above → blue (≠).

Common table reading watchout: Thinking "no bead at this row" means blue. It is blue only when Column 3 stopped exactly one row above this bead.

Verified Reference Data

Key Facts & Table Specifications

RES168 Four-Card Opening Deal
Player A+4=5 vs Banker 8+4=2

Verified non-natural start via handTotal([A,4])=5 and handTotal([8,4])=2.

RES168 Fifth-Card Modulo Proof
(5 + 7) mod 10 = 2 via 7

Player draws fifth-card 7 (value 7), transforming two-card 5 into three-card 2.

RES168 Banker Tableau Lookup
BANKER_TABLEAU[2][7] = true

Banker 2 draws sixth-card 5 (5) so (2+5) mod 10 = 7.

RES168 Card Count & Winner
6 Cards -> B (2 vs 7)

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

RES168 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 · RES168

Step-by-Step Card Arithmetic for RES168: P(A+4)+7 vs B(8+4)

Step-by-step proof [RES168] pairs Player A+4 (5) with Banker 8+4 (2); because 5 sits in the 0..5 draw zone, fifth-card 7 (7) lands and 5+7=12 resolves the unit-digit sum to 2.

[RES168-B] Acting on 7=7 inside [RES168], Banker 2 follows 2-point mandatory draw band and pulls 5 (5) for 2+5=7 -> 7.

Complete 6-Card Resolution Trace for RES168
RES168 StageRES168 CardsRES168 Modulo MathRES168 Status
[RES168:Init]P(A+4)=5 vs B(8+4)=2playerShouldDraw(5)=true4-Card Deal
[RES168:5th]Player +7 (7)(5+7) mod 10 = 25th Card Sideways
[RES168:6th]Banker +5 (5)(2+5) mod 10 = 76-Card Final
[RES168:Settle]P=2 vs B=7Winner: BBig Road +B
  • [RES168-1] Confirm [RES168] opening P=5 (A+4) and B=2 (8+4) lack Natural 8/9.
  • [RES168-2] Add [RES168] fifth-card 7 (7) to P=5 for (5+7) mod 10 = 2.
  • [RES168-3] Run [RES168] BANKER_TABLEAU[2][7]=true to settle 2 vs 7 (B).
SETTLEMENT & SCOREBOARD · RES168

Showdown Settlement & Scoreboard Logging for RES168 (2 vs 7)

[RES168-C0] Comparing [RES168] final totals (6c), Player 2 vs Banker 7 awards [RES168] to Banker (B), which pays 0.95:1 on 5%-commission [RES168] layouts (or 0.5:1 on 6 at No-Commission [RES168] tables) and appends B to PPBBPBPBBB.

[RES168-D12] Side-bet & road check for [RES168] (P5+7->2 vs B2->7, 6c): [RES168] triggers [RES168] Dragon 7 (winning 3-card Banker 7, 40:1) and leaves [RES168] Panda 8 inactive (needs winning 3c Player 8, got P=2); on [RES168] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES168, Banker 2 evaluates Player's three-card total (2) before deciding whether to draw.
TruthBanker 2 inspects only Player's fifth card 7 (value 7) via BANKER_TABLEAU[2][7] = true.
MythBecause RES168 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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