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FINAL TOTAL RESOLUTION [RES343] · 6-CARD PROOF

Player 0 + 7 (7) vs. Banker 5 (Draws 8 (8)): 6-Card Resolution #343

In walkthrough RES343, Player opens with 10+K (0) and draws fifth-card 7 (7) for a modulo-10 total of 7, while Banker opens with A+4 (5) and draws sixth-card 8 (8) for 3 (6-card P outcome).

RES343 Player Path
P:0->7
RES343 Banker Path
B:5->3
RES343 Deal Length
6 Cards
RES343 Showdown
P (7v3)
Engine-Verified Scoreboard · 20 Hands

Read the Board at Table Speed

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

Scoreboard sequence paired with 6-card resolution RES343 (P0+7->7 vs B5->3).

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

RES343 Four-Card Opening Deal
Player 10+K=0 vs Banker A+4=5

Verified non-natural start via handTotal([10,K])=0 and handTotal([A,4])=5.

RES343 Fifth-Card Modulo Proof
(0 + 7) mod 10 = 7 via 7

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

RES343 Banker Tableau Lookup
BANKER_TABLEAU[5][7] = true

Banker 5 draws sixth-card 8 (8) so (5+8) mod 10 = 3.

RES343 Card Count & Winner
6 Cards -> P (7 vs 3)

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

RES343 Derived Road Independence
Red (=) / Blue (≠) Symmetry Only

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

MODULO-10 ARITHMETIC · RES343

Step-by-Step Card Arithmetic for RES343: P(10+K)+7 vs B(A+4)

Matrix coordinate [RES343] isolates Player two-card 0 (10+K) and Banker 5 (A+4); dealing fifth-card 7 (7) yields raw 7 that retains the rightmost digit to 7.

[RES343-B] Six-card branch [RES343] activates as 7 (7) hits Banker 5's 5-point four-value window (4..7); drawing 8 (8) sends 5+8=13 to 3.

Complete 6-Card Resolution Trace for RES343
RES343 StageRES343 CardsRES343 Modulo MathRES343 Status
[RES343:Init]P(10+K)=0 vs B(A+4)=5playerShouldDraw(0)=true4-Card Deal
[RES343:5th]Player +7 (7)(0+7) mod 10 = 75th Card Sideways
[RES343:6th]Banker +8 (8)(5+8) mod 10 = 36-Card Final
[RES343:Settle]P=7 vs B=3Winner: PBig Road +P
  • [RES343-1] Confirm [RES343] opening P=0 (10+K) and B=5 (A+4) lack Natural 8/9.
  • [RES343-2] Add [RES343] fifth-card 7 (7) to P=0 for (0+7) mod 10 = 7.
  • [RES343-3] Run [RES343] BANKER_TABLEAU[5][7]=true to settle 7 vs 3 (P).
SETTLEMENT & SCOREBOARD · RES343

Showdown Settlement & Scoreboard Logging for RES343 (7 vs 3)

[RES343-C6] Comparing [RES343] final totals (6c), Player 7 vs Banker 3 awards [RES343] to Player (P), which pays 1:1 even money on [RES343] Player boxes with zero commission deducted and appends P to BBPPBPBPPP.

[RES343-D1] Side-bet & road check for [RES343] (P0+7->7 vs B5->3, 6c): [RES343] leaves [RES343] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=3) and leaves [RES343] Panda 8 inactive (needs winning 3c Player 8, got P=7); on [RES343] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES343, Banker 5 evaluates Player's three-card total (7) before deciding whether to draw.
TruthBanker 5 inspects only Player's fifth card 7 (value 7) via BANKER_TABLEAU[5][7] = true.
MythBecause RES343 resolves as P, the next derived-road mark must match P'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

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  • Structured step-by-step track across Foundations, Big Eye Boy, Small Road, and Cockroach Pig
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