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FINAL TOTAL RESOLUTION [RES344] · 6-CARD PROOF

Player 1 + 7 (7) vs. Banker 5 (Draws 2 (2)): 6-Card Resolution #344

In walkthrough RES344, Player opens with 7+4 (1) and draws fifth-card 7 (7) for a modulo-10 total of 8, while Banker opens with 2+3 (5) and draws sixth-card 2 (2) for 7 (6-card P outcome).

RES344 Player Path
P:1->8
RES344 Banker Path
B:5->7
RES344 Deal Length
6 Cards
RES344 Showdown
P (8v7)
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 RES344 (P1+7->8 vs B5->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

RES344 Four-Card Opening Deal
Player 7+4=1 vs Banker 2+3=5

Verified non-natural start via handTotal([7,4])=1 and handTotal([2,3])=5.

RES344 Fifth-Card Modulo Proof
(1 + 7) mod 10 = 8 via 7

Player draws fifth-card 7 (value 7), transforming two-card 1 into three-card 8.

RES344 Banker Tableau Lookup
BANKER_TABLEAU[5][7] = true

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

RES344 Card Count & Winner
6 Cards -> P (8 vs 7)

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

RES344 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 · RES344

Step-by-Step Card Arithmetic for RES344: P(7+4)+7 vs B(2+3)

Arithmetic trace [RES344] starts from four-card deal 7+4=1 vs 2+3=5; Player's compulsory draw of 7 (pip value 7) produces raw 8, which wraps modulo-10 to 8.

[RES344-B] Six-card branch [RES344] activates as 7 (7) hits Banker 5's 5-point four-value window (4..7); drawing 2 (2) sends 5+2=7 to 7.

Complete 6-Card Resolution Trace for RES344
RES344 StageRES344 CardsRES344 Modulo MathRES344 Status
[RES344:Init]P(7+4)=1 vs B(2+3)=5playerShouldDraw(1)=true4-Card Deal
[RES344:5th]Player +7 (7)(1+7) mod 10 = 85th Card Sideways
[RES344:6th]Banker +2 (2)(5+2) mod 10 = 76-Card Final
[RES344:Settle]P=8 vs B=7Winner: PBig Road +P
  • [RES344-1] Confirm [RES344] opening P=1 (7+4) and B=5 (2+3) lack Natural 8/9.
  • [RES344-2] Add [RES344] fifth-card 7 (7) to P=1 for (1+7) mod 10 = 8.
  • [RES344-3] Run [RES344] BANKER_TABLEAU[5][7]=true to settle 8 vs 7 (P).
SETTLEMENT & SCOREBOARD · RES344

Showdown Settlement & Scoreboard Logging for RES344 (8 vs 7)

[RES344-C0] Comparing [RES344] final totals (6c), Player 8 vs Banker 7 awards [RES344] to Player (P), which pays 1:1 even money on [RES344] Player boxes with zero commission deducted and appends P to PPBBPBPBBB.

[RES344-D10] Side-bet & road check for [RES344] (P1+7->8 vs B5->7, 6c): [RES344] leaves [RES344] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=7) and triggers [RES344] Panda 8 (winning 3-card Player 8, 25:1); on [RES344] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES344, Banker 5 evaluates Player's three-card total (8) before deciding whether to draw.
TruthBanker 5 inspects only Player's fifth card 7 (value 7) via BANKER_TABLEAU[5][7] = true.
MythBecause RES344 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.
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  • Structured step-by-step track across Foundations, Big Eye Boy, Small Road, and Cockroach Pig
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