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FINAL TOTAL RESOLUTION [RES204] · 6-CARD PROOF

Player 5 + 3 (3) vs. Banker 3 (Draws 10 (0)): 6-Card Resolution #204

In walkthrough RES204, Player opens with A+4 (5) and draws fifth-card 3 (3) for a modulo-10 total of 8, while Banker opens with 10+3 (3) and draws sixth-card 10 (0) for 3 (6-card P outcome).

RES204 Player Path
P:5->8
RES204 Banker Path
B:3->3
RES204 Deal Length
6 Cards
RES204 Showdown
P (8v3)
Engine-Verified Scoreboard · 20 Hands

Read the Board at Table Speed

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

Scoreboard sequence paired with 6-card resolution RES204 (P5+3->8 vs B3->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

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

  1. Column 4 goes down to Row 3, so use Rule 2: look 2 columns back, at Column 2.
  2. Column 2 stopped at Row 2, one row above → blue (≠).

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

  1. Column 5 starts, so use Rule 1: compare Column 4 with Column 1, 3 columns further back.
  2. Column 4 has 3 beads. Column 1 has 2 beads. Different depth → blue (≠).

Common table reading watchout: Comparing the wrong columns. Compare Column 4, the one that just finished, with Column 1.

Verified Reference Data

Key Facts & Table Specifications

RES204 Four-Card Opening Deal
Player A+4=5 vs Banker 10+3=3

Verified non-natural start via handTotal([A,4])=5 and handTotal([10,3])=3.

RES204 Fifth-Card Modulo Proof
(5 + 3) mod 10 = 8 via 3

Player draws fifth-card 3 (value 3), transforming two-card 5 into three-card 8.

RES204 Banker Tableau Lookup
BANKER_TABLEAU[3][3] = true

Banker 3 draws sixth-card 10 (0) so (3+0) mod 10 = 3.

RES204 Card Count & Winner
6 Cards -> P (8 vs 3)

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

RES204 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 · RES204

Step-by-Step Card Arithmetic for RES204: P(A+4)+3 vs B(10+3)

Arithmetic trace [RES204] starts from four-card deal A+4=5 vs 10+3=3; Player's compulsory draw of 3 (pip value 3) produces raw 8, which wraps modulo-10 to 8.

[RES204-B] Next in [RES204], Banker consults 3-point single-shade row (0..7, 9): facing fifth-card 3 (3), Banker 3 draws 10 (0) so 3+0=3 -> 3.

Complete 6-Card Resolution Trace for RES204
RES204 StageRES204 CardsRES204 Modulo MathRES204 Status
[RES204:Init]P(A+4)=5 vs B(10+3)=3playerShouldDraw(5)=true4-Card Deal
[RES204:5th]Player +3 (3)(5+3) mod 10 = 85th Card Sideways
[RES204:6th]Banker +10 (0)(3+0) mod 10 = 36-Card Final
[RES204:Settle]P=8 vs B=3Winner: PBig Road +P
  • [RES204-1] Confirm [RES204] opening P=5 (A+4) and B=3 (10+3) lack Natural 8/9.
  • [RES204-2] Add [RES204] fifth-card 3 (3) to P=5 for (5+3) mod 10 = 8.
  • [RES204-3] Run [RES204] BANKER_TABLEAU[3][3]=true to settle 8 vs 3 (P).
SETTLEMENT & SCOREBOARD · RES204

Showdown Settlement & Scoreboard Logging for RES204 (8 vs 3)

[RES204-C4] Comparing [RES204] final totals (6c), Player 8 vs Banker 3 awards [RES204] to Player (P), which pays 1:1 even money on [RES204] Player boxes with zero commission deducted and appends P to PPBBPBBBPP.

[RES204-D11] Side-bet & road check for [RES204] (P5+3->8 vs B3->3, 6c): [RES204] leaves [RES204] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=3) and triggers [RES204] Panda 8 (winning 3-card Player 8, 25:1); on [RES204] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES204, Banker 3 evaluates Player's three-card total (8) before deciding whether to draw.
TruthBanker 3 inspects only Player's fifth card 3 (value 3) via BANKER_TABLEAU[3][3] = true.
MythBecause RES204 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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