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FINAL TOTAL RESOLUTION [RES040] · 6-CARD PROOF

Player 3 + 6 (6) vs. Banker 0 (Draws 6 (6)): 6-Card Resolution #40

In walkthrough RES040, Player opens with 9+4 (3) and draws fifth-card 6 (6) for a modulo-10 total of 9, while Banker opens with 6+4 (0) and draws sixth-card 6 (6) for 6 (6-card P outcome).

RES040 Player Path
P:3->9
RES040 Banker Path
B:0->6
RES040 Deal Length
6 Cards
RES040 Showdown
P (9v6)
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 RES040 (P3+6->9 vs B0->6).

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

RES040 Four-Card Opening Deal
Player 9+4=3 vs Banker 6+4=0

Verified non-natural start via handTotal([9,4])=3 and handTotal([6,4])=0.

RES040 Fifth-Card Modulo Proof
(3 + 6) mod 10 = 9 via 6

Player draws fifth-card 6 (value 6), transforming two-card 3 into three-card 9.

RES040 Banker Tableau Lookup
BANKER_TABLEAU[0][6] = true

Banker 0 draws sixth-card 6 (6) so (0+6) mod 10 = 6.

RES040 Card Count & Winner
6 Cards -> P (9 vs 6)

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

RES040 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 · RES040

Step-by-Step Card Arithmetic for RES040: P(9+4)+6 vs B(6+4)

Floor verification [RES040] inspects Player 9+4 (3) versus Banker 6+4 (0); once fifth-card 6 (6) is exposed sideways, 3+6=9 drops the tens digit to three-card 9.

[RES040-B] Under 0-point unconditional draw tier for [RES040], exposed 6 (6) obligates Banker 0 to draw 6 (6), converting 0+6=6 into 6.

Complete 6-Card Resolution Trace for RES040
RES040 StageRES040 CardsRES040 Modulo MathRES040 Status
[RES040:Init]P(9+4)=3 vs B(6+4)=0playerShouldDraw(3)=true4-Card Deal
[RES040:5th]Player +6 (6)(3+6) mod 10 = 95th Card Sideways
[RES040:6th]Banker +6 (6)(0+6) mod 10 = 66-Card Final
[RES040:Settle]P=9 vs B=6Winner: PBig Road +P
  • [RES040-1] Confirm [RES040] opening P=3 (9+4) and B=0 (6+4) lack Natural 8/9.
  • [RES040-2] Add [RES040] fifth-card 6 (6) to P=3 for (3+6) mod 10 = 9.
  • [RES040-3] Run [RES040] BANKER_TABLEAU[0][6]=true to settle 9 vs 6 (P).
SETTLEMENT & SCOREBOARD · RES040

Showdown Settlement & Scoreboard Logging for RES040 (9 vs 6)

[RES040-C9] Comparing [RES040] final totals (6c), Player 9 vs Banker 6 awards [RES040] to Player (P), which pays 1:1 even money on [RES040] Player boxes with zero commission deducted and appends P to PPBBPBPBBB.

[RES040-D4] Side-bet & road check for [RES040] (P3+6->9 vs B0->6, 6c): [RES040] leaves [RES040] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=6) and leaves [RES040] Panda 8 inactive (needs winning 3c Player 8, got P=9); on [RES040] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES040, Banker 0 evaluates Player's three-card total (9) before deciding whether to draw.
TruthBanker 0 inspects only Player's fifth card 6 (value 6) via BANKER_TABLEAU[0][6] = true.
MythBecause RES040 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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