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FINAL TOTAL RESOLUTION [RES043] · 6-CARD PROOF

Player 0 + 7 (7) vs. Banker 0 (Draws 3 (3)): 6-Card Resolution #43

In walkthrough RES043, Player opens with 10+K (0) and draws fifth-card 7 (7) for a modulo-10 total of 7, while Banker opens with 10+K (0) and draws sixth-card 3 (3) for 3 (6-card P outcome).

RES043 Player Path
P:0->7
RES043 Banker Path
B:0->3
RES043 Deal Length
6 Cards
RES043 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 P P B B B B P B B P P B B P
Big Eye Boy = = ≠ ≠ = ≠ = = ≠ ≠ ≠ ≠ ≠ = = = =
Small Road ≠ = ≠ ≠ ≠ = = ≠ ≠ = ≠ ≠ ≠ = =
Cockroach Pig = ≠ ≠ = ≠ = ≠ = = ≠ = ≠ ≠ ≠

Scoreboard sequence paired with 6-card resolution RES043 (P0+7->7 vs B0->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

RES043 Four-Card Opening Deal
Player 10+K=0 vs Banker 10+K=0

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

RES043 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.

RES043 Banker Tableau Lookup
BANKER_TABLEAU[0][7] = true

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

RES043 Card Count & Winner
6 Cards -> P (7 vs 3)

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

RES043 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 · RES043

Step-by-Step Card Arithmetic for RES043: P(10+K)+7 vs B(10+K)

[RES043] Walkthrough #43 begins with Player holding 10+K (0) against Banker 10+K (0); since neither side holds 8 or 9, Player draws fifth-card 7 (7) so 0+7=7 applies base-10 modular addition to 7.

[RES043-B] Evaluating bankerShouldDraw(0, 7)=true (0-point unconditional draw tier) in [RES043], sixth-card 3 (3) advances Banker 0 via 0+3=3 to 3.

Complete 6-Card Resolution Trace for RES043
RES043 StageRES043 CardsRES043 Modulo MathRES043 Status
[RES043:Init]P(10+K)=0 vs B(10+K)=0playerShouldDraw(0)=true4-Card Deal
[RES043:5th]Player +7 (7)(0+7) mod 10 = 75th Card Sideways
[RES043:6th]Banker +3 (3)(0+3) mod 10 = 36-Card Final
[RES043:Settle]P=7 vs B=3Winner: PBig Road +P
  • [RES043-1] Confirm [RES043] opening P=0 (10+K) and B=0 (10+K) lack Natural 8/9.
  • [RES043-2] Add [RES043] fifth-card 7 (7) to P=0 for (0+7) mod 10 = 7.
  • [RES043-3] Run [RES043] BANKER_TABLEAU[0][7]=true to settle 7 vs 3 (P).
SETTLEMENT & SCOREBOARD · RES043

Showdown Settlement & Scoreboard Logging for RES043 (7 vs 3)

[RES043-C2] Comparing [RES043] final totals (6c), Player 7 vs Banker 3 awards [RES043] to Player (P), which pays 1:1 even money on [RES043] Player boxes with zero commission deducted and appends P to BBPPBPPPBB.

[RES043-D5] Side-bet & road check for [RES043] (P0+7->7 vs B0->3, 6c): [RES043] leaves [RES043] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=3) and leaves [RES043] Panda 8 inactive (needs winning 3c Player 8, got P=7); on [RES043] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES043, Banker 0 evaluates Player's three-card total (7) before deciding whether to draw.
TruthBanker 0 inspects only Player's fifth card 7 (value 7) via BANKER_TABLEAU[0][7] = true.
MythBecause RES043 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

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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