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FINAL TOTAL RESOLUTION [RES267] · 6-CARD PROOF

Player 2 + 4 (4) vs. Banker 4 (Draws 8 (8)): 6-Card Resolution #267

In walkthrough RES267, Player opens with 10+2 (2) and draws fifth-card 4 (4) for a modulo-10 total of 6, while Banker opens with 2+2 (4) and draws sixth-card 8 (8) for 2 (6-card P outcome).

RES267 Player Path
P:2->6
RES267 Banker Path
B:4->2
RES267 Deal Length
6 Cards
RES267 Showdown
P (6v2)
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 RES267 (P2+4->6 vs B4->2).

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

RES267 Four-Card Opening Deal
Player 10+2=2 vs Banker 2+2=4

Verified non-natural start via handTotal([10,2])=2 and handTotal([2,2])=4.

RES267 Fifth-Card Modulo Proof
(2 + 4) mod 10 = 6 via 4

Player draws fifth-card 4 (value 4), transforming two-card 2 into three-card 6.

RES267 Banker Tableau Lookup
BANKER_TABLEAU[4][4] = true

Banker 4 draws sixth-card 8 (8) so (4+8) mod 10 = 2.

RES267 Card Count & Winner
6 Cards -> P (6 vs 2)

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

RES267 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 · RES267

Step-by-Step Card Arithmetic for RES267: P(10+2)+4 vs B(2+2)

[RES267] Walkthrough #267 begins with Player holding 10+2 (2) against Banker 2+2 (4); since neither side holds 8 or 9, Player draws fifth-card 4 (4) so 2+4=6 applies base-10 modular addition to 6.

[RES267-B] Triggered by 4 (4) in [RES267] (4-point six-value gate (2..7)), Banker 4 receives 8 (8) and computes (4+8) mod 10 = 2.

Complete 6-Card Resolution Trace for RES267
RES267 StageRES267 CardsRES267 Modulo MathRES267 Status
[RES267:Init]P(10+2)=2 vs B(2+2)=4playerShouldDraw(2)=true4-Card Deal
[RES267:5th]Player +4 (4)(2+4) mod 10 = 65th Card Sideways
[RES267:6th]Banker +8 (8)(4+8) mod 10 = 26-Card Final
[RES267:Settle]P=6 vs B=2Winner: PBig Road +P
  • [RES267-1] Confirm [RES267] opening P=2 (10+2) and B=4 (2+2) lack Natural 8/9.
  • [RES267-2] Add [RES267] fifth-card 4 (4) to P=2 for (2+4) mod 10 = 6.
  • [RES267-3] Run [RES267] BANKER_TABLEAU[4][4]=true to settle 6 vs 2 (P).
SETTLEMENT & SCOREBOARD · RES267

Showdown Settlement & Scoreboard Logging for RES267 (6 vs 2)

[RES267-C0] Comparing [RES267] final totals (6c), Player 6 vs Banker 2 awards [RES267] to Player (P), which pays 1:1 even money on [RES267] Player boxes with zero commission deducted and appends P to BBPPBPPPBB.

[RES267-D6] Side-bet & road check for [RES267] (P2+4->6 vs B4->2, 6c): [RES267] leaves [RES267] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=2) and leaves [RES267] Panda 8 inactive (needs winning 3c Player 8, got P=6); on [RES267] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES267, Banker 4 evaluates Player's three-card total (6) before deciding whether to draw.
TruthBanker 4 inspects only Player's fifth card 4 (value 4) via BANKER_TABLEAU[4][4] = true.
MythBecause RES267 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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