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FINAL TOTAL RESOLUTION [RES262] · 6-CARD PROOF

Player 3 + 3 (3) vs. Banker 4 (Draws 3 (3)): 6-Card Resolution #262

In walkthrough RES262, Player opens with 9+4 (3) and draws fifth-card 3 (3) for a modulo-10 total of 6, while Banker opens with A+3 (4) and draws sixth-card 3 (3) for 7 (6-card B outcome).

RES262 Player Path
P:3->6
RES262 Banker Path
B:4->7
RES262 Deal Length
6 Cards
RES262 Showdown
B (6v7)
Engine-Verified Scoreboard · 20 Hands

Read the Board at Table Speed

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

Scoreboard sequence paired with 6-card resolution RES262 (P3+3->6 vs B4->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

This bead is at Row 2. Column 2 has a bead at Row 2 too → red (=).

  1. Column 3 goes down to Row 2, so use Rule 2: look 1 column back, at Column 2.
  2. Column 2 has a bead at Row 2 too → red (=).

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.

Small Road Mark #3

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

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

Common table reading watchout: Comparing the wrong columns. Compare Column 4, the one that just finished, with Column 2.

Cockroach Pig Mark #3

Column 6 has 1 bead. Column 3 has 2 beads. Different depth → blue (≠).

  1. Column 7 starts, so use Rule 1: compare Column 6 with Column 3, 3 columns further back.
  2. Column 6 has 1 bead. Column 3 has 2 beads. Different depth → blue (≠).

Common table reading watchout: Comparing the wrong columns. Compare Column 6, the one that just finished, with Column 3.

Verified Reference Data

Key Facts & Table Specifications

RES262 Four-Card Opening Deal
Player 9+4=3 vs Banker A+3=4

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

RES262 Fifth-Card Modulo Proof
(3 + 3) mod 10 = 6 via 3

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

RES262 Banker Tableau Lookup
BANKER_TABLEAU[4][3] = true

Banker 4 draws sixth-card 3 (3) so (4+3) mod 10 = 7.

RES262 Card Count & Winner
6 Cards -> B (6 vs 7)

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

RES262 Derived Road Independence
Red (=) / Blue (≠) Symmetry Only

Big Eye Boy, Small Road, and Cockroach Pig compare Big Road column depths, not B vs P.

MODULO-10 ARITHMETIC · RES262

Step-by-Step Card Arithmetic for RES262: P(9+4)+3 vs B(A+3)

In coup [RES262], initial cards deal 9+4=3 to Player and A+3=4 to Banker; lacking a four-card natural, Player takes fifth-card 3 (3) where raw sum 6 projects onto the 0..9 ring to 6.

[RES262-B] Under 4-point six-value gate (2..7) for [RES262], exposed 3 (3) obligates Banker 4 to draw 3 (3), converting 4+3=7 into 7.

Complete 6-Card Resolution Trace for RES262
RES262 StageRES262 CardsRES262 Modulo MathRES262 Status
[RES262:Init]P(9+4)=3 vs B(A+3)=4playerShouldDraw(3)=true4-Card Deal
[RES262:5th]Player +3 (3)(3+3) mod 10 = 65th Card Sideways
[RES262:6th]Banker +3 (3)(4+3) mod 10 = 76-Card Final
[RES262:Settle]P=6 vs B=7Winner: BBig Road +B
  • [RES262-1] Confirm [RES262] opening P=3 (9+4) and B=4 (A+3) lack Natural 8/9.
  • [RES262-2] Add [RES262] fifth-card 3 (3) to P=3 for (3+3) mod 10 = 6.
  • [RES262-3] Run [RES262] BANKER_TABLEAU[4][3]=true to settle 6 vs 7 (B).
SETTLEMENT & SCOREBOARD · RES262

Showdown Settlement & Scoreboard Logging for RES262 (6 vs 7)

[RES262-C8] Comparing [RES262] final totals (6c), Player 6 vs Banker 7 awards [RES262] to Banker (B), which pays 0.95:1 on 5%-commission [RES262] layouts (or 0.5:1 on 6 at No-Commission [RES262] tables) and appends B to PPBBPPBPBP.

[RES262-D0] Side-bet & road check for [RES262] (P3+3->6 vs B4->7, 6c): [RES262] triggers [RES262] Dragon 7 (winning 3-card Banker 7, 40:1) and leaves [RES262] Panda 8 inactive (needs winning 3c Player 8, got P=6); on [RES262] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES262, Banker 4 evaluates Player's three-card total (6) before deciding whether to draw.
TruthBanker 4 inspects only Player's fifth card 3 (value 3) via BANKER_TABLEAU[4][3] = true.
MythBecause RES262 resolves as B, the next derived-road mark must match B'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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