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FINAL TOTAL RESOLUTION [RES268] · 6-CARD PROOF

Player 3 + 4 (4) vs. Banker 4 (Draws 2 (2)): 6-Card Resolution #268

In walkthrough RES268, Player opens with 9+4 (3) and draws fifth-card 4 (4) for a modulo-10 total of 7, while Banker opens with A+3 (4) and draws sixth-card 2 (2) for 6 (6-card P outcome).

RES268 Player Path
P:3->7
RES268 Banker Path
B:4->6
RES268 Deal Length
6 Cards
RES268 Showdown
P (7v6)
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 RES268 (P3+4->7 vs B4->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

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

RES268 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.

RES268 Fifth-Card Modulo Proof
(3 + 4) mod 10 = 7 via 4

Player draws fifth-card 4 (value 4), transforming two-card 3 into three-card 7.

RES268 Banker Tableau Lookup
BANKER_TABLEAU[4][4] = true

Banker 4 draws sixth-card 2 (2) so (4+2) mod 10 = 6.

RES268 Card Count & Winner
6 Cards -> P (7 vs 6)

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

RES268 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 · RES268

Step-by-Step Card Arithmetic for RES268: P(9+4)+4 vs B(A+3)

Engine check [RES268] confirms `playerShouldDraw(3) === true` on 9+4 vs Banker A+3 (4); adding fifth-card 4 (4) gives 7, which evaluates modulo ten to 7.

[RES268-B] Next in [RES268], Banker consults 4-point six-value gate (2..7): facing fifth-card 4 (4), Banker 4 draws 2 (2) so 4+2=6 -> 6.

Complete 6-Card Resolution Trace for RES268
RES268 StageRES268 CardsRES268 Modulo MathRES268 Status
[RES268:Init]P(9+4)=3 vs B(A+3)=4playerShouldDraw(3)=true4-Card Deal
[RES268:5th]Player +4 (4)(3+4) mod 10 = 75th Card Sideways
[RES268:6th]Banker +2 (2)(4+2) mod 10 = 66-Card Final
[RES268:Settle]P=7 vs B=6Winner: PBig Road +P
  • [RES268-1] Confirm [RES268] opening P=3 (9+4) and B=4 (A+3) lack Natural 8/9.
  • [RES268-2] Add [RES268] fifth-card 4 (4) to P=3 for (3+4) mod 10 = 7.
  • [RES268-3] Run [RES268] BANKER_TABLEAU[4][4]=true to settle 7 vs 6 (P).
SETTLEMENT & SCOREBOARD · RES268

Showdown Settlement & Scoreboard Logging for RES268 (7 vs 6)

[RES268-C5] Comparing [RES268] final totals (6c), Player 7 vs Banker 6 awards [RES268] to Player (P), which pays 1:1 even money on [RES268] Player boxes with zero commission deducted and appends P to PPBBPBBBPP.

[RES268-D2] Side-bet & road check for [RES268] (P3+4->7 vs B4->6, 6c): [RES268] leaves [RES268] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=6) and leaves [RES268] Panda 8 inactive (needs winning 3c Player 8, got P=7); on [RES268] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES268, Banker 4 evaluates Player's three-card total (7) before deciding whether to draw.
TruthBanker 4 inspects only Player's fifth card 4 (value 4) via BANKER_TABLEAU[4][4] = true.
MythBecause RES268 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
  • 74 interactive lesson scoreboards and 94 inline quiz checks with plain-English mark feedback
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