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FINAL TOTAL RESOLUTION [RES269] · 6-CARD PROOF

Player 4 + 4 (4) vs. Banker 4 (Draws 6 (6)): 6-Card Resolution #269

In walkthrough RES269, Player opens with 2+2 (4) and draws fifth-card 4 (4) for a modulo-10 total of 8, while Banker opens with 2+2 (4) and draws sixth-card 6 (6) for 0 (6-card P outcome).

RES269 Player Path
P:4->8
RES269 Banker Path
B:4->0
RES269 Deal Length
6 Cards
RES269 Showdown
P (8v0)
Engine-Verified Scoreboard · 20 Hands

Read the Board at Table Speed

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

Scoreboard sequence paired with 6-card resolution RES269 (P4+4->8 vs B4->0).

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

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

  1. Column 4 goes down to Row 2, so use Rule 2: look 2 columns 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.

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

RES269 Four-Card Opening Deal
Player 2+2=4 vs Banker 2+2=4

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

RES269 Fifth-Card Modulo Proof
(4 + 4) mod 10 = 8 via 4

Player draws fifth-card 4 (value 4), transforming two-card 4 into three-card 8.

RES269 Banker Tableau Lookup
BANKER_TABLEAU[4][4] = true

Banker 4 draws sixth-card 6 (6) so (4+6) mod 10 = 0.

RES269 Card Count & Winner
6 Cards -> P (8 vs 0)

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

RES269 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 · RES269

Step-by-Step Card Arithmetic for RES269: P(2+2)+4 vs B(2+2)

During tableau case [RES269], Player holds 2+2 for 4 while Banker holds 2+2 for 4; drawing fifth-card 4 (4) shifts Player from 4 to 8, which reduces mod-10 to 8.

[RES269-B] Next in [RES269], Banker consults 4-point six-value gate (2..7): facing fifth-card 4 (4), Banker 4 draws 6 (6) so 4+6=10 -> 0.

Complete 6-Card Resolution Trace for RES269
RES269 StageRES269 CardsRES269 Modulo MathRES269 Status
[RES269:Init]P(2+2)=4 vs B(2+2)=4playerShouldDraw(4)=true4-Card Deal
[RES269:5th]Player +4 (4)(4+4) mod 10 = 85th Card Sideways
[RES269:6th]Banker +6 (6)(4+6) mod 10 = 06-Card Final
[RES269:Settle]P=8 vs B=0Winner: PBig Road +P
  • [RES269-1] Confirm [RES269] opening P=4 (2+2) and B=4 (2+2) lack Natural 8/9.
  • [RES269-2] Add [RES269] fifth-card 4 (4) to P=4 for (4+4) mod 10 = 8.
  • [RES269-3] Run [RES269] BANKER_TABLEAU[4][4]=true to settle 8 vs 0 (P).
SETTLEMENT & SCOREBOARD · RES269

Showdown Settlement & Scoreboard Logging for RES269 (8 vs 0)

[RES269-C10] Comparing [RES269] final totals (6c), Player 8 vs Banker 0 awards [RES269] to Player (P), which pays 1:1 even money on [RES269] Player boxes with zero commission deducted and appends P to BBPPBBPPPB.

[RES269-D11] Side-bet & road check for [RES269] (P4+4->8 vs B4->0, 6c): [RES269] leaves [RES269] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=0) and triggers [RES269] Panda 8 (winning 3-card Player 8, 25:1); on [RES269] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES269, Banker 4 evaluates Player's three-card total (8) before deciding whether to draw.
TruthBanker 4 inspects only Player's fifth card 4 (value 4) via BANKER_TABLEAU[4][4] = true.
MythBecause RES269 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.
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  • Structured step-by-step track across Foundations, Big Eye Boy, Small Road, and Cockroach Pig
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