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FINAL TOTAL RESOLUTION [RES273] · 6-CARD PROOF

Player 2 + 5 (5) vs. Banker 4 (Draws 7 (7)): 6-Card Resolution #273

In walkthrough RES273, Player opens with 10+2 (2) and draws fifth-card 5 (5) for a modulo-10 total of 7, while Banker opens with 2+2 (4) and draws sixth-card 7 (7) for 1 (6-card P outcome).

RES273 Player Path
P:2->7
RES273 Banker Path
B:4->1
RES273 Deal Length
6 Cards
RES273 Showdown
P (7v1)
Engine-Verified Scoreboard · 20 Hands

Read the Board at Table Speed

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

Scoreboard sequence paired with 6-card resolution RES273 (P2+5->7 vs B4->1).

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 2. Column 3 stopped at Row 1, one row above → blue (≠).

  1. Column 5 goes down to Row 2, so use Rule 2: look 2 columns back, at Column 3.
  2. Column 3 stopped at Row 1, one row above → blue (≠).

Common table reading watchout: Thinking "no bead at this row" means blue. It is blue only when Column 3 stopped exactly one row above this bead.

Cockroach Pig Mark #3

Column 5 has 2 beads. Column 2 has 2 beads. Same depth → red (=).

  1. Column 6 starts, so use Rule 1: compare Column 5 with Column 2, 3 columns further back.
  2. Column 5 has 2 beads. Column 2 has 2 beads. Same depth → red (=).

Common table reading watchout: Comparing the wrong columns. Compare Column 5, the one that just finished, with Column 2.

Verified Reference Data

Key Facts & Table Specifications

RES273 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.

RES273 Fifth-Card Modulo Proof
(2 + 5) mod 10 = 7 via 5

Player draws fifth-card 5 (value 5), transforming two-card 2 into three-card 7.

RES273 Banker Tableau Lookup
BANKER_TABLEAU[4][5] = true

Banker 4 draws sixth-card 7 (7) so (4+7) mod 10 = 1.

RES273 Card Count & Winner
6 Cards -> P (7 vs 1)

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

RES273 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 · RES273

Step-by-Step Card Arithmetic for RES273: P(10+2)+5 vs B(2+2)

Matrix coordinate [RES273] isolates Player two-card 2 (10+2) and Banker 4 (2+2); dealing fifth-card 5 (5) yields raw 7 that retains the rightmost digit to 7.

[RES273-B] Acting on 5=5 inside [RES273], Banker 4 follows 4-point six-value gate (2..7) and pulls 7 (7) for 4+7=11 -> 1.

Complete 6-Card Resolution Trace for RES273
RES273 StageRES273 CardsRES273 Modulo MathRES273 Status
[RES273:Init]P(10+2)=2 vs B(2+2)=4playerShouldDraw(2)=true4-Card Deal
[RES273:5th]Player +5 (5)(2+5) mod 10 = 75th Card Sideways
[RES273:6th]Banker +7 (7)(4+7) mod 10 = 16-Card Final
[RES273:Settle]P=7 vs B=1Winner: PBig Road +P
  • [RES273-1] Confirm [RES273] opening P=2 (10+2) and B=4 (2+2) lack Natural 8/9.
  • [RES273-2] Add [RES273] fifth-card 5 (5) to P=2 for (2+5) mod 10 = 7.
  • [RES273-3] Run [RES273] BANKER_TABLEAU[4][5]=true to settle 7 vs 1 (P).
SETTLEMENT & SCOREBOARD · RES273

Showdown Settlement & Scoreboard Logging for RES273 (7 vs 1)

[RES273-C8] Comparing [RES273] final totals (6c), Player 7 vs Banker 1 awards [RES273] to Player (P), which pays 1:1 even money on [RES273] Player boxes with zero commission deducted and appends P to BBPPBPBBPP.

[RES273-D8] Side-bet & road check for [RES273] (P2+5->7 vs B4->1, 6c): [RES273] leaves [RES273] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=1) and leaves [RES273] Panda 8 inactive (needs winning 3c Player 8, got P=7); on [RES273] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES273, Banker 4 evaluates Player's three-card total (7) before deciding whether to draw.
TruthBanker 4 inspects only Player's fifth card 5 (value 5) via BANKER_TABLEAU[4][5] = true.
MythBecause RES273 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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