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FINAL TOTAL RESOLUTION [RES272] · 6-CARD PROOF

Player 1 + 5 (5) vs. Banker 4 (Draws 3 (3)): 6-Card Resolution #272

In walkthrough RES272, Player opens with 7+4 (1) and draws fifth-card 5 (5) 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).

RES272 Player Path
P:1->6
RES272 Banker Path
B:4->7
RES272 Deal Length
6 Cards
RES272 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 B P P B P P P B B B P P P P B
Big Eye Boy = = ≠ = ≠ ≠ ≠ ≠ = ≠ = = = = = ≠ ≠
Small Road ≠ ≠ ≠ ≠ = = ≠ ≠ ≠ = ≠ = = ≠ ≠
Cockroach Pig ≠ = = = ≠ = ≠ = ≠ ≠ ≠ = = ≠

Scoreboard sequence paired with 6-card resolution RES272 (P1+5->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

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

RES272 Four-Card Opening Deal
Player 7+4=1 vs Banker A+3=4

Verified non-natural start via handTotal([7,4])=1 and handTotal([A,3])=4.

RES272 Fifth-Card Modulo Proof
(1 + 5) mod 10 = 6 via 5

Player draws fifth-card 5 (value 5), transforming two-card 1 into three-card 6.

RES272 Banker Tableau Lookup
BANKER_TABLEAU[4][5] = true

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

RES272 Card Count & Winner
6 Cards -> B (6 vs 7)

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

RES272 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 · RES272

Step-by-Step Card Arithmetic for RES272: P(7+4)+5 vs B(A+3)

Canonical test [RES272] examines Player 1 (7+4) against Banker 4 (A+3); the fifth card 5 (5) brings Player's raw count to 6, which computes the single-digit remainder to 6.

[RES272-B] Acting on 5=5 inside [RES272], Banker 4 follows 4-point six-value gate (2..7) and pulls 3 (3) for 4+3=7 -> 7.

Complete 6-Card Resolution Trace for RES272
RES272 StageRES272 CardsRES272 Modulo MathRES272 Status
[RES272:Init]P(7+4)=1 vs B(A+3)=4playerShouldDraw(1)=true4-Card Deal
[RES272:5th]Player +5 (5)(1+5) mod 10 = 65th Card Sideways
[RES272:6th]Banker +3 (3)(4+3) mod 10 = 76-Card Final
[RES272:Settle]P=6 vs B=7Winner: BBig Road +B
  • [RES272-1] Confirm [RES272] opening P=1 (7+4) and B=4 (A+3) lack Natural 8/9.
  • [RES272-2] Add [RES272] fifth-card 5 (5) to P=1 for (1+5) mod 10 = 6.
  • [RES272-3] Run [RES272] BANKER_TABLEAU[4][5]=true to settle 6 vs 7 (B).
SETTLEMENT & SCOREBOARD · RES272

Showdown Settlement & Scoreboard Logging for RES272 (6 vs 7)

[RES272-C3] Comparing [RES272] final totals (6c), Player 6 vs Banker 7 awards [RES272] to Banker (B), which pays 0.95:1 on 5%-commission [RES272] layouts (or 0.5:1 on 6 at No-Commission [RES272] tables) and appends B to PPBBPBPPBP.

[RES272-D12] Side-bet & road check for [RES272] (P1+5->6 vs B4->7, 6c): [RES272] triggers [RES272] Dragon 7 (winning 3-card Banker 7, 40:1) and leaves [RES272] Panda 8 inactive (needs winning 3c Player 8, got P=6); on [RES272] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES272, Banker 4 evaluates Player's three-card total (6) before deciding whether to draw.
TruthBanker 4 inspects only Player's fifth card 5 (value 5) via BANKER_TABLEAU[4][5] = true.
MythBecause RES272 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
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