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FINAL TOTAL RESOLUTION [RES256] · 6-CARD PROOF

Player 3 + 2 (2) vs. Banker 4 (Draws 4 (4)): 6-Card Resolution #256

In walkthrough RES256, Player opens with 9+4 (3) and draws fifth-card 2 (2) for a modulo-10 total of 5, while Banker opens with A+3 (4) and draws sixth-card 4 (4) for 8 (6-card B outcome).

RES256 Player Path
P:3->5
RES256 Banker Path
B:4->8
RES256 Deal Length
6 Cards
RES256 Showdown
B (5v8)
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 RES256 (P3+2->5 vs B4->8).

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

RES256 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.

RES256 Fifth-Card Modulo Proof
(3 + 2) mod 10 = 5 via 2

Player draws fifth-card 2 (value 2), transforming two-card 3 into three-card 5.

RES256 Banker Tableau Lookup
BANKER_TABLEAU[4][2] = true

Banker 4 draws sixth-card 4 (4) so (4+4) mod 10 = 8.

RES256 Card Count & Winner
6 Cards -> B (5 vs 8)

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

RES256 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 · RES256

Step-by-Step Card Arithmetic for RES256: P(9+4)+2 vs B(A+3)

Within resolution [RES256], Player's opening 9+4 totals 3 against Banker's A+3 (4); Punto Banco rules require drawing 2 (2), and 3+2=5 extracts the terminal digit to 5.

[RES256-B] Next in [RES256], Banker consults 4-point six-value gate (2..7): facing fifth-card 2 (2), Banker 4 draws 4 (4) so 4+4=8 -> 8.

Complete 6-Card Resolution Trace for RES256
RES256 StageRES256 CardsRES256 Modulo MathRES256 Status
[RES256:Init]P(9+4)=3 vs B(A+3)=4playerShouldDraw(3)=true4-Card Deal
[RES256:5th]Player +2 (2)(3+2) mod 10 = 55th Card Sideways
[RES256:6th]Banker +4 (4)(4+4) mod 10 = 86-Card Final
[RES256:Settle]P=5 vs B=8Winner: BBig Road +B
  • [RES256-1] Confirm [RES256] opening P=3 (9+4) and B=4 (A+3) lack Natural 8/9.
  • [RES256-2] Add [RES256] fifth-card 2 (2) to P=3 for (3+2) mod 10 = 5.
  • [RES256-3] Run [RES256] BANKER_TABLEAU[4][2]=true to settle 5 vs 8 (B).
SETTLEMENT & SCOREBOARD · RES256

Showdown Settlement & Scoreboard Logging for RES256 (5 vs 8)

[RES256-C0] Comparing [RES256] final totals (6c), Player 5 vs Banker 8 awards [RES256] to Banker (B), which pays 0.95:1 on 5%-commission [RES256] layouts (or 0.5:1 on 6 at No-Commission [RES256] tables) and appends B to PPBBPBPPBP.

[RES256-D11] Side-bet & road check for [RES256] (P3+2->5 vs B4->8, 6c): [RES256] leaves [RES256] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=8) and leaves [RES256] Panda 8 inactive (needs winning 3c Player 8, got P=5); on [RES256] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES256, Banker 4 evaluates Player's three-card total (5) before deciding whether to draw.
TruthBanker 4 inspects only Player's fifth card 2 (value 2) via BANKER_TABLEAU[4][2] = true.
MythBecause RES256 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
  • Cloud Shoe Log and cross-device progress on web, iOS, and Android