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FINAL TOTAL RESOLUTION [RES270] · 6-CARD PROOF

Player 5 + 4 (4) vs. Banker 4 (Draws 10 (0)): 6-Card Resolution #270

In walkthrough RES270, Player opens with A+4 (5) and draws fifth-card 4 (4) for a modulo-10 total of 9, while Banker opens with A+3 (4) and draws sixth-card 10 (0) for 4 (6-card P outcome).

RES270 Player Path
P:5->9
RES270 Banker Path
B:4->4
RES270 Deal Length
6 Cards
RES270 Showdown
P (9v4)
Engine-Verified Scoreboard · 20 Hands

Read the Board at Table Speed

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

Scoreboard sequence paired with 6-card resolution RES270 (P5+4->9 vs B4->4).

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

RES270 Four-Card Opening Deal
Player A+4=5 vs Banker A+3=4

Verified non-natural start via handTotal([A,4])=5 and handTotal([A,3])=4.

RES270 Fifth-Card Modulo Proof
(5 + 4) mod 10 = 9 via 4

Player draws fifth-card 4 (value 4), transforming two-card 5 into three-card 9.

RES270 Banker Tableau Lookup
BANKER_TABLEAU[4][4] = true

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

RES270 Card Count & Winner
6 Cards -> P (9 vs 4)

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

RES270 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 · RES270

Step-by-Step Card Arithmetic for RES270: P(A+4)+4 vs B(A+3)

Within resolution [RES270], Player's opening A+4 totals 5 against Banker's A+3 (4); Punto Banco rules require drawing 4 (4), and 5+4=9 extracts the terminal digit to 9.

[RES270-B] Because BANKER_TABLEAU[4][4]=true (4-point six-value gate (2..7)) in [RES270], Banker 4 takes sixth-card 10 (0) and 4+0=4 settles at 4.

Complete 6-Card Resolution Trace for RES270
RES270 StageRES270 CardsRES270 Modulo MathRES270 Status
[RES270:Init]P(A+4)=5 vs B(A+3)=4playerShouldDraw(5)=true4-Card Deal
[RES270:5th]Player +4 (4)(5+4) mod 10 = 95th Card Sideways
[RES270:6th]Banker +10 (0)(4+0) mod 10 = 46-Card Final
[RES270:Settle]P=9 vs B=4Winner: PBig Road +P
  • [RES270-1] Confirm [RES270] opening P=5 (A+4) and B=4 (A+3) lack Natural 8/9.
  • [RES270-2] Add [RES270] fifth-card 4 (4) to P=5 for (5+4) mod 10 = 9.
  • [RES270-3] Run [RES270] BANKER_TABLEAU[4][4]=true to settle 9 vs 4 (P).
SETTLEMENT & SCOREBOARD · RES270

Showdown Settlement & Scoreboard Logging for RES270 (9 vs 4)

[RES270-C4] Comparing [RES270] final totals (6c), Player 9 vs Banker 4 awards [RES270] to Player (P), which pays 1:1 even money on [RES270] Player boxes with zero commission deducted and appends P to PPBBPPBBBP.

[RES270-D7] Side-bet & road check for [RES270] (P5+4->9 vs B4->4, 6c): [RES270] leaves [RES270] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=4) and leaves [RES270] Panda 8 inactive (needs winning 3c Player 8, got P=9); on [RES270] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES270, Banker 4 evaluates Player's three-card total (9) before deciding whether to draw.
TruthBanker 4 inspects only Player's fifth card 4 (value 4) via BANKER_TABLEAU[4][4] = true.
MythBecause RES270 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

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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