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FINAL TOTAL RESOLUTION [RES032] · 6-CARD PROOF

Player 1 + 5 (5) vs. Banker 0 (Draws 9 (9)): 6-Card Resolution #32

In walkthrough RES032, Player opens with 7+4 (1) and draws fifth-card 5 (5) for a modulo-10 total of 6, while Banker opens with 6+4 (0) and draws sixth-card 9 (9) for 9 (6-card B outcome).

RES032 Player Path
P:1->6
RES032 Banker Path
B:0->9
RES032 Deal Length
6 Cards
RES032 Showdown
B (6v9)
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 RES032 (P1+5->6 vs B0->9).

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

RES032 Four-Card Opening Deal
Player 7+4=1 vs Banker 6+4=0

Verified non-natural start via handTotal([7,4])=1 and handTotal([6,4])=0.

RES032 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.

RES032 Banker Tableau Lookup
BANKER_TABLEAU[0][5] = true

Banker 0 draws sixth-card 9 (9) so (0+9) mod 10 = 9.

RES032 Card Count & Winner
6 Cards -> B (6 vs 9)

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

RES032 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 · RES032

Step-by-Step Card Arithmetic for RES032: P(7+4)+5 vs B(6+4)

Within resolution [RES032], Player's opening 7+4 totals 1 against Banker's 6+4 (0); Punto Banco rules require drawing 5 (5), and 1+5=6 extracts the terminal digit to 6.

[RES032-B] Six-card branch [RES032] activates as 5 (5) hits Banker 0's 0-point unconditional draw tier; drawing 9 (9) sends 0+9=9 to 9.

Complete 6-Card Resolution Trace for RES032
RES032 StageRES032 CardsRES032 Modulo MathRES032 Status
[RES032:Init]P(7+4)=1 vs B(6+4)=0playerShouldDraw(1)=true4-Card Deal
[RES032:5th]Player +5 (5)(1+5) mod 10 = 65th Card Sideways
[RES032:6th]Banker +9 (9)(0+9) mod 10 = 96-Card Final
[RES032:Settle]P=6 vs B=9Winner: BBig Road +B
  • [RES032-1] Confirm [RES032] opening P=1 (7+4) and B=0 (6+4) lack Natural 8/9.
  • [RES032-2] Add [RES032] fifth-card 5 (5) to P=1 for (1+5) mod 10 = 6.
  • [RES032-3] Run [RES032] BANKER_TABLEAU[0][5]=true to settle 6 vs 9 (B).
SETTLEMENT & SCOREBOARD · RES032

Showdown Settlement & Scoreboard Logging for RES032 (6 vs 9)

[RES032-C2] Comparing [RES032] final totals (6c), Player 6 vs Banker 9 awards [RES032] to Banker (B), which pays 0.95:1 on 5%-commission [RES032] layouts (or 0.5:1 on 6 at No-Commission [RES032] tables) and appends B to PPBBPBPPBP.

[RES032-D10] Side-bet & road check for [RES032] (P1+5->6 vs B0->9, 6c): [RES032] leaves [RES032] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=9) and leaves [RES032] Panda 8 inactive (needs winning 3c Player 8, got P=6); on [RES032] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES032, Banker 0 evaluates Player's three-card total (6) before deciding whether to draw.
TruthBanker 0 inspects only Player's fifth card 5 (value 5) via BANKER_TABLEAU[0][5] = true.
MythBecause RES032 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
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