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FINAL TOTAL RESOLUTION [RES046] · 6-CARD PROOF

Player 3 + 7 (7) vs. Banker 0 (Draws 5 (5)): 6-Card Resolution #46

In walkthrough RES046, Player opens with 9+4 (3) and draws fifth-card 7 (7) for a modulo-10 total of 0, while Banker opens with 6+4 (0) and draws sixth-card 5 (5) for 5 (6-card B outcome).

RES046 Player Path
P:3->0
RES046 Banker Path
B:0->5
RES046 Deal Length
6 Cards
RES046 Showdown
B (0v5)
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 RES046 (P3+7->0 vs B0->5).

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

RES046 Four-Card Opening Deal
Player 9+4=3 vs Banker 6+4=0

Verified non-natural start via handTotal([9,4])=3 and handTotal([6,4])=0.

RES046 Fifth-Card Modulo Proof
(3 + 7) mod 10 = 0 via 7

Player draws fifth-card 7 (value 7), transforming two-card 3 into three-card 0.

RES046 Banker Tableau Lookup
BANKER_TABLEAU[0][7] = true

Banker 0 draws sixth-card 5 (5) so (0+5) mod 10 = 5.

RES046 Card Count & Winner
6 Cards -> B (0 vs 5)

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

RES046 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 · RES046

Step-by-Step Card Arithmetic for RES046: P(9+4)+7 vs B(6+4)

Within resolution [RES046], Player's opening 9+4 totals 3 against Banker's 6+4 (0); Punto Banco rules require drawing 7 (7), and 3+7=10 extracts the terminal digit to 0.

[RES046-B] Triggered by 7 (7) in [RES046] (0-point unconditional draw tier), Banker 0 receives 5 (5) and computes (0+5) mod 10 = 5.

Complete 6-Card Resolution Trace for RES046
RES046 StageRES046 CardsRES046 Modulo MathRES046 Status
[RES046:Init]P(9+4)=3 vs B(6+4)=0playerShouldDraw(3)=true4-Card Deal
[RES046:5th]Player +7 (7)(3+7) mod 10 = 05th Card Sideways
[RES046:6th]Banker +5 (5)(0+5) mod 10 = 56-Card Final
[RES046:Settle]P=0 vs B=5Winner: BBig Road +B
  • [RES046-1] Confirm [RES046] opening P=3 (9+4) and B=0 (6+4) lack Natural 8/9.
  • [RES046-2] Add [RES046] fifth-card 7 (7) to P=3 for (3+7) mod 10 = 0.
  • [RES046-3] Run [RES046] BANKER_TABLEAU[0][7]=true to settle 0 vs 5 (B).
SETTLEMENT & SCOREBOARD · RES046

Showdown Settlement & Scoreboard Logging for RES046 (0 vs 5)

[RES046-C6] Comparing [RES046] final totals (6c), Player 0 vs Banker 5 awards [RES046] to Banker (B), which pays 0.95:1 on 5%-commission [RES046] layouts (or 0.5:1 on 6 at No-Commission [RES046] tables) and appends B to PPBBPPBBBP.

[RES046-D6] Side-bet & road check for [RES046] (P3+7->0 vs B0->5, 6c): [RES046] leaves [RES046] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=5) and leaves [RES046] Panda 8 inactive (needs winning 3c Player 8, got P=0); on [RES046] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES046, Banker 0 evaluates Player's three-card total (0) before deciding whether to draw.
TruthBanker 0 inspects only Player's fifth card 7 (value 7) via BANKER_TABLEAU[0][7] = true.
MythBecause RES046 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

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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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