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FINAL TOTAL RESOLUTION [RES047] · 6-CARD PROOF

Player 4 + 7 (7) vs. Banker 0 (Draws 9 (9)): 6-Card Resolution #47

In walkthrough RES047, Player opens with 2+2 (4) and draws fifth-card 7 (7) for a modulo-10 total of 1, while Banker opens with 10+K (0) and draws sixth-card 9 (9) for 9 (6-card B outcome).

RES047 Player Path
P:4->1
RES047 Banker Path
B:0->9
RES047 Deal Length
6 Cards
RES047 Showdown
B (1v9)
Engine-Verified Scoreboard · 20 Hands

Read the Board at Table Speed

Open this shoe in /calculator
Big Road B B P P B P B B P B B B P P P B B B B P
Big Eye Boy = = ≠ = ≠ ≠ ≠ ≠ = ≠ = = = = = ≠ ≠
Small Road ≠ ≠ ≠ ≠ = = ≠ ≠ ≠ = ≠ = = ≠ ≠
Cockroach Pig ≠ = = = ≠ = ≠ = ≠ ≠ ≠ = = ≠

Scoreboard sequence paired with 6-card resolution RES047 (P4+7->1 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

RES047 Four-Card Opening Deal
Player 2+2=4 vs Banker 10+K=0

Verified non-natural start via handTotal([2,2])=4 and handTotal([10,K])=0.

RES047 Fifth-Card Modulo Proof
(4 + 7) mod 10 = 1 via 7

Player draws fifth-card 7 (value 7), transforming two-card 4 into three-card 1.

RES047 Banker Tableau Lookup
BANKER_TABLEAU[0][7] = true

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

RES047 Card Count & Winner
6 Cards -> B (1 vs 9)

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

RES047 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 · RES047

Step-by-Step Card Arithmetic for RES047: P(2+2)+7 vs B(10+K)

Under audit [RES047], Player opens on two-card 4 (2+2) opposite Banker 0 (10+K), triggering a mandatory fifth-card pull of 7 (value 7) that settles via mod-10 arithmetic from 11 into 1.

[RES047-B] Next in [RES047], Banker consults 0-point unconditional draw tier: facing fifth-card 7 (7), Banker 0 draws 9 (9) so 0+9=9 -> 9.

Complete 6-Card Resolution Trace for RES047
RES047 StageRES047 CardsRES047 Modulo MathRES047 Status
[RES047:Init]P(2+2)=4 vs B(10+K)=0playerShouldDraw(4)=true4-Card Deal
[RES047:5th]Player +7 (7)(4+7) mod 10 = 15th Card Sideways
[RES047:6th]Banker +9 (9)(0+9) mod 10 = 96-Card Final
[RES047:Settle]P=1 vs B=9Winner: BBig Road +B
  • [RES047-1] Confirm [RES047] opening P=4 (2+2) and B=0 (10+K) lack Natural 8/9.
  • [RES047-2] Add [RES047] fifth-card 7 (7) to P=4 for (4+7) mod 10 = 1.
  • [RES047-3] Run [RES047] BANKER_TABLEAU[0][7]=true to settle 1 vs 9 (B).
SETTLEMENT & SCOREBOARD · RES047

Showdown Settlement & Scoreboard Logging for RES047 (1 vs 9)

[RES047-C0] Comparing [RES047] final totals (6c), Player 1 vs Banker 9 awards [RES047] to Banker (B), which pays 0.95:1 on 5%-commission [RES047] layouts (or 0.5:1 on 6 at No-Commission [RES047] tables) and appends B to BBPPBPBBPB.

[RES047-D2] Side-bet & road check for [RES047] (P4+7->1 vs B0->9, 6c): [RES047] leaves [RES047] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=9) and leaves [RES047] Panda 8 inactive (needs winning 3c Player 8, got P=1); on [RES047] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES047, Banker 0 evaluates Player's three-card total (1) before deciding whether to draw.
TruthBanker 0 inspects only Player's fifth card 7 (value 7) via BANKER_TABLEAU[0][7] = true.
MythBecause RES047 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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