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FINAL TOTAL RESOLUTION [RES346] · 6-CARD PROOF

Player 3 + 7 (7) vs. Banker 5 (Draws 10 (0)): 6-Card Resolution #346

In walkthrough RES346, Player opens with 9+4 (3) and draws fifth-card 7 (7) for a modulo-10 total of 0, while Banker opens with 2+3 (5) and draws sixth-card 10 (0) for 5 (6-card B outcome).

RES346 Player Path
P:3->0
RES346 Banker Path
B:5->5
RES346 Deal Length
6 Cards
RES346 Showdown
B (0v5)
Engine-Verified Scoreboard · 20 Hands

Read the Board at Table Speed

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

Scoreboard sequence paired with 6-card resolution RES346 (P3+7->0 vs B5->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

Column 2 has 3 beads. Column 1 has 2 beads. Different depth → blue (≠).

  1. Column 3 starts, so use Rule 1: compare Column 2 with Column 1, 1 column further back.
  2. Column 2 has 3 beads. Column 1 has 2 beads. Different depth → blue (≠).

Common table reading watchout: Comparing the wrong columns. Compare Column 2, the one that just finished, with Column 1.

Small Road Mark #3

This bead is at Row 4. Column 1 stopped at Row 2, more than one row above → red (=).

  1. Column 3 goes down to Row 4, so use Rule 2: look 2 columns back, at Column 1.
  2. Column 1 stopped at Row 2, more than one row above → red (=).

Common table reading watchout: Thinking "no bead at this row" means blue. It is blue only when Column 1 stopped exactly one row above this bead.

Cockroach Pig Mark #3

Column 5 has 1 bead. Column 2 has 3 beads. Different depth → blue (≠).

  1. Column 6 starts, so use Rule 1: compare Column 5 with Column 2, 3 columns further back.
  2. Column 5 has 1 bead. Column 2 has 3 beads. Different depth → blue (≠).

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

RES346 Four-Card Opening Deal
Player 9+4=3 vs Banker 2+3=5

Verified non-natural start via handTotal([9,4])=3 and handTotal([2,3])=5.

RES346 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.

RES346 Banker Tableau Lookup
BANKER_TABLEAU[5][7] = true

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

RES346 Card Count & Winner
6 Cards -> B (0 vs 5)

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

RES346 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 · RES346

Step-by-Step Card Arithmetic for RES346: P(9+4)+7 vs B(2+3)

In coup [RES346], initial cards deal 9+4=3 to Player and 2+3=5 to Banker; lacking a four-card natural, Player takes fifth-card 7 (7) where raw sum 10 projects onto the 0..9 ring to 0.

[RES346-B] Next in [RES346], Banker consults 5-point four-value window (4..7): facing fifth-card 7 (7), Banker 5 draws 10 (0) so 5+0=5 -> 5.

Complete 6-Card Resolution Trace for RES346
RES346 StageRES346 CardsRES346 Modulo MathRES346 Status
[RES346:Init]P(9+4)=3 vs B(2+3)=5playerShouldDraw(3)=true4-Card Deal
[RES346:5th]Player +7 (7)(3+7) mod 10 = 05th Card Sideways
[RES346:6th]Banker +10 (0)(5+0) mod 10 = 56-Card Final
[RES346:Settle]P=0 vs B=5Winner: BBig Road +B
  • [RES346-1] Confirm [RES346] opening P=3 (9+4) and B=5 (2+3) lack Natural 8/9.
  • [RES346-2] Add [RES346] fifth-card 7 (7) to P=3 for (3+7) mod 10 = 0.
  • [RES346-3] Run [RES346] BANKER_TABLEAU[5][7]=true to settle 0 vs 5 (B).
SETTLEMENT & SCOREBOARD · RES346

Showdown Settlement & Scoreboard Logging for RES346 (0 vs 5)

[RES346-C10] Comparing [RES346] final totals (6c), Player 0 vs Banker 5 awards [RES346] to Banker (B), which pays 0.95:1 on 5%-commission [RES346] layouts (or 0.5:1 on 6 at No-Commission [RES346] tables) and appends B to PPBBBPPPPB.

[RES346-D2] Side-bet & road check for [RES346] (P3+7->0 vs B5->5, 6c): [RES346] leaves [RES346] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=5) and leaves [RES346] Panda 8 inactive (needs winning 3c Player 8, got P=0); on [RES346] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES346, Banker 5 evaluates Player's three-card total (0) before deciding whether to draw.
TruthBanker 5 inspects only Player's fifth card 7 (value 7) via BANKER_TABLEAU[5][7] = true.
MythBecause RES346 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