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FINAL TOTAL RESOLUTION [RES059] · 6-CARD PROOF

Player 4 + 9 (9) vs. Banker 0 (Draws 7 (7)): 6-Card Resolution #59

In walkthrough RES059, Player opens with 2+2 (4) and draws fifth-card 9 (9) for a modulo-10 total of 3, while Banker opens with 10+K (0) and draws sixth-card 7 (7) for 7 (6-card B outcome).

RES059 Player Path
P:4->3
RES059 Banker Path
B:0->7
RES059 Deal Length
6 Cards
RES059 Showdown
B (3v7)
Engine-Verified Scoreboard · 20 Hands

Read the Board at Table Speed

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

Scoreboard sequence paired with 6-card resolution RES059 (P4+9->3 vs B0->7).

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 3. Column 2 stopped at Row 2, one row above → blue (≠).

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

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

RES059 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.

RES059 Fifth-Card Modulo Proof
(4 + 9) mod 10 = 3 via 9

Player draws fifth-card 9 (value 9), transforming two-card 4 into three-card 3.

RES059 Banker Tableau Lookup
BANKER_TABLEAU[0][9] = true

Banker 0 draws sixth-card 7 (7) so (0+7) mod 10 = 7.

RES059 Card Count & Winner
6 Cards -> B (3 vs 7)

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

RES059 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 · RES059

Step-by-Step Card Arithmetic for RES059: P(2+2)+9 vs B(10+K)

During tableau case [RES059], Player holds 2+2 for 4 while Banker holds 10+K for 0; drawing fifth-card 9 (9) shifts Player from 4 to 13, which reduces mod-10 to 3.

[RES059-B] Triggered by 9 (9) in [RES059] (0-point unconditional draw tier), Banker 0 receives 7 (7) and computes (0+7) mod 10 = 7.

Complete 6-Card Resolution Trace for RES059
RES059 StageRES059 CardsRES059 Modulo MathRES059 Status
[RES059:Init]P(2+2)=4 vs B(10+K)=0playerShouldDraw(4)=true4-Card Deal
[RES059:5th]Player +9 (9)(4+9) mod 10 = 35th Card Sideways
[RES059:6th]Banker +7 (7)(0+7) mod 10 = 76-Card Final
[RES059:Settle]P=3 vs B=7Winner: BBig Road +B
  • [RES059-1] Confirm [RES059] opening P=4 (2+2) and B=0 (10+K) lack Natural 8/9.
  • [RES059-2] Add [RES059] fifth-card 9 (9) to P=4 for (4+9) mod 10 = 3.
  • [RES059-3] Run [RES059] BANKER_TABLEAU[0][9]=true to settle 3 vs 7 (B).
SETTLEMENT & SCOREBOARD · RES059

Showdown Settlement & Scoreboard Logging for RES059 (3 vs 7)

[RES059-C5] Comparing [RES059] final totals (6c), Player 3 vs Banker 7 awards [RES059] to Banker (B), which pays 0.95:1 on 5%-commission [RES059] layouts (or 0.5:1 on 6 at No-Commission [RES059] tables) and appends B to BBPPBPPPBB.

[RES059-D6] Side-bet & road check for [RES059] (P4+9->3 vs B0->7, 6c): [RES059] triggers [RES059] Dragon 7 (winning 3-card Banker 7, 40:1) and leaves [RES059] Panda 8 inactive (needs winning 3c Player 8, got P=3); on [RES059] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES059, Banker 0 evaluates Player's three-card total (3) before deciding whether to draw.
TruthBanker 0 inspects only Player's fifth card 9 (value 9) via BANKER_TABLEAU[0][9] = true.
MythBecause RES059 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