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FINAL TOTAL RESOLUTION [RES057] · 6-CARD PROOF

Player 2 + 9 (9) vs. Banker 0 (Draws 9 (9)): 6-Card Resolution #57

In walkthrough RES057, Player opens with 10+2 (2) and draws fifth-card 9 (9) 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).

RES057 Player Path
P:2->1
RES057 Banker Path
B:0->9
RES057 Deal Length
6 Cards
RES057 Showdown
B (1v9)
Engine-Verified Scoreboard · 20 Hands

Read the Board at Table Speed

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Big Road B B P P P B B B B P P B P P P B B B P B
Big Eye Boy = ≠ ≠ = = ≠ ≠ = ≠ ≠ ≠ = ≠ = = = ≠
Small Road = ≠ = ≠ = ≠ ≠ = ≠ ≠ ≠ = ≠ ≠
Cockroach Pig = = ≠ = = ≠ = ≠ ≠ =

Scoreboard sequence paired with 6-card resolution RES057 (P2+9->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 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

RES057 Four-Card Opening Deal
Player 10+2=2 vs Banker 10+K=0

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

RES057 Fifth-Card Modulo Proof
(2 + 9) mod 10 = 1 via 9

Player draws fifth-card 9 (value 9), transforming two-card 2 into three-card 1.

RES057 Banker Tableau Lookup
BANKER_TABLEAU[0][9] = true

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

RES057 Card Count & Winner
6 Cards -> B (1 vs 9)

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

RES057 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 · RES057

Step-by-Step Card Arithmetic for RES057: P(10+2)+9 vs B(10+K)

[RES057] Walkthrough #57 begins with Player holding 10+2 (2) against Banker 10+K (0); since neither side holds 8 or 9, Player draws fifth-card 9 (9) so 2+9=11 applies base-10 modular addition to 1.

[RES057-B] Six-card branch [RES057] activates as 9 (9) hits Banker 0's 0-point unconditional draw tier; drawing 9 (9) sends 0+9=9 to 9.

Complete 6-Card Resolution Trace for RES057
RES057 StageRES057 CardsRES057 Modulo MathRES057 Status
[RES057:Init]P(10+2)=2 vs B(10+K)=0playerShouldDraw(2)=true4-Card Deal
[RES057:5th]Player +9 (9)(2+9) mod 10 = 15th Card Sideways
[RES057:6th]Banker +9 (9)(0+9) mod 10 = 96-Card Final
[RES057:Settle]P=1 vs B=9Winner: BBig Road +B
  • [RES057-1] Confirm [RES057] opening P=2 (10+2) and B=0 (10+K) lack Natural 8/9.
  • [RES057-2] Add [RES057] fifth-card 9 (9) to P=2 for (2+9) mod 10 = 1.
  • [RES057-3] Run [RES057] BANKER_TABLEAU[0][9]=true to settle 1 vs 9 (B).
SETTLEMENT & SCOREBOARD · RES057

Showdown Settlement & Scoreboard Logging for RES057 (1 vs 9)

[RES057-C6] Comparing [RES057] final totals (6c), Player 1 vs Banker 9 awards [RES057] to Banker (B), which pays 0.95:1 on 5%-commission [RES057] layouts (or 0.5:1 on 6 at No-Commission [RES057] tables) and appends B to BBPPPBBBBP.

[RES057-D1] Side-bet & road check for [RES057] (P2+9->1 vs B0->9, 6c): [RES057] leaves [RES057] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=9) and leaves [RES057] Panda 8 inactive (needs winning 3c Player 8, got P=1); on [RES057] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES057, Banker 0 evaluates Player's three-card total (1) before deciding whether to draw.
TruthBanker 0 inspects only Player's fifth card 9 (value 9) via BANKER_TABLEAU[0][9] = true.
MythBecause RES057 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