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FINAL TOTAL RESOLUTION [RES178] · 6-CARD PROOF

Player 3 + 9 (9) vs. Banker 2 (Draws 5 (5)): 6-Card Resolution #178

In walkthrough RES178, Player opens with 9+4 (3) and draws fifth-card 9 (9) for a modulo-10 total of 2, while Banker opens with 8+4 (2) and draws sixth-card 5 (5) for 7 (6-card B outcome).

RES178 Player Path
P:3->2
RES178 Banker Path
B:2->7
RES178 Deal Length
6 Cards
RES178 Showdown
B (2v7)
Engine-Verified Scoreboard · 20 Hands

Read the Board at Table Speed

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

Scoreboard sequence paired with 6-card resolution RES178 (P3+9->2 vs B2->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 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

RES178 Four-Card Opening Deal
Player 9+4=3 vs Banker 8+4=2

Verified non-natural start via handTotal([9,4])=3 and handTotal([8,4])=2.

RES178 Fifth-Card Modulo Proof
(3 + 9) mod 10 = 2 via 9

Player draws fifth-card 9 (value 9), transforming two-card 3 into three-card 2.

RES178 Banker Tableau Lookup
BANKER_TABLEAU[2][9] = true

Banker 2 draws sixth-card 5 (5) so (2+5) mod 10 = 7.

RES178 Card Count & Winner
6 Cards -> B (2 vs 7)

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

RES178 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 · RES178

Step-by-Step Card Arithmetic for RES178: P(9+4)+9 vs B(8+4)

In coup [RES178], initial cards deal 9+4=3 to Player and 8+4=2 to Banker; lacking a four-card natural, Player takes fifth-card 9 (9) where raw sum 12 projects onto the 0..9 ring to 2.

[RES178-B] Next in [RES178], Banker consults 2-point mandatory draw band: facing fifth-card 9 (9), Banker 2 draws 5 (5) so 2+5=7 -> 7.

Complete 6-Card Resolution Trace for RES178
RES178 StageRES178 CardsRES178 Modulo MathRES178 Status
[RES178:Init]P(9+4)=3 vs B(8+4)=2playerShouldDraw(3)=true4-Card Deal
[RES178:5th]Player +9 (9)(3+9) mod 10 = 25th Card Sideways
[RES178:6th]Banker +5 (5)(2+5) mod 10 = 76-Card Final
[RES178:Settle]P=2 vs B=7Winner: BBig Road +B
  • [RES178-1] Confirm [RES178] opening P=3 (9+4) and B=2 (8+4) lack Natural 8/9.
  • [RES178-2] Add [RES178] fifth-card 9 (9) to P=3 for (3+9) mod 10 = 2.
  • [RES178-3] Run [RES178] BANKER_TABLEAU[2][9]=true to settle 2 vs 7 (B).
SETTLEMENT & SCOREBOARD · RES178

Showdown Settlement & Scoreboard Logging for RES178 (2 vs 7)

[RES178-C6] Comparing [RES178] final totals (6c), Player 2 vs Banker 7 awards [RES178] to Banker (B), which pays 0.95:1 on 5%-commission [RES178] layouts (or 0.5:1 on 6 at No-Commission [RES178] tables) and appends B to PPBBPBPPBB.

[RES178-D11] Side-bet & road check for [RES178] (P3+9->2 vs B2->7, 6c): [RES178] triggers [RES178] Dragon 7 (winning 3-card Banker 7, 40:1) and leaves [RES178] Panda 8 inactive (needs winning 3c Player 8, got P=2); on [RES178] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES178, Banker 2 evaluates Player's three-card total (2) before deciding whether to draw.
TruthBanker 2 inspects only Player's fifth card 9 (value 9) via BANKER_TABLEAU[2][9] = true.
MythBecause RES178 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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