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FINAL TOTAL RESOLUTION [RES231] · 5-CARD PROOF

Player 2 + 8 (8) vs. Banker 3 (Stands at 3): 5-Card Resolution #231

In walkthrough RES231, Player opens with 10+2 (2) and draws fifth-card 8 (8) for a modulo-10 total of 0, while Banker opens with 9+4 (3) and stands pat at 3 (5-card B outcome).

RES231 Player Path
P:2->0
RES231 Banker Path
B:3->3
RES231 Deal Length
5 Cards
RES231 Showdown
B (0v3)
Engine-Verified Scoreboard · 20 Hands

Read the Board at Table Speed

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

Scoreboard sequence paired with 5-card resolution RES231 (P2+8->0 vs B3->3).

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

Column 5 has 1 bead. Column 3 has 1 bead. Same depth → red (=).

  1. Column 6 starts, so use Rule 1: compare Column 5 with Column 3, 2 columns further back.
  2. Column 5 has 1 bead. Column 3 has 1 bead. Same depth → red (=).

Common table reading watchout: Comparing the wrong columns. Compare Column 5, the one that just finished, with Column 3.

Cockroach Pig Mark #3

This bead is at Row 2. Column 3 stopped at Row 1, one row above → blue (≠).

  1. Column 6 goes down to Row 2, so use Rule 2: look 3 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.

Verified Reference Data

Key Facts & Table Specifications

RES231 Four-Card Opening Deal
Player 10+2=2 vs Banker 9+4=3

Verified non-natural start via handTotal([10,2])=2 and handTotal([9,4])=3.

RES231 Fifth-Card Modulo Proof
(2 + 8) mod 10 = 0 via 8

Player draws fifth-card 8 (value 8), transforming two-card 2 into three-card 0.

RES231 Banker Tableau Lookup
BANKER_TABLEAU[3][8] = false

Banker 3 stands pat at 3 without pulling sixth-card 3 (3).

RES231 Card Count & Winner
5 Cards -> B (0 vs 3)

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

RES231 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 · RES231

Step-by-Step Card Arithmetic for RES231: P(10+2)+8 vs B(9+4)

Matrix coordinate [RES231] isolates Player two-card 2 (10+2) and Banker 3 (9+4); dealing fifth-card 8 (8) yields raw 10 that retains the rightmost digit to 0.

[RES231-B] Because BANKER_TABLEAU[3][8]=false (3-point single-shade row (0..7, 9)) in [RES231], Banker 3 locks 3 at 5c (leaving 3=3 -> 6 unpulled).

Complete 5-Card Resolution Trace for RES231
RES231 StageRES231 CardsRES231 Modulo MathRES231 Status
[RES231:Init]P(10+2)=2 vs B(9+4)=3playerShouldDraw(2)=true4-Card Deal
[RES231:5th]Player +8 (8)(2+8) mod 10 = 05th Card Sideways
[RES231:6th]Banker Stands (skip 3=3)Locked at 35-Card Final
[RES231:Settle]P=0 vs B=3Winner: BBig Road +B
  • [RES231-1] Confirm [RES231] opening P=2 (10+2) and B=3 (9+4) lack Natural 8/9.
  • [RES231-2] Add [RES231] fifth-card 8 (8) to P=2 for (2+8) mod 10 = 0.
  • [RES231-3] Run [RES231] BANKER_TABLEAU[3][8]=false to settle 0 vs 3 (B).
SETTLEMENT & SCOREBOARD · RES231

Showdown Settlement & Scoreboard Logging for RES231 (0 vs 3)

[RES231-C7] Comparing [RES231] final totals (5c), Player 0 vs Banker 3 awards [RES231] to Banker (B), which pays 0.95:1 on 5%-commission [RES231] layouts (or 0.5:1 on 6 at No-Commission [RES231] tables) and appends B to BBPPBPBPPP.

[RES231-D7] Side-bet & road check for [RES231] (P2+8->0 vs B3->3, 5c): [RES231] leaves [RES231] Dragon 7 inactive (needs winning 6c Banker 7, got 5c B=3) and leaves [RES231] Panda 8 inactive (needs winning 3c Player 8, got P=0); on [RES231] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES231, Banker 3 evaluates Player's three-card total (0) before deciding whether to draw.
TruthBanker 3 inspects only Player's fifth card 8 (value 8) via BANKER_TABLEAU[3][8] = false.
MythBecause RES231 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

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  • Structured step-by-step track across Foundations, Big Eye Boy, Small Road, and Cockroach Pig
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