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FINAL TOTAL RESOLUTION [RES034] · 6-CARD PROOF

Player 3 + 5 (5) vs. Banker 0 (Draws 7 (7)): 6-Card Resolution #34

In walkthrough RES034, Player opens with 9+4 (3) and draws fifth-card 5 (5) for a modulo-10 total of 8, while Banker opens with 6+4 (0) and draws sixth-card 7 (7) for 7 (6-card P outcome).

RES034 Player Path
P:3->8
RES034 Banker Path
B:0->7
RES034 Deal Length
6 Cards
RES034 Showdown
P (8v7)
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 RES034 (P3+5->8 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 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

RES034 Four-Card Opening Deal
Player 9+4=3 vs Banker 6+4=0

Verified non-natural start via handTotal([9,4])=3 and handTotal([6,4])=0.

RES034 Fifth-Card Modulo Proof
(3 + 5) mod 10 = 8 via 5

Player draws fifth-card 5 (value 5), transforming two-card 3 into three-card 8.

RES034 Banker Tableau Lookup
BANKER_TABLEAU[0][5] = true

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

RES034 Card Count & Winner
6 Cards -> P (8 vs 7)

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

RES034 Derived Road Independence
Red (=) / Blue (≠) Symmetry Only

Big Eye Boy, Small Road, and Cockroach Pig compare Big Road column depths, not P vs B.

MODULO-10 ARITHMETIC · RES034

Step-by-Step Card Arithmetic for RES034: P(9+4)+5 vs B(6+4)

Canonical test [RES034] examines Player 3 (9+4) against Banker 0 (6+4); the fifth card 5 (5) brings Player's raw count to 8, which computes the single-digit remainder to 8.

[RES034-B] Next in [RES034], Banker consults 0-point unconditional draw tier: facing fifth-card 5 (5), Banker 0 draws 7 (7) so 0+7=7 -> 7.

Complete 6-Card Resolution Trace for RES034
RES034 StageRES034 CardsRES034 Modulo MathRES034 Status
[RES034:Init]P(9+4)=3 vs B(6+4)=0playerShouldDraw(3)=true4-Card Deal
[RES034:5th]Player +5 (5)(3+5) mod 10 = 85th Card Sideways
[RES034:6th]Banker +7 (7)(0+7) mod 10 = 76-Card Final
[RES034:Settle]P=8 vs B=7Winner: PBig Road +P
  • [RES034-1] Confirm [RES034] opening P=3 (9+4) and B=0 (6+4) lack Natural 8/9.
  • [RES034-2] Add [RES034] fifth-card 5 (5) to P=3 for (3+5) mod 10 = 8.
  • [RES034-3] Run [RES034] BANKER_TABLEAU[0][5]=true to settle 8 vs 7 (P).
SETTLEMENT & SCOREBOARD · RES034

Showdown Settlement & Scoreboard Logging for RES034 (8 vs 7)

[RES034-C1] Comparing [RES034] final totals (6c), Player 8 vs Banker 7 awards [RES034] to Player (P), which pays 1:1 even money on [RES034] Player boxes with zero commission deducted and appends P to PPBBPBPPBB.

[RES034-D2] Side-bet & road check for [RES034] (P3+5->8 vs B0->7, 6c): [RES034] leaves [RES034] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=7) and triggers [RES034] Panda 8 (winning 3-card Player 8, 25:1); on [RES034] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES034, Banker 0 evaluates Player's three-card total (8) before deciding whether to draw.
TruthBanker 0 inspects only Player's fifth card 5 (value 5) via BANKER_TABLEAU[0][5] = true.
MythBecause RES034 resolves as P, the next derived-road mark must match P'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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