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FINAL TOTAL RESOLUTION [RES080] · 6-CARD PROOF

Player 1 + 3 (3) vs. Banker 1 (Draws 2 (2)): 6-Card Resolution #80

In walkthrough RES080, Player opens with 7+4 (1) and draws fifth-card 3 (3) for a modulo-10 total of 4, while Banker opens with 10+A (1) and draws sixth-card 2 (2) for 3 (6-card P outcome).

RES080 Player Path
P:1->4
RES080 Banker Path
B:1->3
RES080 Deal Length
6 Cards
RES080 Showdown
P (4v3)
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 P P P B B B P P P P B
Big Eye Boy = = ≠ = ≠ ≠ ≠ ≠ = ≠ = = = = = ≠ ≠
Small Road ≠ ≠ ≠ ≠ = = ≠ ≠ ≠ = ≠ = = ≠ ≠
Cockroach Pig ≠ = = = ≠ = ≠ = ≠ ≠ ≠ = = ≠

Scoreboard sequence paired with 6-card resolution RES080 (P1+3->4 vs B1->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

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

RES080 Four-Card Opening Deal
Player 7+4=1 vs Banker 10+A=1

Verified non-natural start via handTotal([7,4])=1 and handTotal([10,A])=1.

RES080 Fifth-Card Modulo Proof
(1 + 3) mod 10 = 4 via 3

Player draws fifth-card 3 (value 3), transforming two-card 1 into three-card 4.

RES080 Banker Tableau Lookup
BANKER_TABLEAU[1][3] = true

Banker 1 draws sixth-card 2 (2) so (1+2) mod 10 = 3.

RES080 Card Count & Winner
6 Cards -> P (4 vs 3)

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

RES080 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 · RES080

Step-by-Step Card Arithmetic for RES080: P(7+4)+3 vs B(10+A)

In coup [RES080], initial cards deal 7+4=1 to Player and 10+A=1 to Banker; lacking a four-card natural, Player takes fifth-card 3 (3) where raw sum 4 projects onto the 0..9 ring to 4.

[RES080-B] Under 1-point automatic draw row for [RES080], exposed 3 (3) obligates Banker 1 to draw 2 (2), converting 1+2=3 into 3.

Complete 6-Card Resolution Trace for RES080
RES080 StageRES080 CardsRES080 Modulo MathRES080 Status
[RES080:Init]P(7+4)=1 vs B(10+A)=1playerShouldDraw(1)=true4-Card Deal
[RES080:5th]Player +3 (3)(1+3) mod 10 = 45th Card Sideways
[RES080:6th]Banker +2 (2)(1+2) mod 10 = 36-Card Final
[RES080:Settle]P=4 vs B=3Winner: PBig Road +P
  • [RES080-1] Confirm [RES080] opening P=1 (7+4) and B=1 (10+A) lack Natural 8/9.
  • [RES080-2] Add [RES080] fifth-card 3 (3) to P=1 for (1+3) mod 10 = 4.
  • [RES080-3] Run [RES080] BANKER_TABLEAU[1][3]=true to settle 4 vs 3 (P).
SETTLEMENT & SCOREBOARD · RES080

Showdown Settlement & Scoreboard Logging for RES080 (4 vs 3)

[RES080-C0] Comparing [RES080] final totals (6c), Player 4 vs Banker 3 awards [RES080] to Player (P), which pays 1:1 even money on [RES080] Player boxes with zero commission deducted and appends P to PPBBPBPPBP.

[RES080-D0] Side-bet & road check for [RES080] (P1+3->4 vs B1->3, 6c): [RES080] leaves [RES080] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=3) and leaves [RES080] Panda 8 inactive (needs winning 3c Player 8, got P=4); on [RES080] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES080, Banker 1 evaluates Player's three-card total (4) before deciding whether to draw.
TruthBanker 1 inspects only Player's fifth card 3 (value 3) via BANKER_TABLEAU[1][3] = true.
MythBecause RES080 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

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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