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FINAL TOTAL RESOLUTION [RES039] · 6-CARD PROOF

Player 2 + 6 (6) vs. Banker 0 (Draws 2 (2)): 6-Card Resolution #39

In walkthrough RES039, Player opens with 10+2 (2) and draws fifth-card 6 (6) for a modulo-10 total of 8, while Banker opens with 10+K (0) and draws sixth-card 2 (2) for 2 (6-card P outcome).

RES039 Player Path
P:2->8
RES039 Banker Path
B:0->2
RES039 Deal Length
6 Cards
RES039 Showdown
P (8v2)
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 6-card resolution RES039 (P2+6->8 vs B0->2).

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

RES039 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.

RES039 Fifth-Card Modulo Proof
(2 + 6) mod 10 = 8 via 6

Player draws fifth-card 6 (value 6), transforming two-card 2 into three-card 8.

RES039 Banker Tableau Lookup
BANKER_TABLEAU[0][6] = true

Banker 0 draws sixth-card 2 (2) so (0+2) mod 10 = 2.

RES039 Card Count & Winner
6 Cards -> P (8 vs 2)

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

RES039 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 · RES039

Step-by-Step Card Arithmetic for RES039: P(10+2)+6 vs B(10+K)

Shoe deal [RES039] places 10+2 (2) on Player and 10+K (0) on Banker; because 2 is below 6, Player draws 6 (6) and 8 truncates the decimal tens place to 8.

[RES039-B] Acting on 6=6 inside [RES039], Banker 0 follows 0-point unconditional draw tier and pulls 2 (2) for 0+2=2 -> 2.

Complete 6-Card Resolution Trace for RES039
RES039 StageRES039 CardsRES039 Modulo MathRES039 Status
[RES039:Init]P(10+2)=2 vs B(10+K)=0playerShouldDraw(2)=true4-Card Deal
[RES039:5th]Player +6 (6)(2+6) mod 10 = 85th Card Sideways
[RES039:6th]Banker +2 (2)(0+2) mod 10 = 26-Card Final
[RES039:Settle]P=8 vs B=2Winner: PBig Road +P
  • [RES039-1] Confirm [RES039] opening P=2 (10+2) and B=0 (10+K) lack Natural 8/9.
  • [RES039-2] Add [RES039] fifth-card 6 (6) to P=2 for (2+6) mod 10 = 8.
  • [RES039-3] Run [RES039] BANKER_TABLEAU[0][6]=true to settle 8 vs 2 (P).
SETTLEMENT & SCOREBOARD · RES039

Showdown Settlement & Scoreboard Logging for RES039 (8 vs 2)

[RES039-C4] Comparing [RES039] final totals (6c), Player 8 vs Banker 2 awards [RES039] to Player (P), which pays 1:1 even money on [RES039] Player boxes with zero commission deducted and appends P to BBPPBPBPPP.

[RES039-D8] Side-bet & road check for [RES039] (P2+6->8 vs B0->2, 6c): [RES039] leaves [RES039] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=2) and triggers [RES039] Panda 8 (winning 3-card Player 8, 25:1); on [RES039] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES039, Banker 0 evaluates Player's three-card total (8) before deciding whether to draw.
TruthBanker 0 inspects only Player's fifth card 6 (value 6) via BANKER_TABLEAU[0][6] = true.
MythBecause RES039 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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