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FINAL TOTAL RESOLUTION [RES038] · 6-CARD PROOF

Player 1 + 6 (6) vs. Banker 0 (Draws 8 (8)): 6-Card Resolution #38

In walkthrough RES038, Player opens with 7+4 (1) and draws fifth-card 6 (6) for a modulo-10 total of 7, while Banker opens with 6+4 (0) and draws sixth-card 8 (8) for 8 (6-card B outcome).

RES038 Player Path
P:1->7
RES038 Banker Path
B:0->8
RES038 Deal Length
6 Cards
RES038 Showdown
B (7v8)
Engine-Verified Scoreboard · 20 Hands

Read the Board at Table Speed

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

Scoreboard sequence paired with 6-card resolution RES038 (P1+6->7 vs B0->8).

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

This bead is at Row 2. Column 2 has a bead at Row 2 too → red (=).

  1. Column 3 goes down to Row 2, so use Rule 2: look 1 column back, at Column 2.
  2. Column 2 has a bead at Row 2 too → red (=).

Common table reading watchout: Thinking "no bead at this row" means blue. It is blue only when Column 2 stopped exactly one row above this bead.

Small Road Mark #3

Column 4 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).

  1. Column 5 starts, so use Rule 1: compare Column 4 with Column 2, 2 columns further back.
  2. Column 4 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).

Common table reading watchout: Comparing the wrong columns. Compare Column 4, the one that just finished, with Column 2.

Cockroach Pig Mark #3

Column 6 has 1 bead. Column 3 has 2 beads. Different depth → blue (≠).

  1. Column 7 starts, so use Rule 1: compare Column 6 with Column 3, 3 columns further back.
  2. Column 6 has 1 bead. Column 3 has 2 beads. Different depth → blue (≠).

Common table reading watchout: Comparing the wrong columns. Compare Column 6, the one that just finished, with Column 3.

Verified Reference Data

Key Facts & Table Specifications

RES038 Four-Card Opening Deal
Player 7+4=1 vs Banker 6+4=0

Verified non-natural start via handTotal([7,4])=1 and handTotal([6,4])=0.

RES038 Fifth-Card Modulo Proof
(1 + 6) mod 10 = 7 via 6

Player draws fifth-card 6 (value 6), transforming two-card 1 into three-card 7.

RES038 Banker Tableau Lookup
BANKER_TABLEAU[0][6] = true

Banker 0 draws sixth-card 8 (8) so (0+8) mod 10 = 8.

RES038 Card Count & Winner
6 Cards -> B (7 vs 8)

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

RES038 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 · RES038

Step-by-Step Card Arithmetic for RES038: P(7+4)+6 vs B(6+4)

In coup [RES038], initial cards deal 7+4=1 to Player and 6+4=0 to Banker; lacking a four-card natural, Player takes fifth-card 6 (6) where raw sum 7 projects onto the 0..9 ring to 7.

[RES038-B] Acting on 6=6 inside [RES038], Banker 0 follows 0-point unconditional draw tier and pulls 8 (8) for 0+8=8 -> 8.

Complete 6-Card Resolution Trace for RES038
RES038 StageRES038 CardsRES038 Modulo MathRES038 Status
[RES038:Init]P(7+4)=1 vs B(6+4)=0playerShouldDraw(1)=true4-Card Deal
[RES038:5th]Player +6 (6)(1+6) mod 10 = 75th Card Sideways
[RES038:6th]Banker +8 (8)(0+8) mod 10 = 86-Card Final
[RES038:Settle]P=7 vs B=8Winner: BBig Road +B
  • [RES038-1] Confirm [RES038] opening P=1 (7+4) and B=0 (6+4) lack Natural 8/9.
  • [RES038-2] Add [RES038] fifth-card 6 (6) to P=1 for (1+6) mod 10 = 7.
  • [RES038-3] Run [RES038] BANKER_TABLEAU[0][6]=true to settle 7 vs 8 (B).
SETTLEMENT & SCOREBOARD · RES038

Showdown Settlement & Scoreboard Logging for RES038 (7 vs 8)

[RES038-C10] Comparing [RES038] final totals (6c), Player 7 vs Banker 8 awards [RES038] to Banker (B), which pays 0.95:1 on 5%-commission [RES038] layouts (or 0.5:1 on 6 at No-Commission [RES038] tables) and appends B to PPBBPPBPBP.

[RES038-D12] Side-bet & road check for [RES038] (P1+6->7 vs B0->8, 6c): [RES038] leaves [RES038] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=8) and leaves [RES038] Panda 8 inactive (needs winning 3c Player 8, got P=7); on [RES038] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES038, Banker 0 evaluates Player's three-card total (7) before deciding whether to draw.
TruthBanker 0 inspects only Player's fifth card 6 (value 6) via BANKER_TABLEAU[0][6] = true.
MythBecause RES038 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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