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FINAL TOTAL RESOLUTION [RES076] · 6-CARD PROOF

Player 3 + 2 (2) vs. Banker 1 (Draws A (1)): 6-Card Resolution #76

In walkthrough RES076, Player opens with 9+4 (3) and draws fifth-card 2 (2) for a modulo-10 total of 5, while Banker opens with 10+A (1) and draws sixth-card A (1) for 2 (6-card P outcome).

RES076 Player Path
P:3->5
RES076 Banker Path
B:1->2
RES076 Deal Length
6 Cards
RES076 Showdown
P (5v2)
Engine-Verified Scoreboard · 20 Hands

Read the Board at Table Speed

Open this shoe in /calculator
Big Road P P B B P B B B P P P P B P P B B P P B
Big Eye Boy = = ≠ ≠ = ≠ = = ≠ ≠ ≠ ≠ ≠ = = = =
Small Road ≠ = ≠ ≠ ≠ = = ≠ ≠ = ≠ ≠ ≠ = =
Cockroach Pig = ≠ ≠ = ≠ = ≠ = = ≠ = ≠ ≠ ≠

Scoreboard sequence paired with 6-card resolution RES076 (P3+2->5 vs B1->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

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

  1. Column 4 goes down to Row 3, so use Rule 2: look 2 columns back, at Column 2.
  2. Column 2 stopped at Row 2, one row above → blue (≠).

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.

Cockroach Pig Mark #3

Column 4 has 3 beads. Column 1 has 2 beads. Different depth → blue (≠).

  1. Column 5 starts, so use Rule 1: compare Column 4 with Column 1, 3 columns further back.
  2. Column 4 has 3 beads. Column 1 has 2 beads. Different depth → blue (≠).

Common table reading watchout: Comparing the wrong columns. Compare Column 4, the one that just finished, with Column 1.

Verified Reference Data

Key Facts & Table Specifications

RES076 Four-Card Opening Deal
Player 9+4=3 vs Banker 10+A=1

Verified non-natural start via handTotal([9,4])=3 and handTotal([10,A])=1.

RES076 Fifth-Card Modulo Proof
(3 + 2) mod 10 = 5 via 2

Player draws fifth-card 2 (value 2), transforming two-card 3 into three-card 5.

RES076 Banker Tableau Lookup
BANKER_TABLEAU[1][2] = true

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

RES076 Card Count & Winner
6 Cards -> P (5 vs 2)

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

RES076 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 · RES076

Step-by-Step Card Arithmetic for RES076: P(9+4)+2 vs B(10+A)

Canonical test [RES076] examines Player 3 (9+4) against Banker 1 (10+A); the fifth card 2 (2) brings Player's raw count to 5, which computes the single-digit remainder to 5.

[RES076-B] Because BANKER_TABLEAU[1][2]=true (1-point automatic draw row) in [RES076], Banker 1 takes sixth-card A (1) and 1+1=2 settles at 2.

Complete 6-Card Resolution Trace for RES076
RES076 StageRES076 CardsRES076 Modulo MathRES076 Status
[RES076:Init]P(9+4)=3 vs B(10+A)=1playerShouldDraw(3)=true4-Card Deal
[RES076:5th]Player +2 (2)(3+2) mod 10 = 55th Card Sideways
[RES076:6th]Banker +A (1)(1+1) mod 10 = 26-Card Final
[RES076:Settle]P=5 vs B=2Winner: PBig Road +P
  • [RES076-1] Confirm [RES076] opening P=3 (9+4) and B=1 (10+A) lack Natural 8/9.
  • [RES076-2] Add [RES076] fifth-card 2 (2) to P=3 for (3+2) mod 10 = 5.
  • [RES076-3] Run [RES076] BANKER_TABLEAU[1][2]=true to settle 5 vs 2 (P).
SETTLEMENT & SCOREBOARD · RES076

Showdown Settlement & Scoreboard Logging for RES076 (5 vs 2)

[RES076-C2] Comparing [RES076] final totals (6c), Player 5 vs Banker 2 awards [RES076] to Player (P), which pays 1:1 even money on [RES076] Player boxes with zero commission deducted and appends P to PPBBPBBBPP.

[RES076-D3] Side-bet & road check for [RES076] (P3+2->5 vs B1->2, 6c): [RES076] leaves [RES076] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=2) and leaves [RES076] Panda 8 inactive (needs winning 3c Player 8, got P=5); on [RES076] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES076, Banker 1 evaluates Player's three-card total (5) before deciding whether to draw.
TruthBanker 1 inspects only Player's fifth card 2 (value 2) via BANKER_TABLEAU[1][2] = true.
MythBecause RES076 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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