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FINAL TOTAL RESOLUTION [RES146] · 6-CARD PROOF

Player 1 + 4 (4) vs. Banker 2 (Draws 2 (2)): 6-Card Resolution #146

In walkthrough RES146, Player opens with 7+4 (1) and draws fifth-card 4 (4) for a modulo-10 total of 5, while Banker opens with 8+4 (2) and draws sixth-card 2 (2) for 4 (6-card P outcome).

RES146 Player Path
P:1->5
RES146 Banker Path
B:2->4
RES146 Deal Length
6 Cards
RES146 Showdown
P (5v4)
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 RES146 (P1+4->5 vs B2->4).

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

RES146 Four-Card Opening Deal
Player 7+4=1 vs Banker 8+4=2

Verified non-natural start via handTotal([7,4])=1 and handTotal([8,4])=2.

RES146 Fifth-Card Modulo Proof
(1 + 4) mod 10 = 5 via 4

Player draws fifth-card 4 (value 4), transforming two-card 1 into three-card 5.

RES146 Banker Tableau Lookup
BANKER_TABLEAU[2][4] = true

Banker 2 draws sixth-card 2 (2) so (2+2) mod 10 = 4.

RES146 Card Count & Winner
6 Cards -> P (5 vs 4)

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

RES146 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 · RES146

Step-by-Step Card Arithmetic for RES146: P(7+4)+4 vs B(8+4)

Canonical test [RES146] examines Player 1 (7+4) against Banker 2 (8+4); the fifth card 4 (4) brings Player's raw count to 5, which computes the single-digit remainder to 5.

[RES146-B] Evaluating bankerShouldDraw(2, 4)=true (2-point mandatory draw band) in [RES146], sixth-card 2 (2) advances Banker 2 via 2+2=4 to 4.

Complete 6-Card Resolution Trace for RES146
RES146 StageRES146 CardsRES146 Modulo MathRES146 Status
[RES146:Init]P(7+4)=1 vs B(8+4)=2playerShouldDraw(1)=true4-Card Deal
[RES146:5th]Player +4 (4)(1+4) mod 10 = 55th Card Sideways
[RES146:6th]Banker +2 (2)(2+2) mod 10 = 46-Card Final
[RES146:Settle]P=5 vs B=4Winner: PBig Road +P
  • [RES146-1] Confirm [RES146] opening P=1 (7+4) and B=2 (8+4) lack Natural 8/9.
  • [RES146-2] Add [RES146] fifth-card 4 (4) to P=1 for (1+4) mod 10 = 5.
  • [RES146-3] Run [RES146] BANKER_TABLEAU[2][4]=true to settle 5 vs 4 (P).
SETTLEMENT & SCOREBOARD · RES146

Showdown Settlement & Scoreboard Logging for RES146 (5 vs 4)

[RES146-C0] Comparing [RES146] final totals (6c), Player 5 vs Banker 4 awards [RES146] to Player (P), which pays 1:1 even money on [RES146] Player boxes with zero commission deducted and appends P to PPBBPBPPBB.

[RES146-D9] Side-bet & road check for [RES146] (P1+4->5 vs B2->4, 6c): [RES146] leaves [RES146] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=4) and leaves [RES146] Panda 8 inactive (needs winning 3c Player 8, got P=5); on [RES146] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES146, Banker 2 evaluates Player's three-card total (5) before deciding whether to draw.
TruthBanker 2 inspects only Player's fifth card 4 (value 4) via BANKER_TABLEAU[2][4] = true.
MythBecause RES146 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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