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FINAL TOTAL RESOLUTION [RES274] · 6-CARD PROOF

Player 3 + 5 (5) vs. Banker 4 (Draws A (1)): 6-Card Resolution #274

In walkthrough RES274, Player opens with 9+4 (3) and draws fifth-card 5 (5) for a modulo-10 total of 8, while Banker opens with A+3 (4) and draws sixth-card A (1) for 5 (6-card P outcome).

RES274 Player Path
P:3->8
RES274 Banker Path
B:4->5
RES274 Deal Length
6 Cards
RES274 Showdown
P (8v5)
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 RES274 (P3+5->8 vs B4->5).

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

RES274 Four-Card Opening Deal
Player 9+4=3 vs Banker A+3=4

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

RES274 Fifth-Card Modulo Proof
(3 + 5) mod 10 = 8 via 5

Player draws fifth-card 5 (value 5), transforming two-card 3 into three-card 8.

RES274 Banker Tableau Lookup
BANKER_TABLEAU[4][5] = true

Banker 4 draws sixth-card A (1) so (4+1) mod 10 = 5.

RES274 Card Count & Winner
6 Cards -> P (8 vs 5)

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

RES274 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 · RES274

Step-by-Step Card Arithmetic for RES274: P(9+4)+5 vs B(A+3)

Arithmetic trace [RES274] starts from four-card deal 9+4=3 vs A+3=4; Player's compulsory draw of 5 (pip value 5) produces raw 8, which wraps modulo-10 to 8.

[RES274-B] Under 4-point six-value gate (2..7) for [RES274], exposed 5 (5) obligates Banker 4 to draw A (1), converting 4+1=5 into 5.

Complete 6-Card Resolution Trace for RES274
RES274 StageRES274 CardsRES274 Modulo MathRES274 Status
[RES274:Init]P(9+4)=3 vs B(A+3)=4playerShouldDraw(3)=true4-Card Deal
[RES274:5th]Player +5 (5)(3+5) mod 10 = 85th Card Sideways
[RES274:6th]Banker +A (1)(4+1) mod 10 = 56-Card Final
[RES274:Settle]P=8 vs B=5Winner: PBig Road +P
  • [RES274-1] Confirm [RES274] opening P=3 (9+4) and B=4 (A+3) lack Natural 8/9.
  • [RES274-2] Add [RES274] fifth-card 5 (5) to P=3 for (3+5) mod 10 = 8.
  • [RES274-3] Run [RES274] BANKER_TABLEAU[4][5]=true to settle 8 vs 5 (P).
SETTLEMENT & SCOREBOARD · RES274

Showdown Settlement & Scoreboard Logging for RES274 (8 vs 5)

[RES274-C2] Comparing [RES274] final totals (6c), Player 8 vs Banker 5 awards [RES274] to Player (P), which pays 1:1 even money on [RES274] Player boxes with zero commission deducted and appends P to PPBBPBPPBB.

[RES274-D4] Side-bet & road check for [RES274] (P3+5->8 vs B4->5, 6c): [RES274] leaves [RES274] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=5) and triggers [RES274] Panda 8 (winning 3-card Player 8, 25:1); on [RES274] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES274, Banker 4 evaluates Player's three-card total (8) before deciding whether to draw.
TruthBanker 4 inspects only Player's fifth card 5 (value 5) via BANKER_TABLEAU[4][5] = true.
MythBecause RES274 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

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  • Structured step-by-step track across Foundations, Big Eye Boy, Small Road, and Cockroach Pig
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