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FINAL TOTAL RESOLUTION [RES374] · 5-CARD PROOF

Player 1 + 2 (2) vs. Banker 6 (Stands at 6): 5-Card Resolution #374

In walkthrough RES374, Player opens with 7+4 (1) and draws fifth-card 2 (2) for a modulo-10 total of 3, while Banker opens with 2+4 (6) and stands pat at 6 (5-card B outcome).

RES374 Player Path
P:1->3
RES374 Banker Path
B:6->6
RES374 Deal Length
5 Cards
RES374 Showdown
B (3v6)
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 5-card resolution RES374 (P1+2->3 vs B6->6).

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

RES374 Four-Card Opening Deal
Player 7+4=1 vs Banker 2+4=6

Verified non-natural start via handTotal([7,4])=1 and handTotal([2,4])=6.

RES374 Fifth-Card Modulo Proof
(1 + 2) mod 10 = 3 via 2

Player draws fifth-card 2 (value 2), transforming two-card 1 into three-card 3.

RES374 Banker Tableau Lookup
BANKER_TABLEAU[6][2] = false

Banker 6 stands pat at 6 without pulling sixth-card 8 (8).

RES374 Card Count & Winner
5 Cards -> B (3 vs 6)

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

RES374 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 · RES374

Step-by-Step Card Arithmetic for RES374: P(7+4)+2 vs B(2+4)

In coup [RES374], initial cards deal 7+4=1 to Player and 2+4=6 to Banker; lacking a four-card natural, Player takes fifth-card 2 (2) where raw sum 3 projects onto the 0..9 ring to 3.

[RES374-B] Because BANKER_TABLEAU[6][2]=false (6-point two-value trigger (6..7)) in [RES374], Banker 6 locks 6 at 5c (leaving 8=8 -> 4 unpulled).

Complete 5-Card Resolution Trace for RES374
RES374 StageRES374 CardsRES374 Modulo MathRES374 Status
[RES374:Init]P(7+4)=1 vs B(2+4)=6playerShouldDraw(1)=true4-Card Deal
[RES374:5th]Player +2 (2)(1+2) mod 10 = 35th Card Sideways
[RES374:6th]Banker Stands (skip 8=8)Locked at 65-Card Final
[RES374:Settle]P=3 vs B=6Winner: BBig Road +B
  • [RES374-1] Confirm [RES374] opening P=1 (7+4) and B=6 (2+4) lack Natural 8/9.
  • [RES374-2] Add [RES374] fifth-card 2 (2) to P=1 for (1+2) mod 10 = 3.
  • [RES374-3] Run [RES374] BANKER_TABLEAU[6][2]=false to settle 3 vs 6 (B).
SETTLEMENT & SCOREBOARD · RES374

Showdown Settlement & Scoreboard Logging for RES374 (3 vs 6)

[RES374-C7] Comparing [RES374] final totals (5c), Player 3 vs Banker 6 awards [RES374] to Banker (B), which pays 0.95:1 on 5%-commission [RES374] layouts (or 0.5:1 on 6 at No-Commission [RES374] tables) and appends B to PPBBPPBPBP.

[RES374-D7] Side-bet & road check for [RES374] (P1+2->3 vs B6->6, 5c): [RES374] leaves [RES374] Dragon 7 inactive (needs winning 6c Banker 7, got 5c B=6) and leaves [RES374] Panda 8 inactive (needs winning 3c Player 8, got P=3); on [RES374] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES374, Banker 6 evaluates Player's three-card total (3) before deciding whether to draw.
TruthBanker 6 inspects only Player's fifth card 2 (value 2) via BANKER_TABLEAU[6][2] = false.
MythBecause RES374 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.
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  • Structured step-by-step track across Foundations, Big Eye Boy, Small Road, and Cockroach Pig
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