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FINAL TOTAL RESOLUTION [RES316] · 5-CARD PROOF

Player 3 + 2 (2) vs. Banker 5 (Stands at 5): 5-Card Resolution #316

In walkthrough RES316, Player opens with 9+4 (3) and draws fifth-card 2 (2) for a modulo-10 total of 5, while Banker opens with 2+3 (5) and stands pat at 5 (5-card T outcome).

RES316 Player Path
P:3->5
RES316 Banker Path
B:5->5
RES316 Deal Length
5 Cards
RES316 Showdown
T (5v5)
Engine-Verified Scoreboard · 20 Hands

Read the Board at Table Speed

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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 5-card resolution RES316 (P3+2->5 vs B5->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 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

RES316 Four-Card Opening Deal
Player 9+4=3 vs Banker 2+3=5

Verified non-natural start via handTotal([9,4])=3 and handTotal([2,3])=5.

RES316 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.

RES316 Banker Tableau Lookup
BANKER_TABLEAU[5][2] = false

Banker 5 stands pat at 5 without pulling sixth-card 5 (5).

RES316 Card Count & Winner
5 Cards -> T (5 vs 5)

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

RES316 Derived Road Independence
Red (=) / Blue (≠) Symmetry Only

Big Eye Boy, Small Road, and Cockroach Pig compare Big Road column depths, not T vs B.

MODULO-10 ARITHMETIC · RES316

Step-by-Step Card Arithmetic for RES316: P(9+4)+2 vs B(2+3)

Arithmetic trace [RES316] starts from four-card deal 9+4=3 vs 2+3=5; Player's compulsory draw of 2 (pip value 2) produces raw 5, which wraps modulo-10 to 5.

[RES316-B] Evaluating bankerShouldDraw(5, 2)=false (5-point four-value window (4..7)) in [RES316], Banker 5 preserves 5 while 5 (5) remains undealt.

Complete 5-Card Resolution Trace for RES316
RES316 StageRES316 CardsRES316 Modulo MathRES316 Status
[RES316:Init]P(9+4)=3 vs B(2+3)=5playerShouldDraw(3)=true4-Card Deal
[RES316:5th]Player +2 (2)(3+2) mod 10 = 55th Card Sideways
[RES316:6th]Banker Stands (skip 5=5)Locked at 55-Card Final
[RES316:Settle]P=5 vs B=5Winner: TBig Road +T
  • [RES316-1] Confirm [RES316] opening P=3 (9+4) and B=5 (2+3) lack Natural 8/9.
  • [RES316-2] Add [RES316] fifth-card 2 (2) to P=3 for (3+2) mod 10 = 5.
  • [RES316-3] Run [RES316] BANKER_TABLEAU[5][2]=false to settle 5 vs 5 (T).
SETTLEMENT & SCOREBOARD · RES316

Showdown Settlement & Scoreboard Logging for RES316 (5 vs 5)

[RES316-C3] Comparing [RES316] final totals (5c), Player 5 vs Banker 5 awards [RES316] to Tie (T), which pushes main [RES316] Player/Banker wagers while settling [RES316] Tie bets at 8:1 or 9:1 and appends T to PPBBPBBBPP.

[RES316-D5] Side-bet & road check for [RES316] (P3+2->5 vs B5->5, 5c): [RES316] leaves [RES316] Dragon 7 inactive (needs winning 6c Banker 7, got 5c B=5) and leaves [RES316] Panda 8 inactive (needs winning 3c Player 8, got P=5); on [RES316] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES316, Banker 5 evaluates Player's three-card total (5) before deciding whether to draw.
TruthBanker 5 inspects only Player's fifth card 2 (value 2) via BANKER_TABLEAU[5][2] = false.
MythBecause RES316 resolves as T, the next derived-road mark must match T'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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