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FINAL TOTAL RESOLUTION [RES310] · 5-CARD PROOF

Player 3 + A (1) vs. Banker 5 (Stands at 5): 5-Card Resolution #310

In walkthrough RES310, Player opens with 9+4 (3) and draws fifth-card A (1) for a modulo-10 total of 4, while Banker opens with 2+3 (5) and stands pat at 5 (5-card B outcome).

RES310 Player Path
P:3->4
RES310 Banker Path
B:5->5
RES310 Deal Length
5 Cards
RES310 Showdown
B (4v5)
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 RES310 (P3+1->4 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

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

RES310 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.

RES310 Fifth-Card Modulo Proof
(3 + 1) mod 10 = 4 via A

Player draws fifth-card A (value 1), transforming two-card 3 into three-card 4.

RES310 Banker Tableau Lookup
BANKER_TABLEAU[5][1] = false

Banker 5 stands pat at 5 without pulling sixth-card 6 (6).

RES310 Card Count & Winner
5 Cards -> B (4 vs 5)

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

RES310 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 · RES310

Step-by-Step Card Arithmetic for RES310: P(9+4)+A vs B(2+3)

Engine check [RES310] confirms `playerShouldDraw(3) === true` on 9+4 vs Banker 2+3 (5); adding fifth-card A (1) gives 4, which evaluates modulo ten to 4.

[RES310-B] Because BANKER_TABLEAU[5][1]=false (5-point four-value window (4..7)) in [RES310], Banker 5 locks 5 at 5c (leaving 6=6 -> 1 unpulled).

Complete 5-Card Resolution Trace for RES310
RES310 StageRES310 CardsRES310 Modulo MathRES310 Status
[RES310:Init]P(9+4)=3 vs B(2+3)=5playerShouldDraw(3)=true4-Card Deal
[RES310:5th]Player +A (1)(3+1) mod 10 = 45th Card Sideways
[RES310:6th]Banker Stands (skip 6=6)Locked at 55-Card Final
[RES310:Settle]P=4 vs B=5Winner: BBig Road +B
  • [RES310-1] Confirm [RES310] opening P=3 (9+4) and B=5 (2+3) lack Natural 8/9.
  • [RES310-2] Add [RES310] fifth-card A (1) to P=3 for (3+1) mod 10 = 4.
  • [RES310-3] Run [RES310] BANKER_TABLEAU[5][1]=false to settle 4 vs 5 (B).
SETTLEMENT & SCOREBOARD · RES310

Showdown Settlement & Scoreboard Logging for RES310 (4 vs 5)

[RES310-C6] Comparing [RES310] final totals (5c), Player 4 vs Banker 5 awards [RES310] to Banker (B), which pays 0.95:1 on 5%-commission [RES310] layouts (or 0.5:1 on 6 at No-Commission [RES310] tables) and appends B to PPBBPPBPBP.

[RES310-D3] Side-bet & road check for [RES310] (P3+1->4 vs B5->5, 5c): [RES310] leaves [RES310] Dragon 7 inactive (needs winning 6c Banker 7, got 5c B=5) and leaves [RES310] Panda 8 inactive (needs winning 3c Player 8, got P=4); on [RES310] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES310, Banker 5 evaluates Player's three-card total (4) before deciding whether to draw.
TruthBanker 5 inspects only Player's fifth card A (value 1) via BANKER_TABLEAU[5][1] = false.
MythBecause RES310 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.
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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