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FINAL TOTAL RESOLUTION [RES319] · 5-CARD PROOF

Player 0 + 3 (3) vs. Banker 5 (Stands at 5): 5-Card Resolution #319

In walkthrough RES319, Player opens with 10+K (0) and draws fifth-card 3 (3) for a modulo-10 total of 3, while Banker opens with A+4 (5) and stands pat at 5 (5-card B outcome).

RES319 Player Path
P:0->3
RES319 Banker Path
B:5->5
RES319 Deal Length
5 Cards
RES319 Showdown
B (3v5)
Engine-Verified Scoreboard · 20 Hands

Read the Board at Table Speed

Open this shoe in /calculator
Big Road B B P P B P B B P B B B P P P B B B B P
Big Eye Boy = = ≠ = ≠ ≠ ≠ ≠ = ≠ = = = = = ≠ ≠
Small Road ≠ ≠ ≠ ≠ = = ≠ ≠ ≠ = ≠ = = ≠ ≠
Cockroach Pig ≠ = = = ≠ = ≠ = ≠ ≠ ≠ = = ≠

Scoreboard sequence paired with 5-card resolution RES319 (P0+3->3 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 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

RES319 Four-Card Opening Deal
Player 10+K=0 vs Banker A+4=5

Verified non-natural start via handTotal([10,K])=0 and handTotal([A,4])=5.

RES319 Fifth-Card Modulo Proof
(0 + 3) mod 10 = 3 via 3

Player draws fifth-card 3 (value 3), transforming two-card 0 into three-card 3.

RES319 Banker Tableau Lookup
BANKER_TABLEAU[5][3] = false

Banker 5 stands pat at 5 without pulling sixth-card 2 (2).

RES319 Card Count & Winner
5 Cards -> B (3 vs 5)

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

RES319 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 · RES319

Step-by-Step Card Arithmetic for RES319: P(10+K)+3 vs B(A+4)

Shoe deal [RES319] places 10+K (0) on Player and A+4 (5) on Banker; because 0 is below 6, Player draws 3 (3) and 3 truncates the decimal tens place to 3.

[RES319-B] Guided by 5-point four-value window (4..7) against 3 (3) in [RES319], Banker 5 stands on 5 so the coup finishes in 5c without 2 (2).

Complete 5-Card Resolution Trace for RES319
RES319 StageRES319 CardsRES319 Modulo MathRES319 Status
[RES319:Init]P(10+K)=0 vs B(A+4)=5playerShouldDraw(0)=true4-Card Deal
[RES319:5th]Player +3 (3)(0+3) mod 10 = 35th Card Sideways
[RES319:6th]Banker Stands (skip 2=2)Locked at 55-Card Final
[RES319:Settle]P=3 vs B=5Winner: BBig Road +B
  • [RES319-1] Confirm [RES319] opening P=0 (10+K) and B=5 (A+4) lack Natural 8/9.
  • [RES319-2] Add [RES319] fifth-card 3 (3) to P=0 for (0+3) mod 10 = 3.
  • [RES319-3] Run [RES319] BANKER_TABLEAU[5][3]=false to settle 3 vs 5 (B).
SETTLEMENT & SCOREBOARD · RES319

Showdown Settlement & Scoreboard Logging for RES319 (3 vs 5)

[RES319-C7] Comparing [RES319] final totals (5c), Player 3 vs Banker 5 awards [RES319] to Banker (B), which pays 0.95:1 on 5%-commission [RES319] layouts (or 0.5:1 on 6 at No-Commission [RES319] tables) and appends B to BBPPBPBBPB.

[RES319-D6] Side-bet & road check for [RES319] (P0+3->3 vs B5->5, 5c): [RES319] leaves [RES319] Dragon 7 inactive (needs winning 6c Banker 7, got 5c B=5) and leaves [RES319] Panda 8 inactive (needs winning 3c Player 8, got P=3); on [RES319] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES319, Banker 5 evaluates Player's three-card total (3) before deciding whether to draw.
TruthBanker 5 inspects only Player's fifth card 3 (value 3) via BANKER_TABLEAU[5][3] = false.
MythBecause RES319 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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