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FINAL TOTAL RESOLUTION [RES312] · 5-CARD PROOF

Player 5 + A (1) vs. Banker 5 (Stands at 5): 5-Card Resolution #312

In walkthrough RES312, Player opens with A+4 (5) and draws fifth-card A (1) for a modulo-10 total of 6, while Banker opens with 2+3 (5) and stands pat at 5 (5-card P outcome).

RES312 Player Path
P:5->6
RES312 Banker Path
B:5->5
RES312 Deal Length
5 Cards
RES312 Showdown
P (6v5)
Engine-Verified Scoreboard · 20 Hands

Read the Board at Table Speed

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Big Road P P B B P B P B B B P P P P B B P B P P
Big Eye Boy = = ≠ = = ≠ = ≠ = = ≠ ≠ = ≠ ≠ = ≠
Small Road ≠ ≠ = ≠ = ≠ ≠ = = ≠ = ≠ ≠ ≠ ≠
Cockroach Pig ≠ ≠ ≠ = ≠ ≠ = = ≠ ≠ ≠ ≠ ≠ =

Scoreboard sequence paired with 5-card resolution RES312 (P5+1->6 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

Column 5 has 1 bead. Column 3 has 1 bead. Same depth → red (=).

  1. Column 6 starts, so use Rule 1: compare Column 5 with Column 3, 2 columns further back.
  2. Column 5 has 1 bead. Column 3 has 1 bead. Same depth → red (=).

Common table reading watchout: Comparing the wrong columns. Compare Column 5, the one that just finished, with Column 3.

Cockroach Pig Mark #3

This bead is at Row 2. Column 3 stopped at Row 1, one row above → blue (≠).

  1. Column 6 goes down to Row 2, so use Rule 2: look 3 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.

Verified Reference Data

Key Facts & Table Specifications

RES312 Four-Card Opening Deal
Player A+4=5 vs Banker 2+3=5

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

RES312 Fifth-Card Modulo Proof
(5 + 1) mod 10 = 6 via A

Player draws fifth-card A (value 1), transforming two-card 5 into three-card 6.

RES312 Banker Tableau Lookup
BANKER_TABLEAU[5][1] = false

Banker 5 stands pat at 5 without pulling sixth-card 4 (4).

RES312 Card Count & Winner
5 Cards -> P (6 vs 5)

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

RES312 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 · RES312

Step-by-Step Card Arithmetic for RES312: P(A+4)+A vs B(2+3)

Within resolution [RES312], Player's opening A+4 totals 5 against Banker's 2+3 (5); Punto Banco rules require drawing A (1), and 5+1=6 extracts the terminal digit to 6.

[RES312-B] Inspecting A=1 via 5-point four-value window (4..7) in [RES312], Banker 5 stands at 5; 4 (4) stays in the shoe instead of 9.

Complete 5-Card Resolution Trace for RES312
RES312 StageRES312 CardsRES312 Modulo MathRES312 Status
[RES312:Init]P(A+4)=5 vs B(2+3)=5playerShouldDraw(5)=true4-Card Deal
[RES312:5th]Player +A (1)(5+1) mod 10 = 65th Card Sideways
[RES312:6th]Banker Stands (skip 4=4)Locked at 55-Card Final
[RES312:Settle]P=6 vs B=5Winner: PBig Road +P
  • [RES312-1] Confirm [RES312] opening P=5 (A+4) and B=5 (2+3) lack Natural 8/9.
  • [RES312-2] Add [RES312] fifth-card A (1) to P=5 for (5+1) mod 10 = 6.
  • [RES312-3] Run [RES312] BANKER_TABLEAU[5][1]=false to settle 6 vs 5 (P).
SETTLEMENT & SCOREBOARD · RES312

Showdown Settlement & Scoreboard Logging for RES312 (6 vs 5)

[RES312-C5] Comparing [RES312] final totals (5c), Player 6 vs Banker 5 awards [RES312] to Player (P), which pays 1:1 even money on [RES312] Player boxes with zero commission deducted and appends P to PPBBPBPBBB.

[RES312-D8] Side-bet & road check for [RES312] (P5+1->6 vs B5->5, 5c): [RES312] leaves [RES312] Dragon 7 inactive (needs winning 6c Banker 7, got 5c B=5) and leaves [RES312] Panda 8 inactive (needs winning 3c Player 8, got P=6); on [RES312] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES312, Banker 5 evaluates Player's three-card total (6) before deciding whether to draw.
TruthBanker 5 inspects only Player's fifth card A (value 1) via BANKER_TABLEAU[5][1] = false.
MythBecause RES312 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.
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  • Structured step-by-step track across Foundations, Big Eye Boy, Small Road, and Cockroach Pig
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