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FINAL TOTAL RESOLUTION [RES246] · 5-CARD PROOF

Player 5 + 10 (0) vs. Banker 4 (Stands at 4): 5-Card Resolution #246

In walkthrough RES246, Player opens with A+4 (5) and draws fifth-card 10 (0) for a modulo-10 total of 5, while Banker opens with A+3 (4) and stands pat at 4 (5-card P outcome).

RES246 Player Path
P:5->5
RES246 Banker Path
B:4->4
RES246 Deal Length
5 Cards
RES246 Showdown
P (5v4)
Engine-Verified Scoreboard · 20 Hands

Read the Board at Table Speed

Open this shoe in /calculator
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 RES246 (P5+0->5 vs B4->4).

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

RES246 Four-Card Opening Deal
Player A+4=5 vs Banker A+3=4

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

RES246 Fifth-Card Modulo Proof
(5 + 0) mod 10 = 5 via 10

Player draws fifth-card 10 (value 0), transforming two-card 5 into three-card 5.

RES246 Banker Tableau Lookup
BANKER_TABLEAU[4][0] = false

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

RES246 Card Count & Winner
5 Cards -> P (5 vs 4)

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

RES246 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 · RES246

Step-by-Step Card Arithmetic for RES246: P(A+4)+10 vs B(A+3)

Arithmetic trace [RES246] starts from four-card deal A+4=5 vs A+3=4; Player's compulsory draw of 10 (pip value 0) produces raw 5, which wraps modulo-10 to 5.

[RES246-B] Inspecting 10=0 via 4-point six-value gate (2..7) in [RES246], Banker 4 stands at 4; 4 (4) stays in the shoe instead of 8.

Complete 5-Card Resolution Trace for RES246
RES246 StageRES246 CardsRES246 Modulo MathRES246 Status
[RES246:Init]P(A+4)=5 vs B(A+3)=4playerShouldDraw(5)=true4-Card Deal
[RES246:5th]Player +10 (0)(5+0) mod 10 = 55th Card Sideways
[RES246:6th]Banker Stands (skip 4=4)Locked at 45-Card Final
[RES246:Settle]P=5 vs B=4Winner: PBig Road +P
  • [RES246-1] Confirm [RES246] opening P=5 (A+4) and B=4 (A+3) lack Natural 8/9.
  • [RES246-2] Add [RES246] fifth-card 10 (0) to P=5 for (5+0) mod 10 = 5.
  • [RES246-3] Run [RES246] BANKER_TABLEAU[4][0]=false to settle 5 vs 4 (P).
SETTLEMENT & SCOREBOARD · RES246

Showdown Settlement & Scoreboard Logging for RES246 (5 vs 4)

[RES246-C5] Comparing [RES246] final totals (5c), Player 5 vs Banker 4 awards [RES246] to Player (P), which pays 1:1 even money on [RES246] Player boxes with zero commission deducted and appends P to PPBBPPBPBP.

[RES246-D12] Side-bet & road check for [RES246] (P5+0->5 vs B4->4, 5c): [RES246] leaves [RES246] Dragon 7 inactive (needs winning 6c Banker 7, got 5c B=4) and leaves [RES246] Panda 8 inactive (needs winning 3c Player 8, got P=5); on [RES246] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES246, Banker 4 evaluates Player's three-card total (5) before deciding whether to draw.
TruthBanker 4 inspects only Player's fifth card 10 (value 0) via BANKER_TABLEAU[4][0] = false.
MythBecause RES246 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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