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FINAL TOTAL RESOLUTION [RES045] · 6-CARD PROOF

Player 2 + 7 (7) vs. Banker 0 (Draws A (1)): 6-Card Resolution #45

In walkthrough RES045, Player opens with 10+2 (2) and draws fifth-card 7 (7) for a modulo-10 total of 9, while Banker opens with 10+K (0) and draws sixth-card A (1) for 1 (6-card P outcome).

RES045 Player Path
P:2->9
RES045 Banker Path
B:0->1
RES045 Deal Length
6 Cards
RES045 Showdown
P (9v1)
Engine-Verified Scoreboard · 20 Hands

Read the Board at Table Speed

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

Scoreboard sequence paired with 6-card resolution RES045 (P2+7->9 vs B0->1).

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

This bead is at Row 2. Column 2 has a bead at Row 2 too → red (=).

  1. Column 4 goes down to Row 2, so use Rule 2: look 2 columns 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.

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

RES045 Four-Card Opening Deal
Player 10+2=2 vs Banker 10+K=0

Verified non-natural start via handTotal([10,2])=2 and handTotal([10,K])=0.

RES045 Fifth-Card Modulo Proof
(2 + 7) mod 10 = 9 via 7

Player draws fifth-card 7 (value 7), transforming two-card 2 into three-card 9.

RES045 Banker Tableau Lookup
BANKER_TABLEAU[0][7] = true

Banker 0 draws sixth-card A (1) so (0+1) mod 10 = 1.

RES045 Card Count & Winner
6 Cards -> P (9 vs 1)

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

RES045 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 · RES045

Step-by-Step Card Arithmetic for RES045: P(10+2)+7 vs B(10+K)

During tableau case [RES045], Player holds 10+2 for 2 while Banker holds 10+K for 0; drawing fifth-card 7 (7) shifts Player from 2 to 9, which reduces mod-10 to 9.

[RES045-B] Six-card branch [RES045] activates as 7 (7) hits Banker 0's 0-point unconditional draw tier; drawing A (1) sends 0+1=1 to 1.

Complete 6-Card Resolution Trace for RES045
RES045 StageRES045 CardsRES045 Modulo MathRES045 Status
[RES045:Init]P(10+2)=2 vs B(10+K)=0playerShouldDraw(2)=true4-Card Deal
[RES045:5th]Player +7 (7)(2+7) mod 10 = 95th Card Sideways
[RES045:6th]Banker +A (1)(0+1) mod 10 = 16-Card Final
[RES045:Settle]P=9 vs B=1Winner: PBig Road +P
  • [RES045-1] Confirm [RES045] opening P=2 (10+2) and B=0 (10+K) lack Natural 8/9.
  • [RES045-2] Add [RES045] fifth-card 7 (7) to P=2 for (2+7) mod 10 = 9.
  • [RES045-3] Run [RES045] BANKER_TABLEAU[0][7]=true to settle 9 vs 1 (P).
SETTLEMENT & SCOREBOARD · RES045

Showdown Settlement & Scoreboard Logging for RES045 (9 vs 1)

[RES045-C1] Comparing [RES045] final totals (6c), Player 9 vs Banker 1 awards [RES045] to Player (P), which pays 1:1 even money on [RES045] Player boxes with zero commission deducted and appends P to BBPPBBPPPB.

[RES045-D10] Side-bet & road check for [RES045] (P2+7->9 vs B0->1, 6c): [RES045] leaves [RES045] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=1) and leaves [RES045] Panda 8 inactive (needs winning 3c Player 8, got P=9); on [RES045] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES045, Banker 0 evaluates Player's three-card total (9) before deciding whether to draw.
TruthBanker 0 inspects only Player's fifth card 7 (value 7) via BANKER_TABLEAU[0][7] = true.
MythBecause RES045 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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