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FINAL TOTAL RESOLUTION [RES145] · 6-CARD PROOF

Player 0 + 4 (4) vs. Banker 2 (Draws 8 (8)): 6-Card Resolution #145

In walkthrough RES145, Player opens with 10+K (0) and draws fifth-card 4 (4) for a modulo-10 total of 4, while Banker opens with 10+2 (2) and draws sixth-card 8 (8) for 0 (6-card P outcome).

RES145 Player Path
P:0->4
RES145 Banker Path
B:2->0
RES145 Deal Length
6 Cards
RES145 Showdown
P (4v0)
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 P B P P P B B B P B B
Big Eye Boy = = ≠ = ≠ ≠ = = ≠ ≠ = ≠ = = = ≠ ≠
Small Road ≠ ≠ ≠ ≠ ≠ ≠ = ≠ ≠ ≠ ≠ = ≠ ≠ =
Cockroach Pig ≠ = = ≠ ≠ = = ≠ ≠ = ≠ ≠ = =

Scoreboard sequence paired with 6-card resolution RES145 (P0+4->4 vs B2->0).

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

RES145 Four-Card Opening Deal
Player 10+K=0 vs Banker 10+2=2

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

RES145 Fifth-Card Modulo Proof
(0 + 4) mod 10 = 4 via 4

Player draws fifth-card 4 (value 4), transforming two-card 0 into three-card 4.

RES145 Banker Tableau Lookup
BANKER_TABLEAU[2][4] = true

Banker 2 draws sixth-card 8 (8) so (2+8) mod 10 = 0.

RES145 Card Count & Winner
6 Cards -> P (4 vs 0)

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

RES145 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 · RES145

Step-by-Step Card Arithmetic for RES145: P(10+K)+4 vs B(10+2)

Under audit [RES145], Player opens on two-card 0 (10+K) opposite Banker 2 (10+2), triggering a mandatory fifth-card pull of 4 (value 4) that settles via mod-10 arithmetic from 4 into 4.

[RES145-B] Under 2-point mandatory draw band for [RES145], exposed 4 (4) obligates Banker 2 to draw 8 (8), converting 2+8=10 into 0.

Complete 6-Card Resolution Trace for RES145
RES145 StageRES145 CardsRES145 Modulo MathRES145 Status
[RES145:Init]P(10+K)=0 vs B(10+2)=2playerShouldDraw(0)=true4-Card Deal
[RES145:5th]Player +4 (4)(0+4) mod 10 = 45th Card Sideways
[RES145:6th]Banker +8 (8)(2+8) mod 10 = 06-Card Final
[RES145:Settle]P=4 vs B=0Winner: PBig Road +P
  • [RES145-1] Confirm [RES145] opening P=0 (10+K) and B=2 (10+2) lack Natural 8/9.
  • [RES145-2] Add [RES145] fifth-card 4 (4) to P=0 for (0+4) mod 10 = 4.
  • [RES145-3] Run [RES145] BANKER_TABLEAU[2][4]=true to settle 4 vs 0 (P).
SETTLEMENT & SCOREBOARD · RES145

Showdown Settlement & Scoreboard Logging for RES145 (4 vs 0)

[RES145-C6] Comparing [RES145] final totals (6c), Player 4 vs Banker 0 awards [RES145] to Player (P), which pays 1:1 even money on [RES145] Player boxes with zero commission deducted and appends P to BBPPBPBBPP.

[RES145-D0] Side-bet & road check for [RES145] (P0+4->4 vs B2->0, 6c): [RES145] leaves [RES145] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=0) and leaves [RES145] Panda 8 inactive (needs winning 3c Player 8, got P=4); on [RES145] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES145, Banker 2 evaluates Player's three-card total (4) before deciding whether to draw.
TruthBanker 2 inspects only Player's fifth card 4 (value 4) via BANKER_TABLEAU[2][4] = true.
MythBecause RES145 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.
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
  • 74 interactive lesson scoreboards and 94 inline quiz checks with plain-English mark feedback
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