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FINAL TOTAL RESOLUTION [RES037] · 6-CARD PROOF

Player 0 + 6 (6) vs. Banker 0 (Draws 4 (4)): 6-Card Resolution #37

In walkthrough RES037, Player opens with 10+K (0) and draws fifth-card 6 (6) for a modulo-10 total of 6, while Banker opens with 10+K (0) and draws sixth-card 4 (4) for 4 (6-card P outcome).

RES037 Player Path
P:0->6
RES037 Banker Path
B:0->4
RES037 Deal Length
6 Cards
RES037 Showdown
P (6v4)
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 B P B B P P P B B B B P P
Big Eye Boy = = = = ≠ = = ≠ ≠ = ≠ ≠ = = ≠ ≠ =
Small Road = = ≠ ≠ = ≠ ≠ ≠ = ≠ = ≠ = ≠ =
Cockroach Pig ≠ ≠ ≠ ≠ ≠ ≠ = ≠ ≠ = = ≠ =

Scoreboard sequence paired with 6-card resolution RES037 (P0+6->6 vs B0->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

RES037 Four-Card Opening Deal
Player 10+K=0 vs Banker 10+K=0

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

RES037 Fifth-Card Modulo Proof
(0 + 6) mod 10 = 6 via 6

Player draws fifth-card 6 (value 6), transforming two-card 0 into three-card 6.

RES037 Banker Tableau Lookup
BANKER_TABLEAU[0][6] = true

Banker 0 draws sixth-card 4 (4) so (0+4) mod 10 = 4.

RES037 Card Count & Winner
6 Cards -> P (6 vs 4)

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

RES037 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 · RES037

Step-by-Step Card Arithmetic for RES037: P(10+K)+6 vs B(10+K)

Evaluating sequence [RES037], the shoe delivers 10+K (0) to Player and 10+K (0) to Banker; after natural checks clear, fifth-card 6 (6) maps the raw pip total mod 10 (0+6=6) to final Player total 6.

[RES037-B] Because BANKER_TABLEAU[0][6]=true (0-point unconditional draw tier) in [RES037], Banker 0 takes sixth-card 4 (4) and 0+4=4 settles at 4.

Complete 6-Card Resolution Trace for RES037
RES037 StageRES037 CardsRES037 Modulo MathRES037 Status
[RES037:Init]P(10+K)=0 vs B(10+K)=0playerShouldDraw(0)=true4-Card Deal
[RES037:5th]Player +6 (6)(0+6) mod 10 = 65th Card Sideways
[RES037:6th]Banker +4 (4)(0+4) mod 10 = 46-Card Final
[RES037:Settle]P=6 vs B=4Winner: PBig Road +P
  • [RES037-1] Confirm [RES037] opening P=0 (10+K) and B=0 (10+K) lack Natural 8/9.
  • [RES037-2] Add [RES037] fifth-card 6 (6) to P=0 for (0+6) mod 10 = 6.
  • [RES037-3] Run [RES037] BANKER_TABLEAU[0][6]=true to settle 6 vs 4 (P).
SETTLEMENT & SCOREBOARD · RES037

Showdown Settlement & Scoreboard Logging for RES037 (6 vs 4)

[RES037-C5] Comparing [RES037] final totals (6c), Player 6 vs Banker 4 awards [RES037] to Player (P), which pays 1:1 even money on [RES037] Player boxes with zero commission deducted and appends P to BBPPBBPBPB.

[RES037-D3] Side-bet & road check for [RES037] (P0+6->6 vs B0->4, 6c): [RES037] leaves [RES037] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=4) and leaves [RES037] Panda 8 inactive (needs winning 3c Player 8, got P=6); on [RES037] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES037, Banker 0 evaluates Player's three-card total (6) before deciding whether to draw.
TruthBanker 0 inspects only Player's fifth card 6 (value 6) via BANKER_TABLEAU[0][6] = true.
MythBecause RES037 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
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