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FINAL TOTAL RESOLUTION [RES205] · 6-CARD PROOF

Player 0 + 4 (4) vs. Banker 3 (Draws 9 (9)): 6-Card Resolution #205

In walkthrough RES205, Player opens with 10+K (0) and draws fifth-card 4 (4) for a modulo-10 total of 4, while Banker opens with 9+4 (3) and draws sixth-card 9 (9) for 2 (6-card P outcome).

RES205 Player Path
P:0->4
RES205 Banker Path
B:3->2
RES205 Deal Length
6 Cards
RES205 Showdown
P (4v2)
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 RES205 (P0+4->4 vs B3->2).

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

RES205 Four-Card Opening Deal
Player 10+K=0 vs Banker 9+4=3

Verified non-natural start via handTotal([10,K])=0 and handTotal([9,4])=3.

RES205 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.

RES205 Banker Tableau Lookup
BANKER_TABLEAU[3][4] = true

Banker 3 draws sixth-card 9 (9) so (3+9) mod 10 = 2.

RES205 Card Count & Winner
6 Cards -> P (4 vs 2)

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

RES205 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 · RES205

Step-by-Step Card Arithmetic for RES205: P(10+K)+4 vs B(9+4)

Evaluating sequence [RES205], the shoe delivers 10+K (0) to Player and 9+4 (3) to Banker; after natural checks clear, fifth-card 4 (4) maps the raw pip total mod 10 (0+4=4) to final Player total 4.

[RES205-B] Because BANKER_TABLEAU[3][4]=true (3-point single-shade row (0..7, 9)) in [RES205], Banker 3 takes sixth-card 9 (9) and 3+9=12 settles at 2.

Complete 6-Card Resolution Trace for RES205
RES205 StageRES205 CardsRES205 Modulo MathRES205 Status
[RES205:Init]P(10+K)=0 vs B(9+4)=3playerShouldDraw(0)=true4-Card Deal
[RES205:5th]Player +4 (4)(0+4) mod 10 = 45th Card Sideways
[RES205:6th]Banker +9 (9)(3+9) mod 10 = 26-Card Final
[RES205:Settle]P=4 vs B=2Winner: PBig Road +P
  • [RES205-1] Confirm [RES205] opening P=0 (10+K) and B=3 (9+4) lack Natural 8/9.
  • [RES205-2] Add [RES205] fifth-card 4 (4) to P=0 for (0+4) mod 10 = 4.
  • [RES205-3] Run [RES205] BANKER_TABLEAU[3][4]=true to settle 4 vs 2 (P).
SETTLEMENT & SCOREBOARD · RES205

Showdown Settlement & Scoreboard Logging for RES205 (4 vs 2)

[RES205-C9] Comparing [RES205] final totals (6c), Player 4 vs Banker 2 awards [RES205] to Player (P), which pays 1:1 even money on [RES205] Player boxes with zero commission deducted and appends P to BBPPBBPPPB.

[RES205-D7] Side-bet & road check for [RES205] (P0+4->4 vs B3->2, 6c): [RES205] leaves [RES205] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=2) and leaves [RES205] Panda 8 inactive (needs winning 3c Player 8, got P=4); on [RES205] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES205, Banker 3 evaluates Player's three-card total (4) before deciding whether to draw.
TruthBanker 3 inspects only Player's fifth card 4 (value 4) via BANKER_TABLEAU[3][4] = true.
MythBecause RES205 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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