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FINAL TOTAL RESOLUTION [RES209] · 6-CARD PROOF

Player 4 + 4 (4) vs. Banker 3 (Draws 5 (5)): 6-Card Resolution #209

In walkthrough RES209, Player opens with 2+2 (4) and draws fifth-card 4 (4) for a modulo-10 total of 8, while Banker opens with 9+4 (3) and draws sixth-card 5 (5) for 8 (6-card T outcome).

RES209 Player Path
P:4->8
RES209 Banker Path
B:3->8
RES209 Deal Length
6 Cards
RES209 Showdown
T (8v8)
Engine-Verified Scoreboard · 20 Hands

Read the Board at Table Speed

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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 RES209 (P4+4->8 vs B3->8).

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

RES209 Four-Card Opening Deal
Player 2+2=4 vs Banker 9+4=3

Verified non-natural start via handTotal([2,2])=4 and handTotal([9,4])=3.

RES209 Fifth-Card Modulo Proof
(4 + 4) mod 10 = 8 via 4

Player draws fifth-card 4 (value 4), transforming two-card 4 into three-card 8.

RES209 Banker Tableau Lookup
BANKER_TABLEAU[3][4] = true

Banker 3 draws sixth-card 5 (5) so (3+5) mod 10 = 8.

RES209 Card Count & Winner
6 Cards -> T (8 vs 8)

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

RES209 Derived Road Independence
Red (=) / Blue (≠) Symmetry Only

Big Eye Boy, Small Road, and Cockroach Pig compare Big Road column depths, not T vs B.

MODULO-10 ARITHMETIC · RES209

Step-by-Step Card Arithmetic for RES209: P(2+2)+4 vs B(9+4)

Hand record [RES209] tracks Player 4 (2+2) facing Banker 3 (9+4); with zero naturals on the felt, the fifth card 4 (worth 4) arrives and 8 calculates the mod-10 residue to 8.

[RES209-B] Under 3-point single-shade row (0..7, 9) for [RES209], exposed 4 (4) obligates Banker 3 to draw 5 (5), converting 3+5=8 into 8.

Complete 6-Card Resolution Trace for RES209
RES209 StageRES209 CardsRES209 Modulo MathRES209 Status
[RES209:Init]P(2+2)=4 vs B(9+4)=3playerShouldDraw(4)=true4-Card Deal
[RES209:5th]Player +4 (4)(4+4) mod 10 = 85th Card Sideways
[RES209:6th]Banker +5 (5)(3+5) mod 10 = 86-Card Final
[RES209:Settle]P=8 vs B=8Winner: TBig Road +T
  • [RES209-1] Confirm [RES209] opening P=4 (2+2) and B=3 (9+4) lack Natural 8/9.
  • [RES209-2] Add [RES209] fifth-card 4 (4) to P=4 for (4+4) mod 10 = 8.
  • [RES209-3] Run [RES209] BANKER_TABLEAU[3][4]=true to settle 8 vs 8 (T).
SETTLEMENT & SCOREBOARD · RES209

Showdown Settlement & Scoreboard Logging for RES209 (8 vs 8)

[RES209-C7] Comparing [RES209] final totals (6c), Player 8 vs Banker 8 awards [RES209] to Tie (T), which pushes main [RES209] Player/Banker wagers while settling [RES209] Tie bets at 8:1 or 9:1 and appends T to BBPPBPBBPP.

[RES209-D4] Side-bet & road check for [RES209] (P4+4->8 vs B3->8, 6c): [RES209] leaves [RES209] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=8) and leaves [RES209] Panda 8 inactive (needs winning 3c Player 8, got P=8); on [RES209] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES209, Banker 3 evaluates Player's three-card total (8) before deciding whether to draw.
TruthBanker 3 inspects only Player's fifth card 4 (value 4) via BANKER_TABLEAU[3][4] = true.
MythBecause RES209 resolves as T, the next derived-road mark must match T'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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