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FINAL TOTAL RESOLUTION [RES129] · 6-CARD PROOF

Player 2 + A (1) vs. Banker 2 (Draws 9 (9)): 6-Card Resolution #129

In walkthrough RES129, Player opens with 10+2 (2) and draws fifth-card A (1) for a modulo-10 total of 3, while Banker opens with 10+2 (2) and draws sixth-card 9 (9) for 1 (6-card P outcome).

RES129 Player Path
P:2->3
RES129 Banker Path
B:2->1
RES129 Deal Length
6 Cards
RES129 Showdown
P (3v1)
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 RES129 (P2+1->3 vs B2->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

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

RES129 Four-Card Opening Deal
Player 10+2=2 vs Banker 10+2=2

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

RES129 Fifth-Card Modulo Proof
(2 + 1) mod 10 = 3 via A

Player draws fifth-card A (value 1), transforming two-card 2 into three-card 3.

RES129 Banker Tableau Lookup
BANKER_TABLEAU[2][1] = true

Banker 2 draws sixth-card 9 (9) so (2+9) mod 10 = 1.

RES129 Card Count & Winner
6 Cards -> P (3 vs 1)

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

RES129 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 · RES129

Step-by-Step Card Arithmetic for RES129: P(10+2)+A vs B(10+2)

During tableau case [RES129], Player holds 10+2 for 2 while Banker holds 10+2 for 2; drawing fifth-card A (1) shifts Player from 2 to 3, which reduces mod-10 to 3.

[RES129-B] Acting on A=1 inside [RES129], Banker 2 follows 2-point mandatory draw band and pulls 9 (9) for 2+9=11 -> 1.

Complete 6-Card Resolution Trace for RES129
RES129 StageRES129 CardsRES129 Modulo MathRES129 Status
[RES129:Init]P(10+2)=2 vs B(10+2)=2playerShouldDraw(2)=true4-Card Deal
[RES129:5th]Player +A (1)(2+1) mod 10 = 35th Card Sideways
[RES129:6th]Banker +9 (9)(2+9) mod 10 = 16-Card Final
[RES129:Settle]P=3 vs B=1Winner: PBig Road +P
  • [RES129-1] Confirm [RES129] opening P=2 (10+2) and B=2 (10+2) lack Natural 8/9.
  • [RES129-2] Add [RES129] fifth-card A (1) to P=2 for (2+1) mod 10 = 3.
  • [RES129-3] Run [RES129] BANKER_TABLEAU[2][1]=true to settle 3 vs 1 (P).
SETTLEMENT & SCOREBOARD · RES129

Showdown Settlement & Scoreboard Logging for RES129 (3 vs 1)

[RES129-C3] Comparing [RES129] final totals (6c), Player 3 vs Banker 1 awards [RES129] to Player (P), which pays 1:1 even money on [RES129] Player boxes with zero commission deducted and appends P to BBPPBPBBPP.

[RES129-D12] Side-bet & road check for [RES129] (P2+1->3 vs B2->1, 6c): [RES129] leaves [RES129] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=1) and leaves [RES129] Panda 8 inactive (needs winning 3c Player 8, got P=3); on [RES129] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES129, Banker 2 evaluates Player's three-card total (3) before deciding whether to draw.
TruthBanker 2 inspects only Player's fifth card A (value 1) via BANKER_TABLEAU[2][1] = true.
MythBecause RES129 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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