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FINAL TOTAL RESOLUTION [RES069] · 6-CARD PROOF

Player 2 + A (1) vs. Banker 1 (Draws 8 (8)): 6-Card Resolution #69

In walkthrough RES069, Player opens with 10+2 (2) and draws fifth-card A (1) for a modulo-10 total of 3, while Banker opens with 7+4 (1) and draws sixth-card 8 (8) for 9 (6-card B outcome).

RES069 Player Path
P:2->3
RES069 Banker Path
B:1->9
RES069 Deal Length
6 Cards
RES069 Showdown
B (3v9)
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 RES069 (P2+1->3 vs B1->9).

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

RES069 Four-Card Opening Deal
Player 10+2=2 vs Banker 7+4=1

Verified non-natural start via handTotal([10,2])=2 and handTotal([7,4])=1.

RES069 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.

RES069 Banker Tableau Lookup
BANKER_TABLEAU[1][1] = true

Banker 1 draws sixth-card 8 (8) so (1+8) mod 10 = 9.

RES069 Card Count & Winner
6 Cards -> B (3 vs 9)

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

RES069 Derived Road Independence
Red (=) / Blue (≠) Symmetry Only

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

MODULO-10 ARITHMETIC · RES069

Step-by-Step Card Arithmetic for RES069: P(10+2)+A vs B(7+4)

Hand record [RES069] tracks Player 2 (10+2) facing Banker 1 (7+4); with zero naturals on the felt, the fifth card A (worth 1) arrives and 3 calculates the mod-10 residue to 3.

[RES069-B] Evaluating bankerShouldDraw(1, 1)=true (1-point automatic draw row) in [RES069], sixth-card 8 (8) advances Banker 1 via 1+8=9 to 9.

Complete 6-Card Resolution Trace for RES069
RES069 StageRES069 CardsRES069 Modulo MathRES069 Status
[RES069:Init]P(10+2)=2 vs B(7+4)=1playerShouldDraw(2)=true4-Card Deal
[RES069:5th]Player +A (1)(2+1) mod 10 = 35th Card Sideways
[RES069:6th]Banker +8 (8)(1+8) mod 10 = 96-Card Final
[RES069:Settle]P=3 vs B=9Winner: BBig Road +B
  • [RES069-1] Confirm [RES069] opening P=2 (10+2) and B=1 (7+4) lack Natural 8/9.
  • [RES069-2] Add [RES069] fifth-card A (1) to P=2 for (2+1) mod 10 = 3.
  • [RES069-3] Run [RES069] BANKER_TABLEAU[1][1]=true to settle 3 vs 9 (B).
SETTLEMENT & SCOREBOARD · RES069

Showdown Settlement & Scoreboard Logging for RES069 (3 vs 9)

[RES069-C0] Comparing [RES069] final totals (6c), Player 3 vs Banker 9 awards [RES069] to Banker (B), which pays 0.95:1 on 5%-commission [RES069] layouts (or 0.5:1 on 6 at No-Commission [RES069] tables) and appends B to BBPPBBPBPB.

[RES069-D5] Side-bet & road check for [RES069] (P2+1->3 vs B1->9, 6c): [RES069] leaves [RES069] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=9) and leaves [RES069] Panda 8 inactive (needs winning 3c Player 8, got P=3); on [RES069] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES069, Banker 1 evaluates Player's three-card total (3) before deciding whether to draw.
TruthBanker 1 inspects only Player's fifth card A (value 1) via BANKER_TABLEAU[1][1] = true.
MythBecause RES069 resolves as B, the next derived-road mark must match B'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

Read Every Derived Road at Table Speed

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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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