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FINAL TOTAL RESOLUTION [RES075] · 6-CARD PROOF

Player 2 + 2 (2) vs. Banker 1 (Draws 7 (7)): 6-Card Resolution #75

In walkthrough RES075, Player opens with 10+2 (2) and draws fifth-card 2 (2) for a modulo-10 total of 4, while Banker opens with 7+4 (1) and draws sixth-card 7 (7) for 8 (6-card B outcome).

RES075 Player Path
P:2->4
RES075 Banker Path
B:1->8
RES075 Deal Length
6 Cards
RES075 Showdown
B (4v8)
Engine-Verified Scoreboard · 20 Hands

Read the Board at Table Speed

Open this shoe in /calculator
Big Road B B P P B P P P B B B B P B B P P B B P
Big Eye Boy = = ≠ ≠ = ≠ = = ≠ ≠ ≠ ≠ ≠ = = = =
Small Road ≠ = ≠ ≠ ≠ = = ≠ ≠ = ≠ ≠ ≠ = =
Cockroach Pig = ≠ ≠ = ≠ = ≠ = = ≠ = ≠ ≠ ≠

Scoreboard sequence paired with 6-card resolution RES075 (P2+2->4 vs B1->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 3. Column 2 stopped at Row 2, one row above → blue (≠).

  1. Column 4 goes down to Row 3, so use Rule 2: look 2 columns back, at Column 2.
  2. Column 2 stopped at Row 2, one row above → blue (≠).

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

RES075 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.

RES075 Fifth-Card Modulo Proof
(2 + 2) mod 10 = 4 via 2

Player draws fifth-card 2 (value 2), transforming two-card 2 into three-card 4.

RES075 Banker Tableau Lookup
BANKER_TABLEAU[1][2] = true

Banker 1 draws sixth-card 7 (7) so (1+7) mod 10 = 8.

RES075 Card Count & Winner
6 Cards -> B (4 vs 8)

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

RES075 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 · RES075

Step-by-Step Card Arithmetic for RES075: P(10+2)+2 vs B(7+4)

Under audit [RES075], Player opens on two-card 2 (10+2) opposite Banker 1 (7+4), triggering a mandatory fifth-card pull of 2 (value 2) that settles via mod-10 arithmetic from 4 into 4.

[RES075-B] Because BANKER_TABLEAU[1][2]=true (1-point automatic draw row) in [RES075], Banker 1 takes sixth-card 7 (7) and 1+7=8 settles at 8.

Complete 6-Card Resolution Trace for RES075
RES075 StageRES075 CardsRES075 Modulo MathRES075 Status
[RES075:Init]P(10+2)=2 vs B(7+4)=1playerShouldDraw(2)=true4-Card Deal
[RES075:5th]Player +2 (2)(2+2) mod 10 = 45th Card Sideways
[RES075:6th]Banker +7 (7)(1+7) mod 10 = 86-Card Final
[RES075:Settle]P=4 vs B=8Winner: BBig Road +B
  • [RES075-1] Confirm [RES075] opening P=2 (10+2) and B=1 (7+4) lack Natural 8/9.
  • [RES075-2] Add [RES075] fifth-card 2 (2) to P=2 for (2+2) mod 10 = 4.
  • [RES075-3] Run [RES075] BANKER_TABLEAU[1][2]=true to settle 4 vs 8 (B).
SETTLEMENT & SCOREBOARD · RES075

Showdown Settlement & Scoreboard Logging for RES075 (4 vs 8)

[RES075-C8] Comparing [RES075] final totals (6c), Player 4 vs Banker 8 awards [RES075] to Banker (B), which pays 0.95:1 on 5%-commission [RES075] layouts (or 0.5:1 on 6 at No-Commission [RES075] tables) and appends B to BBPPBPPPBB.

[RES075-D7] Side-bet & road check for [RES075] (P2+2->4 vs B1->8, 6c): [RES075] leaves [RES075] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=8) and leaves [RES075] Panda 8 inactive (needs winning 3c Player 8, got P=4); on [RES075] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES075, Banker 1 evaluates Player's three-card total (4) before deciding whether to draw.
TruthBanker 1 inspects only Player's fifth card 2 (value 2) via BANKER_TABLEAU[1][2] = true.
MythBecause RES075 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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