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FINAL TOTAL RESOLUTION [RES167] · 6-CARD PROOF

Player 4 + 7 (7) vs. Banker 2 (Draws A (1)): 6-Card Resolution #167

In walkthrough RES167, Player opens with 2+2 (4) and draws fifth-card 7 (7) for a modulo-10 total of 1, while Banker opens with 10+2 (2) and draws sixth-card A (1) for 3 (6-card B outcome).

RES167 Player Path
P:4->1
RES167 Banker Path
B:2->3
RES167 Deal Length
6 Cards
RES167 Showdown
B (1v3)
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 P P P B B B B P P B P B B
Big Eye Boy = = ≠ = = ≠ = ≠ = = ≠ ≠ = ≠ ≠ = ≠
Small Road ≠ ≠ = ≠ = ≠ ≠ = = ≠ = ≠ ≠ ≠ ≠
Cockroach Pig ≠ ≠ ≠ = ≠ ≠ = = ≠ ≠ ≠ ≠ ≠ =

Scoreboard sequence paired with 6-card resolution RES167 (P4+7->1 vs B2->3).

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

Column 5 has 1 bead. Column 3 has 1 bead. Same depth → red (=).

  1. Column 6 starts, so use Rule 1: compare Column 5 with Column 3, 2 columns further back.
  2. Column 5 has 1 bead. Column 3 has 1 bead. Same depth → red (=).

Common table reading watchout: Comparing the wrong columns. Compare Column 5, the one that just finished, with Column 3.

Cockroach Pig Mark #3

This bead is at Row 2. Column 3 stopped at Row 1, one row above → blue (≠).

  1. Column 6 goes down to Row 2, so use Rule 2: look 3 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.

Verified Reference Data

Key Facts & Table Specifications

RES167 Four-Card Opening Deal
Player 2+2=4 vs Banker 10+2=2

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

RES167 Fifth-Card Modulo Proof
(4 + 7) mod 10 = 1 via 7

Player draws fifth-card 7 (value 7), transforming two-card 4 into three-card 1.

RES167 Banker Tableau Lookup
BANKER_TABLEAU[2][7] = true

Banker 2 draws sixth-card A (1) so (2+1) mod 10 = 3.

RES167 Card Count & Winner
6 Cards -> B (1 vs 3)

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

RES167 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 · RES167

Step-by-Step Card Arithmetic for RES167: P(2+2)+7 vs B(10+2)

Hand record [RES167] tracks Player 4 (2+2) facing Banker 2 (10+2); with zero naturals on the felt, the fifth card 7 (worth 7) arrives and 11 calculates the mod-10 residue to 1.

[RES167-B] Because BANKER_TABLEAU[2][7]=true (2-point mandatory draw band) in [RES167], Banker 2 takes sixth-card A (1) and 2+1=3 settles at 3.

Complete 6-Card Resolution Trace for RES167
RES167 StageRES167 CardsRES167 Modulo MathRES167 Status
[RES167:Init]P(2+2)=4 vs B(10+2)=2playerShouldDraw(4)=true4-Card Deal
[RES167:5th]Player +7 (7)(4+7) mod 10 = 15th Card Sideways
[RES167:6th]Banker +A (1)(2+1) mod 10 = 36-Card Final
[RES167:Settle]P=1 vs B=3Winner: BBig Road +B
  • [RES167-1] Confirm [RES167] opening P=4 (2+2) and B=2 (10+2) lack Natural 8/9.
  • [RES167-2] Add [RES167] fifth-card 7 (7) to P=4 for (4+7) mod 10 = 1.
  • [RES167-3] Run [RES167] BANKER_TABLEAU[2][7]=true to settle 1 vs 3 (B).
SETTLEMENT & SCOREBOARD · RES167

Showdown Settlement & Scoreboard Logging for RES167 (1 vs 3)

[RES167-C6] Comparing [RES167] final totals (6c), Player 1 vs Banker 3 awards [RES167] to Banker (B), which pays 0.95:1 on 5%-commission [RES167] layouts (or 0.5:1 on 6 at No-Commission [RES167] tables) and appends B to BBPPBPBPPP.

[RES167-D3] Side-bet & road check for [RES167] (P4+7->1 vs B2->3, 6c): [RES167] leaves [RES167] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=3) and leaves [RES167] Panda 8 inactive (needs winning 3c Player 8, got P=1); on [RES167] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES167, Banker 2 evaluates Player's three-card total (1) before deciding whether to draw.
TruthBanker 2 inspects only Player's fifth card 7 (value 7) via BANKER_TABLEAU[2][7] = true.
MythBecause RES167 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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