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FINAL TOTAL RESOLUTION [RES177] · 6-CARD PROOF

Player 2 + 9 (9) vs. Banker 2 (Draws A (1)): 6-Card Resolution #177

In walkthrough RES177, Player opens with 10+2 (2) and draws fifth-card 9 (9) 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).

RES177 Player Path
P:2->1
RES177 Banker Path
B:2->3
RES177 Deal Length
6 Cards
RES177 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 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 RES177 (P2+9->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

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

RES177 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.

RES177 Fifth-Card Modulo Proof
(2 + 9) mod 10 = 1 via 9

Player draws fifth-card 9 (value 9), transforming two-card 2 into three-card 1.

RES177 Banker Tableau Lookup
BANKER_TABLEAU[2][9] = true

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

RES177 Card Count & Winner
6 Cards -> B (1 vs 3)

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

RES177 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 · RES177

Step-by-Step Card Arithmetic for RES177: P(10+2)+9 vs B(10+2)

Evaluating sequence [RES177], the shoe delivers 10+2 (2) to Player and 10+2 (2) to Banker; after natural checks clear, fifth-card 9 (9) maps the raw pip total mod 10 (2+9=11) to final Player total 1.

[RES177-B] Next in [RES177], Banker consults 2-point mandatory draw band: facing fifth-card 9 (9), Banker 2 draws A (1) so 2+1=3 -> 3.

Complete 6-Card Resolution Trace for RES177
RES177 StageRES177 CardsRES177 Modulo MathRES177 Status
[RES177:Init]P(10+2)=2 vs B(10+2)=2playerShouldDraw(2)=true4-Card Deal
[RES177:5th]Player +9 (9)(2+9) mod 10 = 15th Card Sideways
[RES177:6th]Banker +A (1)(2+1) mod 10 = 36-Card Final
[RES177:Settle]P=1 vs B=3Winner: BBig Road +B
  • [RES177-1] Confirm [RES177] opening P=2 (10+2) and B=2 (10+2) lack Natural 8/9.
  • [RES177-2] Add [RES177] fifth-card 9 (9) to P=2 for (2+9) mod 10 = 1.
  • [RES177-3] Run [RES177] BANKER_TABLEAU[2][9]=true to settle 1 vs 3 (B).
SETTLEMENT & SCOREBOARD · RES177

Showdown Settlement & Scoreboard Logging for RES177 (1 vs 3)

[RES177-C1] Comparing [RES177] final totals (6c), Player 1 vs Banker 3 awards [RES177] to Banker (B), which pays 0.95:1 on 5%-commission [RES177] layouts (or 0.5:1 on 6 at No-Commission [RES177] tables) and appends B to BBPPBPBBPP.

[RES177-D2] Side-bet & road check for [RES177] (P2+9->1 vs B2->3, 6c): [RES177] leaves [RES177] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=3) and leaves [RES177] Panda 8 inactive (needs winning 3c Player 8, got P=1); on [RES177] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES177, Banker 2 evaluates Player's three-card total (1) before deciding whether to draw.
TruthBanker 2 inspects only Player's fifth card 9 (value 9) via BANKER_TABLEAU[2][9] = true.
MythBecause RES177 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
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