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FINAL TOTAL RESOLUTION [RES185] · 6-CARD PROOF

Player 4 + 10 (0) vs. Banker 3 (Draws 9 (9)): 6-Card Resolution #185

In walkthrough RES185, Player opens with 2+2 (4) and draws fifth-card 10 (0) for a modulo-10 total of 4, while Banker opens with 9+4 (3) and draws sixth-card 9 (9) for 2 (6-card P outcome).

RES185 Player Path
P:4->4
RES185 Banker Path
B:3->2
RES185 Deal Length
6 Cards
RES185 Showdown
P (4v2)
Engine-Verified Scoreboard · 20 Hands

Read the Board at Table Speed

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

Scoreboard sequence paired with 6-card resolution RES185 (P4+0->4 vs B3->2).

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 2 has 3 beads. Column 1 has 2 beads. Different depth → blue (≠).

  1. Column 3 starts, so use Rule 1: compare Column 2 with Column 1, 1 column further back.
  2. Column 2 has 3 beads. Column 1 has 2 beads. Different depth → blue (≠).

Common table reading watchout: Comparing the wrong columns. Compare Column 2, the one that just finished, with Column 1.

Small Road Mark #3

This bead is at Row 4. Column 1 stopped at Row 2, more than one row above → red (=).

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

Common table reading watchout: Thinking "no bead at this row" means blue. It is blue only when Column 1 stopped exactly one row above this bead.

Cockroach Pig Mark #3

Column 5 has 1 bead. Column 2 has 3 beads. Different depth → blue (≠).

  1. Column 6 starts, so use Rule 1: compare Column 5 with Column 2, 3 columns further back.
  2. Column 5 has 1 bead. Column 2 has 3 beads. Different depth → blue (≠).

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

RES185 Four-Card Opening Deal
Player 2+2=4 vs Banker 9+4=3

Verified non-natural start via handTotal([2,2])=4 and handTotal([9,4])=3.

RES185 Fifth-Card Modulo Proof
(4 + 0) mod 10 = 4 via 10

Player draws fifth-card 10 (value 0), transforming two-card 4 into three-card 4.

RES185 Banker Tableau Lookup
BANKER_TABLEAU[3][0] = true

Banker 3 draws sixth-card 9 (9) so (3+9) mod 10 = 2.

RES185 Card Count & Winner
6 Cards -> P (4 vs 2)

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

RES185 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 · RES185

Step-by-Step Card Arithmetic for RES185: P(2+2)+10 vs B(9+4)

During tableau case [RES185], Player holds 2+2 for 4 while Banker holds 9+4 for 3; drawing fifth-card 10 (0) shifts Player from 4 to 4, which reduces mod-10 to 4.

[RES185-B] Evaluating bankerShouldDraw(3, 0)=true (3-point single-shade row (0..7, 9)) in [RES185], sixth-card 9 (9) advances Banker 3 via 3+9=12 to 2.

Complete 6-Card Resolution Trace for RES185
RES185 StageRES185 CardsRES185 Modulo MathRES185 Status
[RES185:Init]P(2+2)=4 vs B(9+4)=3playerShouldDraw(4)=true4-Card Deal
[RES185:5th]Player +10 (0)(4+0) mod 10 = 45th Card Sideways
[RES185:6th]Banker +9 (9)(3+9) mod 10 = 26-Card Final
[RES185:Settle]P=4 vs B=2Winner: PBig Road +P
  • [RES185-1] Confirm [RES185] opening P=4 (2+2) and B=3 (9+4) lack Natural 8/9.
  • [RES185-2] Add [RES185] fifth-card 10 (0) to P=4 for (4+0) mod 10 = 4.
  • [RES185-3] Run [RES185] BANKER_TABLEAU[3][0]=true to settle 4 vs 2 (P).
SETTLEMENT & SCOREBOARD · RES185

Showdown Settlement & Scoreboard Logging for RES185 (4 vs 2)

[RES185-C8] Comparing [RES185] final totals (6c), Player 4 vs Banker 2 awards [RES185] to Player (P), which pays 1:1 even money on [RES185] Player boxes with zero commission deducted and appends P to BBPPPBBBBP.

[RES185-D9] Side-bet & road check for [RES185] (P4+0->4 vs B3->2, 6c): [RES185] leaves [RES185] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=2) and leaves [RES185] Panda 8 inactive (needs winning 3c Player 8, got P=4); on [RES185] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES185, Banker 3 evaluates Player's three-card total (4) before deciding whether to draw.
TruthBanker 3 inspects only Player's fifth card 10 (value 0) via BANKER_TABLEAU[3][0] = true.
MythBecause RES185 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

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
  • Cloud Shoe Log and cross-device progress on web, iOS, and Android