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FINAL TOTAL RESOLUTION [RES010] · 6-CARD PROOF

Player 3 + A (1) vs. Banker 0 (Draws A (1)): 6-Card Resolution #10

In walkthrough RES010, Player opens with 9+4 (3) and draws fifth-card A (1) for a modulo-10 total of 4, while Banker opens with 6+4 (0) and draws sixth-card A (1) for 1 (6-card P outcome).

RES010 Player Path
P:3->4
RES010 Banker Path
B:0->1
RES010 Deal Length
6 Cards
RES010 Showdown
P (4v1)
Engine-Verified Scoreboard · 20 Hands

Read the Board at Table Speed

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

Scoreboard sequence paired with 6-card resolution RES010 (P3+1->4 vs B0->1).

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

RES010 Four-Card Opening Deal
Player 9+4=3 vs Banker 6+4=0

Verified non-natural start via handTotal([9,4])=3 and handTotal([6,4])=0.

RES010 Fifth-Card Modulo Proof
(3 + 1) mod 10 = 4 via A

Player draws fifth-card A (value 1), transforming two-card 3 into three-card 4.

RES010 Banker Tableau Lookup
BANKER_TABLEAU[0][1] = true

Banker 0 draws sixth-card A (1) so (0+1) mod 10 = 1.

RES010 Card Count & Winner
6 Cards -> P (4 vs 1)

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

RES010 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 · RES010

Step-by-Step Card Arithmetic for RES010: P(9+4)+A vs B(6+4)

In coup [RES010], initial cards deal 9+4=3 to Player and 6+4=0 to Banker; lacking a four-card natural, Player takes fifth-card A (1) where raw sum 4 projects onto the 0..9 ring to 4.

[RES010-B] Because BANKER_TABLEAU[0][1]=true (0-point unconditional draw tier) in [RES010], Banker 0 takes sixth-card A (1) and 0+1=1 settles at 1.

Complete 6-Card Resolution Trace for RES010
RES010 StageRES010 CardsRES010 Modulo MathRES010 Status
[RES010:Init]P(9+4)=3 vs B(6+4)=0playerShouldDraw(3)=true4-Card Deal
[RES010:5th]Player +A (1)(3+1) mod 10 = 45th Card Sideways
[RES010:6th]Banker +A (1)(0+1) mod 10 = 16-Card Final
[RES010:Settle]P=4 vs B=1Winner: PBig Road +P
  • [RES010-1] Confirm [RES010] opening P=3 (9+4) and B=0 (6+4) lack Natural 8/9.
  • [RES010-2] Add [RES010] fifth-card A (1) to P=3 for (3+1) mod 10 = 4.
  • [RES010-3] Run [RES010] BANKER_TABLEAU[0][1]=true to settle 4 vs 1 (P).
SETTLEMENT & SCOREBOARD · RES010

Showdown Settlement & Scoreboard Logging for RES010 (4 vs 1)

[RES010-C2] Comparing [RES010] final totals (6c), Player 4 vs Banker 1 awards [RES010] to Player (P), which pays 1:1 even money on [RES010] Player boxes with zero commission deducted and appends P to PPBBBPPPPB.

[RES010-D7] Side-bet & road check for [RES010] (P3+1->4 vs B0->1, 6c): [RES010] leaves [RES010] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=1) and leaves [RES010] Panda 8 inactive (needs winning 3c Player 8, got P=4); on [RES010] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES010, Banker 0 evaluates Player's three-card total (4) before deciding whether to draw.
TruthBanker 0 inspects only Player's fifth card A (value 1) via BANKER_TABLEAU[0][1] = true.
MythBecause RES010 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