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FINAL TOTAL RESOLUTION [RES050] · 6-CARD PROOF

Player 1 + 8 (8) vs. Banker 0 (Draws 6 (6)): 6-Card Resolution #50

In walkthrough RES050, Player opens with 7+4 (1) and draws fifth-card 8 (8) for a modulo-10 total of 9, while Banker opens with 6+4 (0) and draws sixth-card 6 (6) for 6 (6-card P outcome).

RES050 Player Path
P:1->9
RES050 Banker Path
B:0->6
RES050 Deal Length
6 Cards
RES050 Showdown
P (9v6)
Engine-Verified Scoreboard · 20 Hands

Read the Board at Table Speed

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Big Road P P B B P B P P B B P B B B P P P B P P
Big Eye Boy = = ≠ = ≠ ≠ = = ≠ ≠ = ≠ = = = ≠ ≠
Small Road ≠ ≠ ≠ ≠ ≠ ≠ = ≠ ≠ ≠ ≠ = ≠ ≠ =
Cockroach Pig ≠ = = ≠ ≠ = = ≠ ≠ = ≠ ≠ = =

Scoreboard sequence paired with 6-card resolution RES050 (P1+8->9 vs B0->6).

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

RES050 Four-Card Opening Deal
Player 7+4=1 vs Banker 6+4=0

Verified non-natural start via handTotal([7,4])=1 and handTotal([6,4])=0.

RES050 Fifth-Card Modulo Proof
(1 + 8) mod 10 = 9 via 8

Player draws fifth-card 8 (value 8), transforming two-card 1 into three-card 9.

RES050 Banker Tableau Lookup
BANKER_TABLEAU[0][8] = true

Banker 0 draws sixth-card 6 (6) so (0+6) mod 10 = 6.

RES050 Card Count & Winner
6 Cards -> P (9 vs 6)

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

RES050 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 · RES050

Step-by-Step Card Arithmetic for RES050: P(7+4)+8 vs B(6+4)

Arithmetic trace [RES050] starts from four-card deal 7+4=1 vs 6+4=0; Player's compulsory draw of 8 (pip value 8) produces raw 9, which wraps modulo-10 to 9.

[RES050-B] Because BANKER_TABLEAU[0][8]=true (0-point unconditional draw tier) in [RES050], Banker 0 takes sixth-card 6 (6) and 0+6=6 settles at 6.

Complete 6-Card Resolution Trace for RES050
RES050 StageRES050 CardsRES050 Modulo MathRES050 Status
[RES050:Init]P(7+4)=1 vs B(6+4)=0playerShouldDraw(1)=true4-Card Deal
[RES050:5th]Player +8 (8)(1+8) mod 10 = 95th Card Sideways
[RES050:6th]Banker +6 (6)(0+6) mod 10 = 66-Card Final
[RES050:Settle]P=9 vs B=6Winner: PBig Road +P
  • [RES050-1] Confirm [RES050] opening P=1 (7+4) and B=0 (6+4) lack Natural 8/9.
  • [RES050-2] Add [RES050] fifth-card 8 (8) to P=1 for (1+8) mod 10 = 9.
  • [RES050-3] Run [RES050] BANKER_TABLEAU[0][8]=true to settle 9 vs 6 (P).
SETTLEMENT & SCOREBOARD · RES050

Showdown Settlement & Scoreboard Logging for RES050 (9 vs 6)

[RES050-C4] Comparing [RES050] final totals (6c), Player 9 vs Banker 6 awards [RES050] to Player (P), which pays 1:1 even money on [RES050] Player boxes with zero commission deducted and appends P to PPBBPBPPBB.

[RES050-D3] Side-bet & road check for [RES050] (P1+8->9 vs B0->6, 6c): [RES050] leaves [RES050] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=6) and leaves [RES050] Panda 8 inactive (needs winning 3c Player 8, got P=9); on [RES050] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES050, Banker 0 evaluates Player's three-card total (9) before deciding whether to draw.
TruthBanker 0 inspects only Player's fifth card 8 (value 8) via BANKER_TABLEAU[0][8] = true.
MythBecause RES050 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