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FINAL TOTAL RESOLUTION [RES164] · 6-CARD PROOF

Player 1 + 7 (7) vs. Banker 2 (Draws 9 (9)): 6-Card Resolution #164

In walkthrough RES164, Player opens with 7+4 (1) and draws fifth-card 7 (7) for a modulo-10 total of 8, while Banker opens with 8+4 (2) and draws sixth-card 9 (9) for 1 (6-card P outcome).

RES164 Player Path
P:1->8
RES164 Banker Path
B:2->1
RES164 Deal Length
6 Cards
RES164 Showdown
P (8v1)
Engine-Verified Scoreboard · 20 Hands

Read the Board at Table Speed

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

Scoreboard sequence paired with 6-card resolution RES164 (P1+7->8 vs B2->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

Column 4 has 1 bead. Column 2 has 3 beads. Different depth → blue (≠).

  1. Column 5 starts, so use Rule 1: compare Column 4 with Column 2, 2 columns further back.
  2. Column 4 has 1 bead. Column 2 has 3 beads. Different depth → blue (≠).

Common table reading watchout: Comparing the wrong columns. Compare Column 4, the one that just finished, with Column 2.

Cockroach Pig Mark #3

Column 5 has 2 beads. 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 2 beads. 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

RES164 Four-Card Opening Deal
Player 7+4=1 vs Banker 8+4=2

Verified non-natural start via handTotal([7,4])=1 and handTotal([8,4])=2.

RES164 Fifth-Card Modulo Proof
(1 + 7) mod 10 = 8 via 7

Player draws fifth-card 7 (value 7), transforming two-card 1 into three-card 8.

RES164 Banker Tableau Lookup
BANKER_TABLEAU[2][7] = true

Banker 2 draws sixth-card 9 (9) so (2+9) mod 10 = 1.

RES164 Card Count & Winner
6 Cards -> P (8 vs 1)

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

RES164 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 · RES164

Step-by-Step Card Arithmetic for RES164: P(7+4)+7 vs B(8+4)

In coup [RES164], initial cards deal 7+4=1 to Player and 8+4=2 to Banker; lacking a four-card natural, Player takes fifth-card 7 (7) where raw sum 8 projects onto the 0..9 ring to 8.

[RES164-B] Next in [RES164], Banker consults 2-point mandatory draw band: facing fifth-card 7 (7), Banker 2 draws 9 (9) so 2+9=11 -> 1.

Complete 6-Card Resolution Trace for RES164
RES164 StageRES164 CardsRES164 Modulo MathRES164 Status
[RES164:Init]P(7+4)=1 vs B(8+4)=2playerShouldDraw(1)=true4-Card Deal
[RES164:5th]Player +7 (7)(1+7) mod 10 = 85th Card Sideways
[RES164:6th]Banker +9 (9)(2+9) mod 10 = 16-Card Final
[RES164:Settle]P=8 vs B=1Winner: PBig Road +P
  • [RES164-1] Confirm [RES164] opening P=1 (7+4) and B=2 (8+4) lack Natural 8/9.
  • [RES164-2] Add [RES164] fifth-card 7 (7) to P=1 for (1+7) mod 10 = 8.
  • [RES164-3] Run [RES164] BANKER_TABLEAU[2][7]=true to settle 8 vs 1 (P).
SETTLEMENT & SCOREBOARD · RES164

Showdown Settlement & Scoreboard Logging for RES164 (8 vs 1)

[RES164-C2] Comparing [RES164] final totals (6c), Player 8 vs Banker 1 awards [RES164] to Player (P), which pays 1:1 even money on [RES164] Player boxes with zero commission deducted and appends P to PPBBBPPBPP.

[RES164-D2] Side-bet & road check for [RES164] (P1+7->8 vs B2->1, 6c): [RES164] leaves [RES164] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=1) and triggers [RES164] Panda 8 (winning 3-card Player 8, 25:1); on [RES164] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES164, Banker 2 evaluates Player's three-card total (8) before deciding whether to draw.
TruthBanker 2 inspects only Player's fifth card 7 (value 7) via BANKER_TABLEAU[2][7] = true.
MythBecause RES164 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

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  • Structured step-by-step track across Foundations, Big Eye Boy, Small Road, and Cockroach Pig
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