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FINAL TOTAL RESOLUTION [RES265] · 6-CARD PROOF

Player 0 + 4 (4) vs. Banker 4 (Draws 10 (0)): 6-Card Resolution #265

In walkthrough RES265, Player opens with 10+K (0) and draws fifth-card 4 (4) for a modulo-10 total of 4, while Banker opens with 2+2 (4) and draws sixth-card 10 (0) for 4 (6-card T outcome).

RES265 Player Path
P:0->4
RES265 Banker Path
B:4->4
RES265 Deal Length
6 Cards
RES265 Showdown
T (4v4)
Engine-Verified Scoreboard · 20 Hands

Read the Board at Table Speed

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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 RES265 (P0+4->4 vs B4->4).

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

RES265 Four-Card Opening Deal
Player 10+K=0 vs Banker 2+2=4

Verified non-natural start via handTotal([10,K])=0 and handTotal([2,2])=4.

RES265 Fifth-Card Modulo Proof
(0 + 4) mod 10 = 4 via 4

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

RES265 Banker Tableau Lookup
BANKER_TABLEAU[4][4] = true

Banker 4 draws sixth-card 10 (0) so (4+0) mod 10 = 4.

RES265 Card Count & Winner
6 Cards -> T (4 vs 4)

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

RES265 Derived Road Independence
Red (=) / Blue (≠) Symmetry Only

Big Eye Boy, Small Road, and Cockroach Pig compare Big Road column depths, not T vs B.

MODULO-10 ARITHMETIC · RES265

Step-by-Step Card Arithmetic for RES265: P(10+K)+4 vs B(2+2)

Hand record [RES265] tracks Player 0 (10+K) facing Banker 4 (2+2); with zero naturals on the felt, the fifth card 4 (worth 4) arrives and 4 calculates the mod-10 residue to 4.

[RES265-B] Six-card branch [RES265] activates as 4 (4) hits Banker 4's 4-point six-value gate (2..7); drawing 10 (0) sends 4+0=4 to 4.

Complete 6-Card Resolution Trace for RES265
RES265 StageRES265 CardsRES265 Modulo MathRES265 Status
[RES265:Init]P(10+K)=0 vs B(2+2)=4playerShouldDraw(0)=true4-Card Deal
[RES265:5th]Player +4 (4)(0+4) mod 10 = 45th Card Sideways
[RES265:6th]Banker +10 (0)(4+0) mod 10 = 46-Card Final
[RES265:Settle]P=4 vs B=4Winner: TBig Road +T
  • [RES265-1] Confirm [RES265] opening P=0 (10+K) and B=4 (2+2) lack Natural 8/9.
  • [RES265-2] Add [RES265] fifth-card 4 (4) to P=0 for (0+4) mod 10 = 4.
  • [RES265-3] Run [RES265] BANKER_TABLEAU[4][4]=true to settle 4 vs 4 (T).
SETTLEMENT & SCOREBOARD · RES265

Showdown Settlement & Scoreboard Logging for RES265 (4 vs 4)

[RES265-C1] Comparing [RES265] final totals (6c), Player 4 vs Banker 4 awards [RES265] to Tie (T), which pushes main [RES265] Player/Banker wagers while settling [RES265] Tie bets at 8:1 or 9:1 and appends T to BBPPPBBBBP.

[RES265-D1] Side-bet & road check for [RES265] (P0+4->4 vs B4->4, 6c): [RES265] leaves [RES265] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=4) and leaves [RES265] Panda 8 inactive (needs winning 3c Player 8, got P=4); on [RES265] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES265, Banker 4 evaluates Player's three-card total (4) before deciding whether to draw.
TruthBanker 4 inspects only Player's fifth card 4 (value 4) via BANKER_TABLEAU[4][4] = true.
MythBecause RES265 resolves as T, the next derived-road mark must match T'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
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