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FINAL TOTAL RESOLUTION [RES136] · 6-CARD PROOF

Player 3 + 2 (2) vs. Banker 2 (Draws 2 (2)): 6-Card Resolution #136

In walkthrough RES136, Player opens with 9+4 (3) and draws fifth-card 2 (2) for a modulo-10 total of 5, while Banker opens with 8+4 (2) and draws sixth-card 2 (2) for 4 (6-card P outcome).

RES136 Player Path
P:3->5
RES136 Banker Path
B:2->4
RES136 Deal Length
6 Cards
RES136 Showdown
P (5v4)
Engine-Verified Scoreboard · 20 Hands

Read the Board at Table Speed

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

Scoreboard sequence paired with 6-card resolution RES136 (P3+2->5 vs B2->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 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

Column 5 has 1 bead. Column 3 has 1 bead. Same depth → red (=).

  1. Column 6 starts, so use Rule 1: compare Column 5 with Column 3, 2 columns further back.
  2. Column 5 has 1 bead. Column 3 has 1 bead. Same depth → red (=).

Common table reading watchout: Comparing the wrong columns. Compare Column 5, the one that just finished, with Column 3.

Cockroach Pig Mark #3

This bead is at Row 2. Column 3 stopped at Row 1, one row above → blue (≠).

  1. Column 6 goes down to Row 2, so use Rule 2: look 3 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.

Verified Reference Data

Key Facts & Table Specifications

RES136 Four-Card Opening Deal
Player 9+4=3 vs Banker 8+4=2

Verified non-natural start via handTotal([9,4])=3 and handTotal([8,4])=2.

RES136 Fifth-Card Modulo Proof
(3 + 2) mod 10 = 5 via 2

Player draws fifth-card 2 (value 2), transforming two-card 3 into three-card 5.

RES136 Banker Tableau Lookup
BANKER_TABLEAU[2][2] = true

Banker 2 draws sixth-card 2 (2) so (2+2) mod 10 = 4.

RES136 Card Count & Winner
6 Cards -> P (5 vs 4)

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

RES136 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 · RES136

Step-by-Step Card Arithmetic for RES136: P(9+4)+2 vs B(8+4)

In coup [RES136], initial cards deal 9+4=3 to Player and 8+4=2 to Banker; lacking a four-card natural, Player takes fifth-card 2 (2) where raw sum 5 projects onto the 0..9 ring to 5.

[RES136-B] Six-card branch [RES136] activates as 2 (2) hits Banker 2's 2-point mandatory draw band; drawing 2 (2) sends 2+2=4 to 4.

Complete 6-Card Resolution Trace for RES136
RES136 StageRES136 CardsRES136 Modulo MathRES136 Status
[RES136:Init]P(9+4)=3 vs B(8+4)=2playerShouldDraw(3)=true4-Card Deal
[RES136:5th]Player +2 (2)(3+2) mod 10 = 55th Card Sideways
[RES136:6th]Banker +2 (2)(2+2) mod 10 = 46-Card Final
[RES136:Settle]P=5 vs B=4Winner: PBig Road +P
  • [RES136-1] Confirm [RES136] opening P=3 (9+4) and B=2 (8+4) lack Natural 8/9.
  • [RES136-2] Add [RES136] fifth-card 2 (2) to P=3 for (3+2) mod 10 = 5.
  • [RES136-3] Run [RES136] BANKER_TABLEAU[2][2]=true to settle 5 vs 4 (P).
SETTLEMENT & SCOREBOARD · RES136

Showdown Settlement & Scoreboard Logging for RES136 (5 vs 4)

[RES136-C5] Comparing [RES136] final totals (6c), Player 5 vs Banker 4 awards [RES136] to Player (P), which pays 1:1 even money on [RES136] Player boxes with zero commission deducted and appends P to PPBBPBPBBB.

[RES136-D10] Side-bet & road check for [RES136] (P3+2->5 vs B2->4, 6c): [RES136] leaves [RES136] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=4) and leaves [RES136] Panda 8 inactive (needs winning 3c Player 8, got P=5); on [RES136] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES136, Banker 2 evaluates Player's three-card total (5) before deciding whether to draw.
TruthBanker 2 inspects only Player's fifth card 2 (value 2) via BANKER_TABLEAU[2][2] = true.
MythBecause RES136 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
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