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FINAL TOTAL RESOLUTION [RES115] · 6-CARD PROOF

Player 0 + 9 (9) vs. Banker 1 (Draws 2 (2)): 6-Card Resolution #115

In walkthrough RES115, Player opens with 10+K (0) and draws fifth-card 9 (9) for a modulo-10 total of 9, while Banker opens with 7+4 (1) and draws sixth-card 2 (2) for 3 (6-card P outcome).

RES115 Player Path
P:0->9
RES115 Banker Path
B:1->3
RES115 Deal Length
6 Cards
RES115 Showdown
P (9v3)
Engine-Verified Scoreboard · 20 Hands

Read the Board at Table Speed

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

Scoreboard sequence paired with 6-card resolution RES115 (P0+9->9 vs B1->3).

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

RES115 Four-Card Opening Deal
Player 10+K=0 vs Banker 7+4=1

Verified non-natural start via handTotal([10,K])=0 and handTotal([7,4])=1.

RES115 Fifth-Card Modulo Proof
(0 + 9) mod 10 = 9 via 9

Player draws fifth-card 9 (value 9), transforming two-card 0 into three-card 9.

RES115 Banker Tableau Lookup
BANKER_TABLEAU[1][9] = true

Banker 1 draws sixth-card 2 (2) so (1+2) mod 10 = 3.

RES115 Card Count & Winner
6 Cards -> P (9 vs 3)

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

RES115 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 · RES115

Step-by-Step Card Arithmetic for RES115: P(10+K)+9 vs B(7+4)

During tableau case [RES115], Player holds 10+K for 0 while Banker holds 7+4 for 1; drawing fifth-card 9 (9) shifts Player from 0 to 9, which reduces mod-10 to 9.

[RES115-B] Because BANKER_TABLEAU[1][9]=true (1-point automatic draw row) in [RES115], Banker 1 takes sixth-card 2 (2) and 1+2=3 settles at 3.

Complete 6-Card Resolution Trace for RES115
RES115 StageRES115 CardsRES115 Modulo MathRES115 Status
[RES115:Init]P(10+K)=0 vs B(7+4)=1playerShouldDraw(0)=true4-Card Deal
[RES115:5th]Player +9 (9)(0+9) mod 10 = 95th Card Sideways
[RES115:6th]Banker +2 (2)(1+2) mod 10 = 36-Card Final
[RES115:Settle]P=9 vs B=3Winner: PBig Road +P
  • [RES115-1] Confirm [RES115] opening P=0 (10+K) and B=1 (7+4) lack Natural 8/9.
  • [RES115-2] Add [RES115] fifth-card 9 (9) to P=0 for (0+9) mod 10 = 9.
  • [RES115-3] Run [RES115] BANKER_TABLEAU[1][9]=true to settle 9 vs 3 (P).
SETTLEMENT & SCOREBOARD · RES115

Showdown Settlement & Scoreboard Logging for RES115 (9 vs 3)

[RES115-C10] Comparing [RES115] final totals (6c), Player 9 vs Banker 3 awards [RES115] to Player (P), which pays 1:1 even money on [RES115] Player boxes with zero commission deducted and appends P to BBPPPBBPBB.

[RES115-D3] Side-bet & road check for [RES115] (P0+9->9 vs B1->3, 6c): [RES115] leaves [RES115] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=3) and leaves [RES115] Panda 8 inactive (needs winning 3c Player 8, got P=9); on [RES115] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES115, Banker 1 evaluates Player's three-card total (9) before deciding whether to draw.
TruthBanker 1 inspects only Player's fifth card 9 (value 9) via BANKER_TABLEAU[1][9] = true.
MythBecause RES115 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
  • 74 interactive lesson scoreboards and 94 inline quiz checks with plain-English mark feedback
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