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FINAL TOTAL RESOLUTION [RES109] · 6-CARD PROOF

Player 0 + 8 (8) vs. Banker 1 (Draws 3 (3)): 6-Card Resolution #109

In walkthrough RES109, Player opens with 10+K (0) and draws fifth-card 8 (8) for a modulo-10 total of 8, while Banker opens with 7+4 (1) and draws sixth-card 3 (3) for 4 (6-card P outcome).

RES109 Player Path
P:0->8
RES109 Banker Path
B:1->4
RES109 Deal Length
6 Cards
RES109 Showdown
P (8v4)
Engine-Verified Scoreboard · 20 Hands

Read the Board at Table Speed

Open this shoe in /calculator
Big Road B B P P B B P P P B B B B P P B P P P B
Big Eye Boy = = = = = ≠ ≠ = = ≠ ≠ = ≠ ≠ ≠ = ≠
Small Road = = = ≠ ≠ = ≠ = ≠ = ≠ ≠ = ≠ ≠
Cockroach Pig = ≠ ≠ = ≠ = ≠ = = ≠ = = ≠

Scoreboard sequence paired with 6-card resolution RES109 (P0+8->8 vs B1->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

This bead is at Row 2. Column 2 has a bead at Row 2 too → red (=).

  1. Column 3 goes down to Row 2, so use Rule 2: look 1 column back, at Column 2.
  2. Column 2 has a bead at Row 2 too → red (=).

Common table reading watchout: Thinking "no bead at this row" means blue. It is blue only when Column 2 stopped exactly one row above this bead.

Small Road Mark #3

This bead is at Row 2. Column 2 has a bead at Row 2 too → red (=).

  1. Column 4 goes down to Row 2, so use Rule 2: look 2 columns back, at Column 2.
  2. Column 2 has a bead at Row 2 too → red (=).

Common table reading watchout: Thinking "no bead at this row" means blue. It is blue only when Column 2 stopped exactly one row above this bead.

Cockroach Pig Mark #3

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

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

Common table reading watchout: Comparing the wrong columns. Compare Column 4, the one that just finished, with Column 1.

Verified Reference Data

Key Facts & Table Specifications

RES109 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.

RES109 Fifth-Card Modulo Proof
(0 + 8) mod 10 = 8 via 8

Player draws fifth-card 8 (value 8), transforming two-card 0 into three-card 8.

RES109 Banker Tableau Lookup
BANKER_TABLEAU[1][8] = true

Banker 1 draws sixth-card 3 (3) so (1+3) mod 10 = 4.

RES109 Card Count & Winner
6 Cards -> P (8 vs 4)

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

RES109 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 · RES109

Step-by-Step Card Arithmetic for RES109: P(10+K)+8 vs B(7+4)

Shoe deal [RES109] places 10+K (0) on Player and 7+4 (1) on Banker; because 0 is below 6, Player draws 8 (8) and 8 truncates the decimal tens place to 8.

[RES109-B] Six-card branch [RES109] activates as 8 (8) hits Banker 1's 1-point automatic draw row; drawing 3 (3) sends 1+3=4 to 4.

Complete 6-Card Resolution Trace for RES109
RES109 StageRES109 CardsRES109 Modulo MathRES109 Status
[RES109:Init]P(10+K)=0 vs B(7+4)=1playerShouldDraw(0)=true4-Card Deal
[RES109:5th]Player +8 (8)(0+8) mod 10 = 85th Card Sideways
[RES109:6th]Banker +3 (3)(1+3) mod 10 = 46-Card Final
[RES109:Settle]P=8 vs B=4Winner: PBig Road +P
  • [RES109-1] Confirm [RES109] opening P=0 (10+K) and B=1 (7+4) lack Natural 8/9.
  • [RES109-2] Add [RES109] fifth-card 8 (8) to P=0 for (0+8) mod 10 = 8.
  • [RES109-3] Run [RES109] BANKER_TABLEAU[1][8]=true to settle 8 vs 4 (P).
SETTLEMENT & SCOREBOARD · RES109

Showdown Settlement & Scoreboard Logging for RES109 (8 vs 4)

[RES109-C2] Comparing [RES109] final totals (6c), Player 8 vs Banker 4 awards [RES109] to Player (P), which pays 1:1 even money on [RES109] Player boxes with zero commission deducted and appends P to BBPPBBPPPB.

[RES109-D1] Side-bet & road check for [RES109] (P0+8->8 vs B1->4, 6c): [RES109] leaves [RES109] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=4) and triggers [RES109] Panda 8 (winning 3-card Player 8, 25:1); on [RES109] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES109, Banker 1 evaluates Player's three-card total (8) before deciding whether to draw.
TruthBanker 1 inspects only Player's fifth card 8 (value 8) via BANKER_TABLEAU[1][8] = true.
MythBecause RES109 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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