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FINAL TOTAL RESOLUTION [RES103] · 6-CARD PROOF

Player 0 + 7 (7) vs. Banker 1 (Draws 4 (4)): 6-Card Resolution #103

In walkthrough RES103, Player opens with 10+K (0) and draws fifth-card 7 (7) for a modulo-10 total of 7, while Banker opens with 7+4 (1) and draws sixth-card 4 (4) for 5 (6-card P outcome).

RES103 Player Path
P:0->7
RES103 Banker Path
B:1->5
RES103 Deal Length
6 Cards
RES103 Showdown
P (7v5)
Engine-Verified Scoreboard · 20 Hands

Read the Board at Table Speed

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

Scoreboard sequence paired with 6-card resolution RES103 (P0+7->7 vs B1->5).

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

RES103 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.

RES103 Fifth-Card Modulo Proof
(0 + 7) mod 10 = 7 via 7

Player draws fifth-card 7 (value 7), transforming two-card 0 into three-card 7.

RES103 Banker Tableau Lookup
BANKER_TABLEAU[1][7] = true

Banker 1 draws sixth-card 4 (4) so (1+4) mod 10 = 5.

RES103 Card Count & Winner
6 Cards -> P (7 vs 5)

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

RES103 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 · RES103

Step-by-Step Card Arithmetic for RES103: P(10+K)+7 vs B(7+4)

Under audit [RES103], Player opens on two-card 0 (10+K) opposite Banker 1 (7+4), triggering a mandatory fifth-card pull of 7 (value 7) that settles via mod-10 arithmetic from 7 into 7.

[RES103-B] Acting on 7=7 inside [RES103], Banker 1 follows 1-point automatic draw row and pulls 4 (4) for 1+4=5 -> 5.

Complete 6-Card Resolution Trace for RES103
RES103 StageRES103 CardsRES103 Modulo MathRES103 Status
[RES103:Init]P(10+K)=0 vs B(7+4)=1playerShouldDraw(0)=true4-Card Deal
[RES103:5th]Player +7 (7)(0+7) mod 10 = 75th Card Sideways
[RES103:6th]Banker +4 (4)(1+4) mod 10 = 56-Card Final
[RES103:Settle]P=7 vs B=5Winner: PBig Road +P
  • [RES103-1] Confirm [RES103] opening P=0 (10+K) and B=1 (7+4) lack Natural 8/9.
  • [RES103-2] Add [RES103] fifth-card 7 (7) to P=0 for (0+7) mod 10 = 7.
  • [RES103-3] Run [RES103] BANKER_TABLEAU[1][7]=true to settle 7 vs 5 (P).
SETTLEMENT & SCOREBOARD · RES103

Showdown Settlement & Scoreboard Logging for RES103 (7 vs 5)

[RES103-C5] Comparing [RES103] final totals (6c), Player 7 vs Banker 5 awards [RES103] to Player (P), which pays 1:1 even money on [RES103] Player boxes with zero commission deducted and appends P to BBPPBPBPPP.

[RES103-D12] Side-bet & road check for [RES103] (P0+7->7 vs B1->5, 6c): [RES103] leaves [RES103] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=5) and leaves [RES103] Panda 8 inactive (needs winning 3c Player 8, got P=7); on [RES103] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES103, Banker 1 evaluates Player's three-card total (7) before deciding whether to draw.
TruthBanker 1 inspects only Player's fifth card 7 (value 7) via BANKER_TABLEAU[1][7] = true.
MythBecause RES103 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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