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FINAL TOTAL RESOLUTION [RES175] · 6-CARD PROOF

Player 0 + 9 (9) vs. Banker 2 (Draws 3 (3)): 6-Card Resolution #175

In walkthrough RES175, Player opens with 10+K (0) and draws fifth-card 9 (9) for a modulo-10 total of 9, while Banker opens with 10+2 (2) and draws sixth-card 3 (3) for 5 (6-card P outcome).

RES175 Player Path
P:0->9
RES175 Banker Path
B:2->5
RES175 Deal Length
6 Cards
RES175 Showdown
P (9v5)
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 B P B B B P P P B B B B P
Big Eye Boy = = ≠ = ≠ ≠ ≠ ≠ = ≠ = = = = = ≠ ≠
Small Road ≠ ≠ ≠ ≠ = = ≠ ≠ ≠ = ≠ = = ≠ ≠
Cockroach Pig ≠ = = = ≠ = ≠ = ≠ ≠ ≠ = = ≠

Scoreboard sequence paired with 6-card resolution RES175 (P0+9->9 vs B2->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

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

  1. Column 5 goes down to Row 2, so use Rule 2: look 2 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.

Cockroach Pig Mark #3

Column 5 has 2 beads. Column 2 has 2 beads. Same depth → red (=).

  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 2 beads. Same depth → red (=).

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

RES175 Four-Card Opening Deal
Player 10+K=0 vs Banker 10+2=2

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

RES175 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.

RES175 Banker Tableau Lookup
BANKER_TABLEAU[2][9] = true

Banker 2 draws sixth-card 3 (3) so (2+3) mod 10 = 5.

RES175 Card Count & Winner
6 Cards -> P (9 vs 5)

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

RES175 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 · RES175

Step-by-Step Card Arithmetic for RES175: P(10+K)+9 vs B(10+2)

Matrix coordinate [RES175] isolates Player two-card 0 (10+K) and Banker 2 (10+2); dealing fifth-card 9 (9) yields raw 9 that retains the rightmost digit to 9.

[RES175-B] Six-card branch [RES175] activates as 9 (9) hits Banker 2's 2-point mandatory draw band; drawing 3 (3) sends 2+3=5 to 5.

Complete 6-Card Resolution Trace for RES175
RES175 StageRES175 CardsRES175 Modulo MathRES175 Status
[RES175:Init]P(10+K)=0 vs B(10+2)=2playerShouldDraw(0)=true4-Card Deal
[RES175:5th]Player +9 (9)(0+9) mod 10 = 95th Card Sideways
[RES175:6th]Banker +3 (3)(2+3) mod 10 = 56-Card Final
[RES175:Settle]P=9 vs B=5Winner: PBig Road +P
  • [RES175-1] Confirm [RES175] opening P=0 (10+K) and B=2 (10+2) lack Natural 8/9.
  • [RES175-2] Add [RES175] fifth-card 9 (9) to P=0 for (0+9) mod 10 = 9.
  • [RES175-3] Run [RES175] BANKER_TABLEAU[2][9]=true to settle 9 vs 5 (P).
SETTLEMENT & SCOREBOARD · RES175

Showdown Settlement & Scoreboard Logging for RES175 (9 vs 5)

[RES175-C2] Comparing [RES175] final totals (6c), Player 9 vs Banker 5 awards [RES175] to Player (P), which pays 1:1 even money on [RES175] Player boxes with zero commission deducted and appends P to BBPPBPBBPB.

[RES175-D10] Side-bet & road check for [RES175] (P0+9->9 vs B2->5, 6c): [RES175] leaves [RES175] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=5) and leaves [RES175] Panda 8 inactive (needs winning 3c Player 8, got P=9); on [RES175] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES175, Banker 2 evaluates Player's three-card total (9) before deciding whether to draw.
TruthBanker 2 inspects only Player's fifth card 9 (value 9) via BANKER_TABLEAU[2][9] = true.
MythBecause RES175 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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