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FINAL TOTAL RESOLUTION [RES165] · 6-CARD PROOF

Player 2 + 7 (7) vs. Banker 2 (Draws 3 (3)): 6-Card Resolution #165

In walkthrough RES165, Player opens with 10+2 (2) and draws fifth-card 7 (7) 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).

RES165 Player Path
P:2->9
RES165 Banker Path
B:2->5
RES165 Deal Length
6 Cards
RES165 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 B P B P B B P P P B B B B P P
Big Eye Boy = = = = ≠ = = ≠ ≠ = ≠ ≠ = = ≠ ≠ =
Small Road = = ≠ ≠ = ≠ ≠ ≠ = ≠ = ≠ = ≠ =
Cockroach Pig ≠ ≠ ≠ ≠ ≠ ≠ = ≠ ≠ = = ≠ =

Scoreboard sequence paired with 6-card resolution RES165 (P2+7->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

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

Column 4 has 1 bead. Column 2 has 2 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 2 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 6 has 1 bead. Column 3 has 2 beads. Different depth → blue (≠).

  1. Column 7 starts, so use Rule 1: compare Column 6 with Column 3, 3 columns further back.
  2. Column 6 has 1 bead. Column 3 has 2 beads. Different depth → blue (≠).

Common table reading watchout: Comparing the wrong columns. Compare Column 6, the one that just finished, with Column 3.

Verified Reference Data

Key Facts & Table Specifications

RES165 Four-Card Opening Deal
Player 10+2=2 vs Banker 10+2=2

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

RES165 Fifth-Card Modulo Proof
(2 + 7) mod 10 = 9 via 7

Player draws fifth-card 7 (value 7), transforming two-card 2 into three-card 9.

RES165 Banker Tableau Lookup
BANKER_TABLEAU[2][7] = true

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

RES165 Card Count & Winner
6 Cards -> P (9 vs 5)

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

RES165 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 · RES165

Step-by-Step Card Arithmetic for RES165: P(10+2)+7 vs B(10+2)

Shoe deal [RES165] places 10+2 (2) on Player and 10+2 (2) on Banker; because 2 is below 6, Player draws 7 (7) and 9 truncates the decimal tens place to 9.

[RES165-B] Next in [RES165], Banker consults 2-point mandatory draw band: facing fifth-card 7 (7), Banker 2 draws 3 (3) so 2+3=5 -> 5.

Complete 6-Card Resolution Trace for RES165
RES165 StageRES165 CardsRES165 Modulo MathRES165 Status
[RES165:Init]P(10+2)=2 vs B(10+2)=2playerShouldDraw(2)=true4-Card Deal
[RES165:5th]Player +7 (7)(2+7) mod 10 = 95th Card Sideways
[RES165:6th]Banker +3 (3)(2+3) mod 10 = 56-Card Final
[RES165:Settle]P=9 vs B=5Winner: PBig Road +P
  • [RES165-1] Confirm [RES165] opening P=2 (10+2) and B=2 (10+2) lack Natural 8/9.
  • [RES165-2] Add [RES165] fifth-card 7 (7) to P=2 for (2+7) mod 10 = 9.
  • [RES165-3] Run [RES165] BANKER_TABLEAU[2][7]=true to settle 9 vs 5 (P).
SETTLEMENT & SCOREBOARD · RES165

Showdown Settlement & Scoreboard Logging for RES165 (9 vs 5)

[RES165-C7] Comparing [RES165] final totals (6c), Player 9 vs Banker 5 awards [RES165] to Player (P), which pays 1:1 even money on [RES165] Player boxes with zero commission deducted and appends P to BBPPBBPBPB.

[RES165-D11] Side-bet & road check for [RES165] (P2+7->9 vs B2->5, 6c): [RES165] leaves [RES165] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=5) and leaves [RES165] Panda 8 inactive (needs winning 3c Player 8, got P=9); on [RES165] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES165, Banker 2 evaluates Player's three-card total (9) before deciding whether to draw.
TruthBanker 2 inspects only Player's fifth card 7 (value 7) via BANKER_TABLEAU[2][7] = true.
MythBecause RES165 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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