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FINAL TOTAL RESOLUTION [RES234] · 5-CARD PROOF

Player 5 + 8 (8) vs. Banker 3 (Stands at 3): 5-Card Resolution #234

In walkthrough RES234, Player opens with A+4 (5) and draws fifth-card 8 (8) for a modulo-10 total of 3, while Banker opens with 10+3 (3) and stands pat at 3 (5-card T outcome).

RES234 Player Path
P:5->3
RES234 Banker Path
B:3->3
RES234 Deal Length
5 Cards
RES234 Showdown
T (3v3)
Engine-Verified Scoreboard · 20 Hands

Read the Board at Table Speed

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

Scoreboard sequence paired with 5-card resolution RES234 (P5+8->3 vs B3->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

This bead is at Row 4. Column 1 stopped at Row 2, more than one row above → red (=).

  1. Column 3 goes down to Row 4, so use Rule 2: look 2 columns back, at Column 1.
  2. Column 1 stopped at Row 2, more than one row above → red (=).

Common table reading watchout: Thinking "no bead at this row" means blue. It is blue only when Column 1 stopped exactly one row above this bead.

Cockroach Pig Mark #3

Column 5 has 1 bead. 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 1 bead. 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

RES234 Four-Card Opening Deal
Player A+4=5 vs Banker 10+3=3

Verified non-natural start via handTotal([A,4])=5 and handTotal([10,3])=3.

RES234 Fifth-Card Modulo Proof
(5 + 8) mod 10 = 3 via 8

Player draws fifth-card 8 (value 8), transforming two-card 5 into three-card 3.

RES234 Banker Tableau Lookup
BANKER_TABLEAU[3][8] = false

Banker 3 stands pat at 3 without pulling sixth-card 5 (5).

RES234 Card Count & Winner
5 Cards -> T (3 vs 3)

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

RES234 Derived Road Independence
Red (=) / Blue (≠) Symmetry Only

Big Eye Boy, Small Road, and Cockroach Pig compare Big Road column depths, not T vs B.

MODULO-10 ARITHMETIC · RES234

Step-by-Step Card Arithmetic for RES234: P(A+4)+8 vs B(10+3)

In coup [RES234], initial cards deal A+4=5 to Player and 10+3=3 to Banker; lacking a four-card natural, Player takes fifth-card 8 (8) where raw sum 13 projects onto the 0..9 ring to 3.

[RES234-B] Inspecting 8=8 via 3-point single-shade row (0..7, 9) in [RES234], Banker 3 stands at 3; 5 (5) stays in the shoe instead of 8.

Complete 5-Card Resolution Trace for RES234
RES234 StageRES234 CardsRES234 Modulo MathRES234 Status
[RES234:Init]P(A+4)=5 vs B(10+3)=3playerShouldDraw(5)=true4-Card Deal
[RES234:5th]Player +8 (8)(5+8) mod 10 = 35th Card Sideways
[RES234:6th]Banker Stands (skip 5=5)Locked at 35-Card Final
[RES234:Settle]P=3 vs B=3Winner: TBig Road +T
  • [RES234-1] Confirm [RES234] opening P=5 (A+4) and B=3 (10+3) lack Natural 8/9.
  • [RES234-2] Add [RES234] fifth-card 8 (8) to P=5 for (5+8) mod 10 = 3.
  • [RES234-3] Run [RES234] BANKER_TABLEAU[3][8]=false to settle 3 vs 3 (T).
SETTLEMENT & SCOREBOARD · RES234

Showdown Settlement & Scoreboard Logging for RES234 (3 vs 3)

[RES234-C0] Comparing [RES234] final totals (5c), Player 3 vs Banker 3 awards [RES234] to Tie (T), which pushes main [RES234] Player/Banker wagers while settling [RES234] Tie bets at 8:1 or 9:1 and appends T to PPBBBPPPPB.

[RES234-D8] Side-bet & road check for [RES234] (P5+8->3 vs B3->3, 5c): [RES234] leaves [RES234] Dragon 7 inactive (needs winning 6c Banker 7, got 5c B=3) and leaves [RES234] Panda 8 inactive (needs winning 3c Player 8, got P=3); on [RES234] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES234, Banker 3 evaluates Player's three-card total (3) before deciding whether to draw.
TruthBanker 3 inspects only Player's fifth card 8 (value 8) via BANKER_TABLEAU[3][8] = false.
MythBecause RES234 resolves as T, the next derived-road mark must match T'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
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