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FINAL TOTAL RESOLUTION [RES321] · 5-CARD PROOF

Player 2 + 3 (3) vs. Banker 5 (Stands at 5): 5-Card Resolution #321

In walkthrough RES321, Player opens with 10+2 (2) and draws fifth-card 3 (3) for a modulo-10 total of 5, while Banker opens with A+4 (5) and stands pat at 5 (5-card T outcome).

RES321 Player Path
P:2->5
RES321 Banker Path
B:5->5
RES321 Deal Length
5 Cards
RES321 Showdown
T (5v5)
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 P B P P P B B B P B B
Big Eye Boy = = ≠ = ≠ ≠ = = ≠ ≠ = ≠ = = = ≠ ≠
Small Road ≠ ≠ ≠ ≠ ≠ ≠ = ≠ ≠ ≠ ≠ = ≠ ≠ =
Cockroach Pig ≠ = = ≠ ≠ = = ≠ ≠ = ≠ ≠ = =

Scoreboard sequence paired with 5-card resolution RES321 (P2+3->5 vs B5->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

RES321 Four-Card Opening Deal
Player 10+2=2 vs Banker A+4=5

Verified non-natural start via handTotal([10,2])=2 and handTotal([A,4])=5.

RES321 Fifth-Card Modulo Proof
(2 + 3) mod 10 = 5 via 3

Player draws fifth-card 3 (value 3), transforming two-card 2 into three-card 5.

RES321 Banker Tableau Lookup
BANKER_TABLEAU[5][3] = false

Banker 5 stands pat at 5 without pulling sixth-card 10 (0).

RES321 Card Count & Winner
5 Cards -> T (5 vs 5)

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

RES321 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 · RES321

Step-by-Step Card Arithmetic for RES321: P(10+2)+3 vs B(A+4)

Hand record [RES321] tracks Player 2 (10+2) facing Banker 5 (A+4); with zero naturals on the felt, the fifth card 3 (worth 3) arrives and 5 calculates the mod-10 residue to 5.

[RES321-B] Next in [RES321], Banker applies 5-point four-value window (4..7): vs 3 (3), Banker 5 stands at 5 in 5c (skipping 10=0 -> 5).

Complete 5-Card Resolution Trace for RES321
RES321 StageRES321 CardsRES321 Modulo MathRES321 Status
[RES321:Init]P(10+2)=2 vs B(A+4)=5playerShouldDraw(2)=true4-Card Deal
[RES321:5th]Player +3 (3)(2+3) mod 10 = 55th Card Sideways
[RES321:6th]Banker Stands (skip 10=0)Locked at 55-Card Final
[RES321:Settle]P=5 vs B=5Winner: TBig Road +T
  • [RES321-1] Confirm [RES321] opening P=2 (10+2) and B=5 (A+4) lack Natural 8/9.
  • [RES321-2] Add [RES321] fifth-card 3 (3) to P=2 for (2+3) mod 10 = 5.
  • [RES321-3] Run [RES321] BANKER_TABLEAU[5][3]=false to settle 5 vs 5 (T).
SETTLEMENT & SCOREBOARD · RES321

Showdown Settlement & Scoreboard Logging for RES321 (5 vs 5)

[RES321-C6] Comparing [RES321] final totals (5c), Player 5 vs Banker 5 awards [RES321] to Tie (T), which pushes main [RES321] Player/Banker wagers while settling [RES321] Tie bets at 8:1 or 9:1 and appends T to BBPPBPBBPP.

[RES321-D11] Side-bet & road check for [RES321] (P2+3->5 vs B5->5, 5c): [RES321] leaves [RES321] Dragon 7 inactive (needs winning 6c Banker 7, got 5c B=5) and leaves [RES321] Panda 8 inactive (needs winning 3c Player 8, got P=5); on [RES321] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES321, Banker 5 evaluates Player's three-card total (5) before deciding whether to draw.
TruthBanker 5 inspects only Player's fifth card 3 (value 3) via BANKER_TABLEAU[5][3] = false.
MythBecause RES321 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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