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FINAL TOTAL RESOLUTION [RES031] · 6-CARD PROOF

Player 0 + 5 (5) vs. Banker 0 (Draws 5 (5)): 6-Card Resolution #31

In walkthrough RES031, Player opens with 10+K (0) and draws fifth-card 5 (5) for a modulo-10 total of 5, while Banker opens with 10+K (0) and draws sixth-card 5 (5) for 5 (6-card T outcome).

RES031 Player Path
P:0->5
RES031 Banker Path
B:0->5
RES031 Deal Length
6 Cards
RES031 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 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 RES031 (P0+5->5 vs B0->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

RES031 Four-Card Opening Deal
Player 10+K=0 vs Banker 10+K=0

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

RES031 Fifth-Card Modulo Proof
(0 + 5) mod 10 = 5 via 5

Player draws fifth-card 5 (value 5), transforming two-card 0 into three-card 5.

RES031 Banker Tableau Lookup
BANKER_TABLEAU[0][5] = true

Banker 0 draws sixth-card 5 (5) so (0+5) mod 10 = 5.

RES031 Card Count & Winner
6 Cards -> T (5 vs 5)

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

RES031 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 · RES031

Step-by-Step Card Arithmetic for RES031: P(10+K)+5 vs B(10+K)

During tableau case [RES031], Player holds 10+K for 0 while Banker holds 10+K for 0; drawing fifth-card 5 (5) shifts Player from 0 to 5, which reduces mod-10 to 5.

[RES031-B] Six-card branch [RES031] activates as 5 (5) hits Banker 0's 0-point unconditional draw tier; drawing 5 (5) sends 0+5=5 to 5.

Complete 6-Card Resolution Trace for RES031
RES031 StageRES031 CardsRES031 Modulo MathRES031 Status
[RES031:Init]P(10+K)=0 vs B(10+K)=0playerShouldDraw(0)=true4-Card Deal
[RES031:5th]Player +5 (5)(0+5) mod 10 = 55th Card Sideways
[RES031:6th]Banker +5 (5)(0+5) mod 10 = 56-Card Final
[RES031:Settle]P=5 vs B=5Winner: TBig Road +T
  • [RES031-1] Confirm [RES031] opening P=0 (10+K) and B=0 (10+K) lack Natural 8/9.
  • [RES031-2] Add [RES031] fifth-card 5 (5) to P=0 for (0+5) mod 10 = 5.
  • [RES031-3] Run [RES031] BANKER_TABLEAU[0][5]=true to settle 5 vs 5 (T).
SETTLEMENT & SCOREBOARD · RES031

Showdown Settlement & Scoreboard Logging for RES031 (5 vs 5)

[RES031-C8] Comparing [RES031] final totals (6c), Player 5 vs Banker 5 awards [RES031] to Tie (T), which pushes main [RES031] Player/Banker wagers while settling [RES031] Tie bets at 8:1 or 9:1 and appends T to BBPPBPBBPB.

[RES031-D1] Side-bet & road check for [RES031] (P0+5->5 vs B0->5, 6c): [RES031] leaves [RES031] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=5) and leaves [RES031] Panda 8 inactive (needs winning 3c Player 8, got P=5); on [RES031] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES031, Banker 0 evaluates Player's three-card total (5) before deciding whether to draw.
TruthBanker 0 inspects only Player's fifth card 5 (value 5) via BANKER_TABLEAU[0][5] = true.
MythBecause RES031 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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