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FINAL TOTAL RESOLUTION [RES331] · 6-CARD PROOF

Player 0 + 5 (5) vs. Banker 5 (Draws 10 (0)): 6-Card Resolution #331

In walkthrough RES331, Player opens with 10+K (0) and draws fifth-card 5 (5) for a modulo-10 total of 5, while Banker opens with A+4 (5) and draws sixth-card 10 (0) for 5 (6-card T outcome).

RES331 Player Path
P:0->5
RES331 Banker Path
B:5->5
RES331 Deal Length
6 Cards
RES331 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 P P B B B B P B B P P B B P
Big Eye Boy = = ≠ ≠ = ≠ = = ≠ ≠ ≠ ≠ ≠ = = = =
Small Road ≠ = ≠ ≠ ≠ = = ≠ ≠ = ≠ ≠ ≠ = =
Cockroach Pig = ≠ ≠ = ≠ = ≠ = = ≠ = ≠ ≠ ≠

Scoreboard sequence paired with 6-card resolution RES331 (P0+5->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 3. Column 2 stopped at Row 2, one row above → blue (≠).

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

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.

Cockroach Pig Mark #3

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

  1. Column 5 starts, so use Rule 1: compare Column 4 with Column 1, 3 columns further back.
  2. Column 4 has 3 beads. Column 1 has 2 beads. Different depth → blue (≠).

Common table reading watchout: Comparing the wrong columns. Compare Column 4, the one that just finished, with Column 1.

Verified Reference Data

Key Facts & Table Specifications

RES331 Four-Card Opening Deal
Player 10+K=0 vs Banker A+4=5

Verified non-natural start via handTotal([10,K])=0 and handTotal([A,4])=5.

RES331 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.

RES331 Banker Tableau Lookup
BANKER_TABLEAU[5][5] = true

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

RES331 Card Count & Winner
6 Cards -> T (5 vs 5)

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

RES331 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 · RES331

Step-by-Step Card Arithmetic for RES331: P(10+K)+5 vs B(A+4)

Evaluating sequence [RES331], the shoe delivers 10+K (0) to Player and A+4 (5) to Banker; after natural checks clear, fifth-card 5 (5) maps the raw pip total mod 10 (0+5=5) to final Player total 5.

[RES331-B] Six-card branch [RES331] activates as 5 (5) hits Banker 5's 5-point four-value window (4..7); drawing 10 (0) sends 5+0=5 to 5.

Complete 6-Card Resolution Trace for RES331
RES331 StageRES331 CardsRES331 Modulo MathRES331 Status
[RES331:Init]P(10+K)=0 vs B(A+4)=5playerShouldDraw(0)=true4-Card Deal
[RES331:5th]Player +5 (5)(0+5) mod 10 = 55th Card Sideways
[RES331:6th]Banker +10 (0)(5+0) mod 10 = 56-Card Final
[RES331:Settle]P=5 vs B=5Winner: TBig Road +T
  • [RES331-1] Confirm [RES331] opening P=0 (10+K) and B=5 (A+4) lack Natural 8/9.
  • [RES331-2] Add [RES331] fifth-card 5 (5) to P=0 for (0+5) mod 10 = 5.
  • [RES331-3] Run [RES331] BANKER_TABLEAU[5][5]=true to settle 5 vs 5 (T).
SETTLEMENT & SCOREBOARD · RES331

Showdown Settlement & Scoreboard Logging for RES331 (5 vs 5)

[RES331-C1] Comparing [RES331] final totals (6c), Player 5 vs Banker 5 awards [RES331] to Tie (T), which pushes main [RES331] Player/Banker wagers while settling [RES331] Tie bets at 8:1 or 9:1 and appends T to BBPPBPPPBB.

[RES331-D10] Side-bet & road check for [RES331] (P0+5->5 vs B5->5, 6c): [RES331] leaves [RES331] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=5) and leaves [RES331] Panda 8 inactive (needs winning 3c Player 8, got P=5); on [RES331] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES331, Banker 5 evaluates Player's three-card total (5) before deciding whether to draw.
TruthBanker 5 inspects only Player's fifth card 5 (value 5) via BANKER_TABLEAU[5][5] = true.
MythBecause RES331 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

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  • Structured step-by-step track across Foundations, Big Eye Boy, Small Road, and Cockroach Pig
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