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FINAL TOTAL RESOLUTION [RES033] · 6-CARD PROOF

Player 2 + 5 (5) vs. Banker 0 (Draws 3 (3)): 6-Card Resolution #33

In walkthrough RES033, Player opens with 10+2 (2) and draws fifth-card 5 (5) for a modulo-10 total of 7, while Banker opens with 10+K (0) and draws sixth-card 3 (3) for 3 (6-card P outcome).

RES033 Player Path
P:2->7
RES033 Banker Path
B:0->3
RES033 Deal Length
6 Cards
RES033 Showdown
P (7v3)
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 6-card resolution RES033 (P2+5->7 vs B0->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 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

RES033 Four-Card Opening Deal
Player 10+2=2 vs Banker 10+K=0

Verified non-natural start via handTotal([10,2])=2 and handTotal([10,K])=0.

RES033 Fifth-Card Modulo Proof
(2 + 5) mod 10 = 7 via 5

Player draws fifth-card 5 (value 5), transforming two-card 2 into three-card 7.

RES033 Banker Tableau Lookup
BANKER_TABLEAU[0][5] = true

Banker 0 draws sixth-card 3 (3) so (0+3) mod 10 = 3.

RES033 Card Count & Winner
6 Cards -> P (7 vs 3)

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

RES033 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 · RES033

Step-by-Step Card Arithmetic for RES033: P(10+2)+5 vs B(10+K)

Under audit [RES033], Player opens on two-card 2 (10+2) opposite Banker 0 (10+K), triggering a mandatory fifth-card pull of 5 (value 5) that settles via mod-10 arithmetic from 7 into 7.

[RES033-B] Triggered by 5 (5) in [RES033] (0-point unconditional draw tier), Banker 0 receives 3 (3) and computes (0+3) mod 10 = 3.

Complete 6-Card Resolution Trace for RES033
RES033 StageRES033 CardsRES033 Modulo MathRES033 Status
[RES033:Init]P(10+2)=2 vs B(10+K)=0playerShouldDraw(2)=true4-Card Deal
[RES033:5th]Player +5 (5)(2+5) mod 10 = 75th Card Sideways
[RES033:6th]Banker +3 (3)(0+3) mod 10 = 36-Card Final
[RES033:Settle]P=7 vs B=3Winner: PBig Road +P
  • [RES033-1] Confirm [RES033] opening P=2 (10+2) and B=0 (10+K) lack Natural 8/9.
  • [RES033-2] Add [RES033] fifth-card 5 (5) to P=2 for (2+5) mod 10 = 7.
  • [RES033-3] Run [RES033] BANKER_TABLEAU[0][5]=true to settle 7 vs 3 (P).
SETTLEMENT & SCOREBOARD · RES033

Showdown Settlement & Scoreboard Logging for RES033 (7 vs 3)

[RES033-C7] Comparing [RES033] final totals (6c), Player 7 vs Banker 3 awards [RES033] to Player (P), which pays 1:1 even money on [RES033] Player boxes with zero commission deducted and appends P to BBPPBPBBPP.

[RES033-D6] Side-bet & road check for [RES033] (P2+5->7 vs B0->3, 6c): [RES033] leaves [RES033] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=3) and leaves [RES033] Panda 8 inactive (needs winning 3c Player 8, got P=7); on [RES033] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES033, Banker 0 evaluates Player's three-card total (7) before deciding whether to draw.
TruthBanker 0 inspects only Player's fifth card 5 (value 5) via BANKER_TABLEAU[0][5] = true.
MythBecause RES033 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.
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  • Structured step-by-step track across Foundations, Big Eye Boy, Small Road, and Cockroach Pig
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