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FINAL TOTAL RESOLUTION [RES055] · 6-CARD PROOF

Player 0 + 9 (9) vs. Banker 0 (Draws A (1)): 6-Card Resolution #55

In walkthrough RES055, Player opens with 10+K (0) and draws fifth-card 9 (9) for a modulo-10 total of 9, while Banker opens with 10+K (0) and draws sixth-card A (1) for 1 (6-card P outcome).

RES055 Player Path
P:0->9
RES055 Banker Path
B:0->1
RES055 Deal Length
6 Cards
RES055 Showdown
P (9v1)
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 P P P B B B B P P B P B B
Big Eye Boy = = ≠ = = ≠ = ≠ = = ≠ ≠ = ≠ ≠ = ≠
Small Road ≠ ≠ = ≠ = ≠ ≠ = = ≠ = ≠ ≠ ≠ ≠
Cockroach Pig ≠ ≠ ≠ = ≠ ≠ = = ≠ ≠ ≠ ≠ ≠ =

Scoreboard sequence paired with 6-card resolution RES055 (P0+9->9 vs B0->1).

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

Column 5 has 1 bead. Column 3 has 1 bead. Same depth → red (=).

  1. Column 6 starts, so use Rule 1: compare Column 5 with Column 3, 2 columns further back.
  2. Column 5 has 1 bead. Column 3 has 1 bead. Same depth → red (=).

Common table reading watchout: Comparing the wrong columns. Compare Column 5, the one that just finished, with Column 3.

Cockroach Pig Mark #3

This bead is at Row 2. Column 3 stopped at Row 1, one row above → blue (≠).

  1. Column 6 goes down to Row 2, so use Rule 2: look 3 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.

Verified Reference Data

Key Facts & Table Specifications

RES055 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.

RES055 Fifth-Card Modulo Proof
(0 + 9) mod 10 = 9 via 9

Player draws fifth-card 9 (value 9), transforming two-card 0 into three-card 9.

RES055 Banker Tableau Lookup
BANKER_TABLEAU[0][9] = true

Banker 0 draws sixth-card A (1) so (0+1) mod 10 = 1.

RES055 Card Count & Winner
6 Cards -> P (9 vs 1)

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

RES055 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 · RES055

Step-by-Step Card Arithmetic for RES055: P(10+K)+9 vs B(10+K)

Hand record [RES055] tracks Player 0 (10+K) facing Banker 0 (10+K); with zero naturals on the felt, the fifth card 9 (worth 9) arrives and 9 calculates the mod-10 residue to 9.

[RES055-B] Evaluating bankerShouldDraw(0, 9)=true (0-point unconditional draw tier) in [RES055], sixth-card A (1) advances Banker 0 via 0+1=1 to 1.

Complete 6-Card Resolution Trace for RES055
RES055 StageRES055 CardsRES055 Modulo MathRES055 Status
[RES055:Init]P(10+K)=0 vs B(10+K)=0playerShouldDraw(0)=true4-Card Deal
[RES055:5th]Player +9 (9)(0+9) mod 10 = 95th Card Sideways
[RES055:6th]Banker +A (1)(0+1) mod 10 = 16-Card Final
[RES055:Settle]P=9 vs B=1Winner: PBig Road +P
  • [RES055-1] Confirm [RES055] opening P=0 (10+K) and B=0 (10+K) lack Natural 8/9.
  • [RES055-2] Add [RES055] fifth-card 9 (9) to P=0 for (0+9) mod 10 = 9.
  • [RES055-3] Run [RES055] BANKER_TABLEAU[0][9]=true to settle 9 vs 1 (P).
SETTLEMENT & SCOREBOARD · RES055

Showdown Settlement & Scoreboard Logging for RES055 (9 vs 1)

[RES055-C7] Comparing [RES055] final totals (6c), Player 9 vs Banker 1 awards [RES055] to Player (P), which pays 1:1 even money on [RES055] Player boxes with zero commission deducted and appends P to BBPPBPBPPP.

[RES055-D9] Side-bet & road check for [RES055] (P0+9->9 vs B0->1, 6c): [RES055] leaves [RES055] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=1) and leaves [RES055] Panda 8 inactive (needs winning 3c Player 8, got P=9); on [RES055] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES055, Banker 0 evaluates Player's three-card total (9) before deciding whether to draw.
TruthBanker 0 inspects only Player's fifth card 9 (value 9) via BANKER_TABLEAU[0][9] = true.
MythBecause RES055 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.
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
  • 74 interactive lesson scoreboards and 94 inline quiz checks with plain-English mark feedback
  • Cloud Shoe Log and cross-device progress on web, iOS, and Android