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FINAL TOTAL RESOLUTION [RES276] · 6-CARD PROOF

Player 5 + 5 (5) vs. Banker 4 (Draws 9 (9)): 6-Card Resolution #276

In walkthrough RES276, Player opens with A+4 (5) and draws fifth-card 5 (5) for a modulo-10 total of 0, while Banker opens with A+3 (4) and draws sixth-card 9 (9) for 3 (6-card B outcome).

RES276 Player Path
P:5->0
RES276 Banker Path
B:4->3
RES276 Deal Length
6 Cards
RES276 Showdown
B (0v3)
Engine-Verified Scoreboard · 20 Hands

Read the Board at Table Speed

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Big Road P P B B B P P B P P B B P B B B P P P P
Big Eye Boy = ≠ ≠ = ≠ ≠ ≠ ≠ = = ≠ ≠ = ≠ = = ≠
Small Road = = ≠ = = ≠ ≠ ≠ = ≠ ≠ ≠ = =
Cockroach Pig ≠ = ≠ = = = = ≠ ≠ = ≠ =

Scoreboard sequence paired with 6-card resolution RES276 (P5+5->0 vs B4->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 2 has 3 beads. Column 1 has 2 beads. Different depth → blue (≠).

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

Common table reading watchout: Comparing the wrong columns. Compare Column 2, the one that just finished, with Column 1.

Small Road Mark #3

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

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

Common table reading watchout: Comparing the wrong columns. Compare Column 4, the one that just finished, with Column 2.

Cockroach Pig Mark #3

Column 5 has 2 beads. Column 2 has 3 beads. Different depth → blue (≠).

  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 3 beads. Different depth → blue (≠).

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

RES276 Four-Card Opening Deal
Player A+4=5 vs Banker A+3=4

Verified non-natural start via handTotal([A,4])=5 and handTotal([A,3])=4.

RES276 Fifth-Card Modulo Proof
(5 + 5) mod 10 = 0 via 5

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

RES276 Banker Tableau Lookup
BANKER_TABLEAU[4][5] = true

Banker 4 draws sixth-card 9 (9) so (4+9) mod 10 = 3.

RES276 Card Count & Winner
6 Cards -> B (0 vs 3)

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

RES276 Derived Road Independence
Red (=) / Blue (≠) Symmetry Only

Big Eye Boy, Small Road, and Cockroach Pig compare Big Road column depths, not B vs P.

MODULO-10 ARITHMETIC · RES276

Step-by-Step Card Arithmetic for RES276: P(A+4)+5 vs B(A+3)

In coup [RES276], initial cards deal A+4=5 to Player and A+3=4 to Banker; lacking a four-card natural, Player takes fifth-card 5 (5) where raw sum 10 projects onto the 0..9 ring to 0.

[RES276-B] Evaluating bankerShouldDraw(4, 5)=true (4-point six-value gate (2..7)) in [RES276], sixth-card 9 (9) advances Banker 4 via 4+9=13 to 3.

Complete 6-Card Resolution Trace for RES276
RES276 StageRES276 CardsRES276 Modulo MathRES276 Status
[RES276:Init]P(A+4)=5 vs B(A+3)=4playerShouldDraw(5)=true4-Card Deal
[RES276:5th]Player +5 (5)(5+5) mod 10 = 05th Card Sideways
[RES276:6th]Banker +9 (9)(4+9) mod 10 = 36-Card Final
[RES276:Settle]P=0 vs B=3Winner: BBig Road +B
  • [RES276-1] Confirm [RES276] opening P=5 (A+4) and B=4 (A+3) lack Natural 8/9.
  • [RES276-2] Add [RES276] fifth-card 5 (5) to P=5 for (5+5) mod 10 = 0.
  • [RES276-3] Run [RES276] BANKER_TABLEAU[4][5]=true to settle 0 vs 3 (B).
SETTLEMENT & SCOREBOARD · RES276

Showdown Settlement & Scoreboard Logging for RES276 (0 vs 3)

[RES276-C1] Comparing [RES276] final totals (6c), Player 0 vs Banker 3 awards [RES276] to Banker (B), which pays 0.95:1 on 5%-commission [RES276] layouts (or 0.5:1 on 6 at No-Commission [RES276] tables) and appends B to PPBBBPPBPP.

[RES276-D9] Side-bet & road check for [RES276] (P5+5->0 vs B4->3, 6c): [RES276] leaves [RES276] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=3) and leaves [RES276] Panda 8 inactive (needs winning 3c Player 8, got P=0); on [RES276] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES276, Banker 4 evaluates Player's three-card total (0) before deciding whether to draw.
TruthBanker 4 inspects only Player's fifth card 5 (value 5) via BANKER_TABLEAU[4][5] = true.
MythBecause RES276 resolves as B, the next derived-road mark must match B'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
  • 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