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FINAL TOTAL RESOLUTION [RES275] · 6-CARD PROOF

Player 4 + 5 (5) vs. Banker 4 (Draws 5 (5)): 6-Card Resolution #275

In walkthrough RES275, Player opens with 2+2 (4) and draws fifth-card 5 (5) for a modulo-10 total of 9, while Banker opens with 2+2 (4) and draws sixth-card 5 (5) for 9 (6-card T outcome).

RES275 Player Path
P:4->9
RES275 Banker Path
B:4->9
RES275 Deal Length
6 Cards
RES275 Showdown
T (9v9)
Engine-Verified Scoreboard · 20 Hands

Read the Board at Table Speed

Open this shoe in /calculator
Big Road B B P P P B B P B B P P B P P P B B B B
Big Eye Boy = ≠ ≠ = ≠ ≠ ≠ ≠ = = ≠ ≠ = ≠ = = ≠
Small Road = = ≠ = = ≠ ≠ ≠ = ≠ ≠ ≠ = =
Cockroach Pig ≠ = ≠ = = = = ≠ ≠ = ≠ =

Scoreboard sequence paired with 6-card resolution RES275 (P4+5->9 vs B4->9).

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

RES275 Four-Card Opening Deal
Player 2+2=4 vs Banker 2+2=4

Verified non-natural start via handTotal([2,2])=4 and handTotal([2,2])=4.

RES275 Fifth-Card Modulo Proof
(4 + 5) mod 10 = 9 via 5

Player draws fifth-card 5 (value 5), transforming two-card 4 into three-card 9.

RES275 Banker Tableau Lookup
BANKER_TABLEAU[4][5] = true

Banker 4 draws sixth-card 5 (5) so (4+5) mod 10 = 9.

RES275 Card Count & Winner
6 Cards -> T (9 vs 9)

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

RES275 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 · RES275

Step-by-Step Card Arithmetic for RES275: P(2+2)+5 vs B(2+2)

Evaluating sequence [RES275], the shoe delivers 2+2 (4) to Player and 2+2 (4) to Banker; after natural checks clear, fifth-card 5 (5) maps the raw pip total mod 10 (4+5=9) to final Player total 9.

[RES275-B] Under 4-point six-value gate (2..7) for [RES275], exposed 5 (5) obligates Banker 4 to draw 5 (5), converting 4+5=9 into 9.

Complete 6-Card Resolution Trace for RES275
RES275 StageRES275 CardsRES275 Modulo MathRES275 Status
[RES275:Init]P(2+2)=4 vs B(2+2)=4playerShouldDraw(4)=true4-Card Deal
[RES275:5th]Player +5 (5)(4+5) mod 10 = 95th Card Sideways
[RES275:6th]Banker +5 (5)(4+5) mod 10 = 96-Card Final
[RES275:Settle]P=9 vs B=9Winner: TBig Road +T
  • [RES275-1] Confirm [RES275] opening P=4 (2+2) and B=4 (2+2) lack Natural 8/9.
  • [RES275-2] Add [RES275] fifth-card 5 (5) to P=4 for (4+5) mod 10 = 9.
  • [RES275-3] Run [RES275] BANKER_TABLEAU[4][5]=true to settle 9 vs 9 (T).
SETTLEMENT & SCOREBOARD · RES275

Showdown Settlement & Scoreboard Logging for RES275 (9 vs 9)

[RES275-C7] Comparing [RES275] final totals (6c), Player 9 vs Banker 9 awards [RES275] to Tie (T), which pushes main [RES275] Player/Banker wagers while settling [RES275] Tie bets at 8:1 or 9:1 and appends T to BBPPPBBPBB.

[RES275-D0] Side-bet & road check for [RES275] (P4+5->9 vs B4->9, 6c): [RES275] leaves [RES275] Dragon 7 inactive (needs winning 6c Banker 7, got 6c B=9) and leaves [RES275] Panda 8 inactive (needs winning 3c Player 8, got P=9); on [RES275] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES275, Banker 4 evaluates Player's three-card total (9) before deciding whether to draw.
TruthBanker 4 inspects only Player's fifth card 5 (value 5) via BANKER_TABLEAU[4][5] = true.
MythBecause RES275 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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